Very Heavy MSSM Higgs-Boson Production at the Linear Collider

Ultra-High-Performance Concrete:Research, Development andApplication in EuropeMichael Schmidt and Ekkehard FehlingSynopsis: One of the breakthroughs in concrete technology is ultra-high-performance concrete with a steel like compressive strength of up to 250 N/mm2 and a remarkable increase in durability compared even with high-performance concrete. In combination with steel fibres it is now possible to design sustainable filigree, lightweight concrete constructions with or even without additional reinforcement. Wide span girders, bridges, shells and high rise towers are ideal applications widening the range of concrete applications by far. In addition e.g. to some pedestrian bridges heavily trafficked road bridges has been build in France and in the Netherlands. Bridges are already under construction in Germany as well. A wide range of new concrete formulations has been developed to cover an increasing number of applications. Technical recommendations have recently been published in France and in Germany covering material as well as design aspects.The paper will report on the state of research and application of UHPC in Europe, on material and design aspects of UHPC and will present the state-of-the-art based on an International Symposium on UHPC held in Kassel in 2004.Keywords: ultra high performance concrete; raw materials; durability; design aspectsMichael Schmidtborn 1947, studied Civil Engineering 1967-1973 at the Technical University of Hanover (Germany), received doctoral degree in 1977 from TU Hanover.Research Engineer and Senior Specialist at the Research Institute of the German Cement Industry in Düsseldorf 1978-1989. Director of Research and Development of the HeidelbergCement Group 1989-1998. Since 1998 Independent Public Consultant and Court Expert for building materials and cement and gypsum industry in Germany, Europe and Asia. Since 1999 Professor, head of Building Materials Department and Director of Governmental Testing Institute at the University of Kassel.Ekkehard Fehlingborn 1959, studied Civil Engineering 1978 -1983 at the Technical University of Darmstadt (Germany), received doctoral degree in 1990 from TU Darmstadt.Since 1988 registered Consulting Engineer, since 1997 State licensed Checking Engineer and Professor of Structural Engineering, University of Kassel,Partner of IBB Fehling+Jungmann, Consulting Engineers, Kassel / Fulda (Germany)INTRODUCTIONWithin the last two decades amazing progress has been made in concrete technology. One of the breakthroughs is the development of ultra-high-performance concrete with a steel like compressive strength of up to 250 N/mm2 and a remarkable increase in durability compared even with high-performance concrete. In combination with a sufficiently high amount of steel fibers it is now possible to design sustainable filigree, lightweight concrete constructions without any additional reinforcement. In prestressed construction elements the prestressing forces may be increased significantly especially if high-strength steel is used. Long span girders, bridges and shells are ideal applications widening the range of concrete applications by far. First practical steps into the future of concrete constructions have already been done. In addition to the well known pedestrian bridge in Sherbrooke in Canada and in South Korea heavily used road bridges has been build or reconstructed in France and in the Netherlands. A long span footbridge is under construction in Germany and the construction of a road bridge used by traffic under severe climatic conditions with intensive salt attacks in winter will start this year to gain more practical experiences with the durability of UHPC.The growing store of knowledge about the material itself and about the adequate design of constructions with UHPC enabled a technical working groups in France to draw up first technical recommendations primarily focussing on the design (Resplendino 2004, SETRA-AFGC 2002). In Germany a state-of-the-art report has recently been published covering all material and design aspects (DAfStB UHPC 2003).That means that the concrete itself is steadily optimized and a wide range of new formulations are developed to cover the individual needs of an increasing number of different applications. This paper will report on the state of research and development on UHPC in Europe and about recent applications either already realized, under construction or under development.HISTORY OF DEVELOPMENT AND APPLICATIONSIn the 1960s concretes with an compressive strength of up to 800 N/mm2 has been developed and produced under specific laboratory conditions. They were compacted under high pressure and thermally treated. In the early 1980s the idea was born to develop fine grained concretes with a very dense and homogeneous cement matrix preventing the development of microcracks within the structure when being loaded. Because of the restricted grain size of less than 1 mm and of the high packing density due to the use of different inert or reactive mineral additions they were called “Reactive Powder Concretes (RPC)” (Bache 1981; Richard and Cheyrezy 1995). Meanwhile there existed a wider range of formulations and the term “Ultra-High-Performance Concrete” or – in short – UHPC was established worldwide for concretes with a minimum compressive strength of 150 N/mm2.The first commercial applications started around 1980, based on the development of so called D.S.P. mortars in Denmark (Buitelaar 2004). It was primarily used for special applications in the security industry – like vaults, strong rooms and protective defense constructions.First research and developments aiming at an application of UHPC in constructions started in about 1985. Since then different technical solutions were developed one after the other or parallelly: Heavily (conventionally) reinforced UHPC precast elements for bridge decks; in situ applications for the rehabilitation of deteriorated concrete bridges and industrial floors (Buitelaar 2004) ductile fiber reinforced fine grained “Reactive Powder Concrete” (RPC) like “Ductal” produced by Lafarge in France or Densit produced in Denmark (Acker and Behloul 2004). With or without additional “passive” reinforcement it is used for precast elements and other applications like offshore bucked foundations. In addition, coarse grained UHPC with artificial or natural high strength aggregates were developed e.g. for highly loaded columns and for extremely high-rise buildings (Schmidt et al. 2003). Nowadays an increasing range of formulations is available and can be adjusted to meet the specific requirements of an individual design, construction or architectural approach.Breakthroughs in application were the very first prestressed hybride pedestrian bridge at Sherbrooke in Canada in 1997, the replacement of steel parts of the cooling tower at Cattenom and two 20.50 and 22.50 m long road bridges used by cars and trucks at Bourg-lès-Valence in France build in 2001 (Hajar et al. 2004), see fig. 1.For these projects the UHPC was reinforced with about 2.5 to 3 Vol.-% of steel fibers of different shape. The bridges in Bourg-lès-Valence consists of five precast beams which are pre-tensioned. They were placed on site and then joined together with in-situ UHPC. Other footbridges with decks and/or other load bearing components made of fine grained, fiber reinforced UHPC exist in Seoul and in Japan (Acker and Behloul 2004).A spectacular example of architectural taking advantage of the special benefits of UHPC is the toll-gate of the Millau Viaduct in France, currently under construction. Fig. 2 shows the elegant roof “looking like an enormous twisted sheet of paper”, 98 m long and 28 m wide with a maximum thickness of 85 cm at the center (Resplendino 2004). The structure remembers an aircraft wing. It will be made of match-cast prefabricated 2 m wide segments connected by an internal longitudinal prestressing.In other European countries UHPC is gaining increasing interest as well. In Germany, asa result of an extensive research project financed by the government, technical criteria and measures have been already developed to use regionally available raw materials forfine or coarse grained UHPC, to reduce the cement content and to use fiber mixtures and noncorrosive high strength plastic fibers to control the strength and the ductility depending on the requirements given by an individual design and construction (Fehling et al. 2003; Bornemann et al. 2001; Schmidt et al. 2003; Bornemann and Faber 2004). As a first application, a hybrid bridge is under construction (Fehling et al. 2004) for pedestrian and bicycles with a length of about 135 m and a maximum span of 40 m consisting of precast prestessed chords and precast bridge deck elements made of UHPC with a maximum grain size of 2 mm using local materials. Fig. 3 shows an animation of the bridge, fig. 4 its cross section. The 4.50 x 2.00 x 0.08 m wide bridge deck elements are prestessed transversely. As an additional step of innovation, the load bearing UHPC-elements are glued together without any additional mechanical connection. This means a further step towards an economic material adequate construction technique for UHPC. Inspired by first applications in Canada, South Korea and Europe and by intensive research and development efforts at different universities and of the cement- and construction industry, the DAfStB draw up a state-of-the-art-report on Ultra-High-Performance Concrete (DAfStB UHPC 2003). The DAfStB is part of the German Standardization Organization DIN being responsible for all standards and technical requirements related to the production and application of concrete and giving the rules for the design of concrete structures.The German state-of-the-art-report covers the technical know-how and the experience with UHPC worldwide published. It covers nearly all applications that exist hitherto – primarily based on commercially available UHPC mixtures – the main principles and the characteristic behavior criteria, durability aspects and the resistance against fire. A second part report refers to the adequate design and construction of structures using UHPC. The report traditionally is a first step towards a reliable technical guideline and a latter standard for UHPC.In the following some of the material and design aspects covered by the German state-of-the-art-report and by the French design recommendations are presented in more detail.MATERIALSRaw materials and material structureBoth the high compressive strength and the improved durability of UHPC are based upon the same four principles- a very low water-cement-ratio of about 0.20 to 0.25 resulting in a very dense and strong structure of the hydration products and minimizing the capillary pores, which are ductile to prevent brittle failure and to be able to use more or less traditional design approaches against the transport of harmful gases and liquids into and through the concrete,- a high packing density especially of the fine grains in the binder matrix reducing thewater demand of the fresh mix and increasing the compressive strength – as well as the brittleness of the concrete,- the use of higher amounts of effective superplastizisers to adjust the workability and – if needed –- the use of steel or other fibers to increase the tension, the bending tension and theshear strength and to make the concrete sufficiently ductile.Fig. 5 shows the packing effect schematically. As a simplified example, fig. 6 shows how the packing density develops when two quartz powders of different fineness (Q 1 and Q 2) are mixed together in different amounts (Geisenhanslüke and Schmidt 2004a). Up to a ratio of about 30 % of the fine and 70% of the “coarse” powder the packing density – defined by the part by volume of particles per unit volume - increases from 48 to 54 Vol.-%. The finer particles by and by fill up the hollow space in between the coarser grains. At the same time, the viscosity of a lime prepared with the powder-mixes at a constant water/fines-ratio of 0.26 decreased from 7500 to less than 5000 mPa s. If the amount of fine particles is further increased beyond the maximum packing density, the rheology of the mix becomes suboptimal again.To optimize the packing density of UHPC, usually specified quartz powders are used.Table 1 shows typical compositions of fine and course grained UHPC developed andused in Germany, fig. 7 the optimized grain size distribution of mix M1Q in table 1 consisting of four different fines. The correlation between the packing density – characterized by the water/fines-ratio of the matrix w/F v – and the compressive strength of heat treated (90°C) and water cured Cylinders (150/300 mm) is shown in fig.8. It is obvious that the packing density not only affects the rheology but also the strength of UHPC as well: at nearly the same water-cement ratio of 0.20 the compressive strength increased by about 25 % when the w/F v-value decreased from 0.53 to 0.40 by adding an pre-calculated amount of another quartz filler with a specified fineness. And table 1 a fig. 8 show that the use of coarser grains help to reduce the cement content and contributes to the compressive strength as well. Further tests showed that autogenous shrinkage and creeping were significantly reduced. The effectiveness of the fibers was reduced as well. This disadvantage could be partly compensated for using longer and stiffer fibers with a length of 17 mm and a diameter of 0.25 mm (Bornemann and Faber 2004).Due to an European Directive, quartz fillers containing particles with a diameter of less than 5 micron are suspected to cause health problems. This led to intensive efforts to replace those particles by other mineral powders. Positive experiences have been gained with finely ground granulated blast furnace slag, the fine and glassy parts of ground or assorted fly ashes from stone coal power plants and with some high quality stone dusts e.g. produced from basalt. Ultra fine slag particles are even adequate to partly replace microsilica. Common limestone fillers are – as a rule – less beneficial. Research is done to further improve the rheological and the strength performance of UHPC by adding nanotubes (Kowald 2004).The optimization process can be based on both a theoretical and experimental approaches. Usually the procedure of Okamura (Okamura 1995) is used. In Germany the actual packing density of cements or other powders is tested using the fast and easy Puntke-test (Puntke 2002). A specimen of about 100 g of the powder is filled into a container and slightly compacted. Than water or – for tests on powder mixes containingcement - a non-reactive liquid of known density is added until the surface is just wet.The amount of liquid added is a measure for the hollow space and – indirectly – for the packing density.Testing is time consuming and expensive, especially if the existing information about the powders is lacking and the grain size optimization needs several steps of iteration. Therefore some mathematically based, computer aided calculation procedures have been developed to pre-calculate the best fitting powders and the amounts of each being adequate to reach a maximum packing density (Geisenhanslüke and Schmidt 2004a). Experiences have shown that the results of the existing calculation procedures do not reflect sufficiently the reality when powders of different grain size, grain size distribution, shape and roughness of the surface are mixed in different proportions. In an active research project these procedures are developed further considering the 3-dimensionality of the structure, the shape, the friction of the grains and the so called “particle handicap” schematically shown in figure 9. These effects hinder the individual grains to really reach their theoretical optimum position within the structure of the powder mix.Strength and deformation behaviorBasis of an adequate, economic and safe design of structures fully or even partly consisting of UHPC elements are reliable reference values characterizing the strength and the deformation behavior under static and dynamic loads. Fiber free fine or coarsely grained UHPC mixtures as shown in table 1are characterized by both, a high compressive strength in between 150 and 250 N/mm2 primarily depending on the water-cement ratio, the volumetric water-to-fines ratio w/F v = w/Σ Vol.(cement+silica+fillers) of the matrix and the grain size of the aggregates as well as a linear elastic deformation up to about 95% of the fracture load. That means UHPC without fibers is a glass like brittle material with a comparatively high modulus of elasticity of 50.000 to 70.000 N/mm2. The typical tension strength of the pure matrix is about 8 N/mm2.Using steel or other adequate fibers with a sufficiently high modulus of elasticity of more than about 45.000 N/mm2, the compressive strength keeps constant or increases slightly while the tension, the bending tension and the shear strength as well as the ductility are significantly improved. As an example, table 2 (Bornemann et al. 2001; Fehling and Bunje 2004) shows that the bending tension strength of concrete prisms 40/40/160 mm made of fine grained UHPC (Mix M1Q) with 2.5 Vol-% of short steel fibers (length 6 to 9 mm, diameter 0.15 mm) was up to 36N/mm2, that of beams 150/150/700 mm made from the same concrete but without steel fibers was 22 N/mm2 only.That means if the bending strength of fibered UHPC is introduced into the design of structures it has to be considered that the bending strength primarily depends on the kind and the amount of fibers used, but the orientation and the distribution of the fibers within the matrix and the shape of the specimen used and of the structural element produced with the specific concrete may have a significant influence as well. As a rule, the spread of test results of a specific mixture exceeds that of UHPC mixtures without fibers significantly. Therefore the number of tests done to characterize one specific mix has to be increased to allow a calculation based on the standard deviation (…Characteristic Strength“, 5% fractile). In some active research projects these aspects are furtherinvestigated. Until sufficient knowledge has been gathered and measures have beendeveloped in order to influence e.g. the fiber orientation by the production process, elements of the designed shape should be placed and tested to validate the theoreticallyassumed design criteria.The same aspects have to be considered regarding the ductility of UHPC. The “amount”of ductility being necessary to fit the needs depends on the individual design andconstruction approach: if the UHPC is assigned for bearing the full tension and bending tension loads without any additional active or passive reinforcement – like in some of the applications e.g. of Ductal – the fiber content has to be sufficiently high to prevent sudden failure even if cracks due to uncalculating stresses and strains appearing locally . In those cases a fiber content of about 2.5 to 3 Vol.-% may give a satisfying compromise regarding workability of the fresh concrete, bending strength and ductility. For other applications, a reduced amount of e.g. 1 Vol.-% of fibers may satisfy the needs, e.g. if slabs, girders or other elements made from UHPC are fully pre-stressed and/or have a passive reinforcement. The fibers are some kind of “transportation reinforcement” and/or allow to utilize the high compressive strength more efficiently due to a higher safety margin to failure. As explained later a combination of passive reinforcement and fibers allow the shear reinforcement of beams to be omitted under bending loads. And in some cases UHPC may be applied even without fibers, e.g. for highly loaded columns or framework constructions consisting of ductile steel pipes filled with UHPC (Tue, Schneider, and Schenk 2004).In Fig. 10 the effectiveness of steel fibers, high strength non-corrosive Polyvinyl fibersand a mixture of both, a so called “fiber cocktail” is shown (Bornemann and Faber 2004). Mixes consisting of steel and other suitable fibers of different kind, length and diameter may fulfill the individual needs of a construction more effective by and more economically than fibers of one uniform type.DurabilityThe improved resistance of UHPC to all kinds of harmful gases and liquids, to chloride and frost or freezing and thawing attacks is related to the improved density both of the grain structure of the matrix and the much denser contact zone between the matrix and the (coarser) aggregates as well as by the denser structure of the hydration products. Fig.11 gives an impression of the dense structure.The porosity of UHPC is characterized by the absence of capillary pores, as one can see from the pore size distribution shown in fig. 12 tested by mercury intrusion. As a result, the extremely high resistance e.g. to chloride diffusion is shown in fig. 13. The resistance to attacks by freezing and salting are significantly improved even when compared with High Performance Concrete, see fig. 14.In table 3 some characteristic durability indicators are given based on different sources (Schmidt et al. 2003, Teichmann and Schmidt 2004; Resplendino 2004;)DESIGN ASPECTSAs a rule, the design of concrete structures has to be based on reliable but simplified material reference values, e.g. for the strength and the deformation behavior. For ordinary concrete those approaches are given in the relevant standards. For UHPC two similar approaches have been developed, one established by AFGC/SETRA in France in 2002 (SETRA-AFCG 2002) and one as part of the state-of-the-art report of the DAfStB in Germany in 2003 (DAfStB UHPC 2003). They both consider the fact, that as a rule the material properties of fiber reinforced UHPC show a significant higher deviation due to an inhomogenious distibution and orientation of the fibres in the matrix (Bernier and Behloul 1996).The French recommendations consist of three parts:– the first part gives specifications on the mechanical performance to be obtained and recommendations for characterizing UHPC including checks of finished products and of the concrete being produced,– the second part deals with the design and analysis of structures made with fibre reinforced, non-prestressed and/or non-reinforced UHPC-elements and– a third part dealing with the durability of UHPC.An important part deals with the behavior of fiber containing UHPC under tensile loading. As fig. 15 (Resplendino 2004; SETRA-AFCG) shows, the stress-strain relation is characterized by an elastic stage limited by the tensile strength of the cement matrix f tj and a post cracking stage characterized by the tensile strength of the composite material reached by fiber action.Using characterization tests depending on the type of structure studied (thin or thick slabs, beams, shells) and on the kind of load (direct or flexural tensile) the recommendations give the transfer factors to come from the test results to an “intrinsic” curve for tensile behavior independent of the size of the specimen and the kind of test used. In addition, a reduction factor is given to take into account the effect placement methods has on the real strength values to be obtained in a specific structural element. The French design methods proposed are in accordance with the French codes for pre-stressed or reinforced concrete BAEL 91 and BPEL 91 based on semi-probabilistic limit state values. Supplementary to the design codes the recommendations contain specificities concerning UHPC like the strength provided by fibers which allows the design of structures without any conventional reinforcement.For normal stress verification, the French recommendations use the AFREM-BFM method which concerns fiber concrete, and use a stress-crack width constitutive law σ = f(w). Moreover the characteristic length l c is introduced, to go from crack width w to strain ε:ε = f tj / E ij + w/ I c,The value of I c depends on the sections area. The analysis for standard sections is based on the assumptions that plane sections remain plane and the concrete behavior law follows fig. 16. The limit stresses at the SLS are the same as for a reinforced orprestressed structure: 0.3 mm for normal cracking, 0.2 mm for detrimental and 0.1 mm for highly detrimental cracking. For calculation of the Serviceability Limit State (SLS), a somewhat more simplified stress strain relationship as shown in Fig. 17 may be used according to the recommendations given by (DAfStb UHPC 2003).The German report describes a standard test procedure as shown in fig. 18 to evaluate the load-deformation behavior of UHPC under bending loads in order to determine a stress strain relationship.Fig. 19 shows the result of such a test. To transform it into a stress-strain relation, the stresses at a crack width of 0.5 and 3.5 mm are being considered.Fig. 20 shows the stress-strain curves calculated according to this proposal. The stresses at the significant points of the curve are determined from the equationsσ2.0 – 3.5 ‰ = f ctk0.5 • 0.37 σ25‰ = β ٠f ctk3,5.The factor β as well as the factor 0.37 have been established by recalculating test results. As for ordinary concrete, the factor β depends on the relation f ctk,3.5 / f ctk,0.5. It can be taken from fig. 21.Normally a strain limit of 25‰ is adequate. But re-calculations of test results already showed that for a ratio f 3.5 / f 0.5 < 0,5 the design may fall short of the necessary safety margin. In fig. 21 the reduced strain for f 3.5/f 0.5 < - 0.5 is characterized by the marked curve. For the design in the Ultimate Limit State, the stress strain law according to DIN 1045-1 is proposed. It is defined by the following equation (1):c c20≥ε≥ε (1) The exponent n in Eq. 1 can be taken from table 4. This enables a transition to the rules for High Strength Concrete (HSC/HPC). For UHPC 210 and higher strength classes, hence, a linear relationship results. Furthermore, for UHPC without fibers or insufficient confinement,εc2 = εc2u shall be assumed in order to account for the brittleness in such cases. The design value of the compressive strength follows Eq. 2.'85,0c c ck cd f f γγ⋅⋅= (2)withc γpartial safety coefficient according to table 2 in DIN 1045-1 'c γadditional partial safety factor taking into account the sensibility for deviationsThe strain at the maximum stress can be assumed to be 2,2‰ starting with strength classC 100/115 acc. to EN 206. For the special permit required in Germany for structures built of new materials, different values may be proposed by the obligatory expertise. For UHPC with fibers or sufficient confinement, a plastic branch until the strain fc2u ε can be used in order to account for the improved ductility. The value of f c2u ε can be determined in such a way that the capacity in bending is adjusted to the bending capacity obtained from a stress strain law with a descending branch and assuming yielding of steel in the tension zone. However, since the influence of the descending branch of the stress strain relationship is of minor importance, the additional strain (length of the horizontal branch in the stress strain diagram) can be assumed to be quasi linear.Shear and TorsionIn order to determine the reinforcement possibly required for shear loading, the resistance due to the concrete, the shear reinforcement (e.g. stirrups) and the fibers can be added according to the SETRA–AFGC regulations:V u = V Rb + V a + V f(3) with: V Rb = shear resistance of concrete section V a= shear resistance to discrete reinforcementV f = shear resistance due to fibers (4)with:σpKw lim = max(w u ; 0,3 mm), where w u = l c ⋅ εu and l c ... characteristic length σ(w) = characteristic post cracking tensile resistance for crack width w (according to tests)S = area of fiber action:S = 0,9 b 0 ⋅ d bzw. b 0 ⋅ z for rectangular and T-shape sectionsS = 0,8 ⋅ (0,9 d)2 bzw. 0,8 z 2 for circular sectionsγbf= particular safety coefficient for fiber concrete in tension βu = angle of compression struts。

a rXiv:h ep-ph/952267v11Fe b1995BUHEP 95-3hep-ph/9502267February 9,1995The profile of a nonstandard Higgs boson at the LHC Dimitris Kominis ∗and Vassilis Koulovassilopoulos †Boston University,Physics Department,590Commonwealth Avenue,Boston,MA 02215USA ABSTRACT In a wide class of extensions of the Standard Model there is a scalar resonance with the quantum numbers of the usual Higgs boson but with different couplings to fermions and gauge ing an effective Lagrangian description,we examine the phe-nomenology of such a generic nonstandard Higgs boson at the LHC.In particular,wedetermine the circumstances under which such a particle can be observed in its ZZ decay mode and distinguished from the Higgs boson of the Standard Model.We briefly comment on the energy scale effectively probed at the LHC,if the nonstandard nature of an observed Higgs particle can be asserted.1IntroductionThe operation of the next generation of high-energy colliders(such as the LHC,LEP-II, NLC)within the coming decade is expected to bring us closer to an understanding of the mechanism of electroweak symmetry breaking.The minimal Standard Model(SM) is the simplest possibility,but its confirmation requires the discovery of a neutral scalar particle,the Higgs boson,with properties completely specified once given its mass.In the SM this is an undetermined parameter,and so far direct searches have set a lower limit of about60GeV[1].An upper bound of approximately1TeV has been suggested on the basis of“triviality”[2],and the validity of the perturbation expansion[3],which makes it likely that,if the SM Higgs boson exists,it will be discovered at the next generation colliders.However,it is widely believed[2,4]that the SM,despite its experimental success,can not be complete and that new physics,beyond the SM,should arise at somefinite energy scaleΛ.IfΛis very large,then the low-energy theory would look like the SM,while if Λis low(such as a few TeV),then deviations should be expected and the properties of a Higgs-like resonance(if present)could differ substantially from those predicted in the context of the SM.A resonance lighter than other massive degrees of freedom that shares the quantum numbers of the SM Higgs boson but couples to the electroweak gauge bosons and to fermions with nonstandard strength has been generically called a“Nonstandard Higgs”boson[5,6].Such an object is featured in a variety of models of electroweak symmetry breaking; namely,some models with dynamical symmetry breaking,such as Composite Higgs mod-els[7,8,9,10,6]and“top-condensate”models[11],as well as linear models with many fundamental scalars in which a mass gap exists between a light scalar-isoscalar(under custodial isospin)particle and all other resonances.If these models describe electroweak symmetry breaking,the isoscalar resonance presumably will be thefirst to be discov-ered in a collider experiment.It is not clear a priori,however,whether its nonstandard properties can be measured accurately enough to distinguish it from the SM Higgs boson.The question we wish to address in this paper is whether it will be possible in future experiments at the Large Hadron Collider(LHC)to detect a nonstandard Higgs boson and to differentiate it from the SM Higgs.As a model,we consider the most general low-energy effective Lagrangian in terms of the usual SU(2)L×SU(2)R/SU(2)V symmetry breaking pattern which,below the cutoffscaleΛ,has the same spectrum as the SM.The SM is2a particular case and corresponds to the limit whereΛ→∞.This Lagrangian is then used to explore the prospects of the LHC to detect and distinguish a nonstandard from a Standard Higgs boson.In particular,for a variety of Higgs boson masses m H(assuming that m H>2m Z),we determine the values of couplings in the effective Lagrangian for which this is possible by looking at the Higgs boson decay mode H→ZZ→l+l−l+l−, where l is an electron or a muon.It has been shown[5,6]that if a scalar isoscalar resonance is observed,then the measurement of its width offers the best way to distinguish it from the SM Higgs.The deviations from the SM couplings can be used within specific models to estimate the scaleΛof new physics,provided no other nonstandard physics is discovered.As an indication,we have done so for a number of simple Composite Higgs models.This is similar in spirit to an early study by Kosower[10],who also proposed the measurement of the width as a tool to probe the compositeness scale within Composite Higgs models. However,we performed a more detailed statistical analysis and reached somewhat different (less optimistic)conclusions.In the next section we review the theoretical framework and construct the effective Lagrangian of the most general theory with a nonstandard Higgs boson.In Section3we describe the calculation of the signal and ZZ background cross-sections and discuss the issue of whether one can discriminate between a nonstandard Higgs boson and its SM counterpart on the basis of a width measurement.In particular,we derive the statistical significance of a possible discrepancy between the result of such a measurement and the SM expectation.Finally,Section4contains our conclusions.2The Effective LagrangianIn this section,we briefly describe the construction of the most general effective theory with a nonstandard Higgs boson[5,6].The electroweak symmetry breaking sector at low energies contains,besides the Goldstone bosons w a(which become the longitudinal components of W±and Z),one extra scalar particle H(the nonstandard Higgs boson) with the quantum numbers of the SM Higgs boson1.As in the SM,we assume that the Goldstone bosons arise from the spontaneous break-down of a chiral SU(2)L×SU(2)R symmetry down to its diagonal SU(2)V subgroup.As usual,SU(2)L is identified with the gauge group SU(2)W and SU(2)R is the“custodial”symmetry whoseτ3component is identified with hypercharge.The interactions of the Goldstone bosons are described conveniently by using a nonlinear realization[12]of the chiral symmetry,in terms of thefieldΣ=exp i w· τ4 v2+2ξvH+ξ′H2+... Tr ∂µΣ†∂µΣ +L H(3) where L H is the Lagrangian that describes the Higgs boson self-interactionsL H=12H2−λ3v4!H4− (4)andξ,ξ′,λ3andλ4are unknown coefficients.For simplicity,in eqs.(3)and(4)we only show the leading terms,with the ellipsis denoting higher powers in H.The gauge bosons can be introduced by replacing the ordinary derivative in eq.(3)by the covariant one,which,by virtue of the transformation law(2),takes the formDµΣ=∂µΣ+i g2BµΣτ3(5)where g,g′are the usual SU(2)W and U(1)Y gauge couplings respectively.Hence the parametersξ,ξ′etc,represent the couplings of one or more nonstandard Higgs bosons to a pair of weak gauge bosons W aµ.4The fermions are incorporated into the effective Lagrangian as matterfields[12].We shall only consider the quarks of the third family,since these will be the only important ones in our phenomenological investigation.These fermions can be included in thefieldsψL= t L b L ,ψR= t R b R (6)which transform asψL→LψL andψR→RψR under SU(2)L×SU(2)R.Their interactions with the scalars are given byLΣf¯f=h1(v+y1H+...)¯ψLΣψR+h2(v+y2H+...)¯ψLΣτ3ψR+h.c.(7) where h1and h2correspond to Yukawa couplings and can be replaced by the fermion masses,through m t=(h1+h2)v and m b=(h1−h2)v,while y1and y2are new unknown couplings.Again,the ellipsis denotes higher powers in the Higgsfield which are not included in our ing the explicit form(6)in eq.(7),we can read offthe Higgs boson couplings to the top and bottom quarks:L Hf¯f=(h1y1+h2y2)H¯t L t R+(h1y1−h2y2)H¯b L b R+h.c.≡y t(m t/v)H¯t L t R+y b(m b/v)H¯b L b R+h.c.(8) Thus,this Lagrangian introduces two new unknown parameters y t,y b.The SM is a particular case of the effective theory defined above,with the only non-zero couplings being3m2Hξ,ξ′=1,λ3,λ4=(10)16πv2At a scale16πv2s=partial wave unitarity breaks down.Consequently the cutoffΛof the theory,physically associated with the scale at which new degrees of freedom emerge,must lie at or below this scale.From eq.(11)itbecomesclear thatthelargerthe deviation of ξfrom its SM value of 1,the lower the energy scale at which new physics is expected.If Λ≡4πf is the scale of new physics,then by inverting eq.(11),we can write,roughly,ξ2=1+O v 232πv2ξ2 2√4x 2W )+√4x 2Z ) +3m 2t m H m 2H 3/2.(13)where x V =4m 2V /m 2H ,V =W,Z .Here we are assuming that the underlying short-distance dynamics acts so as not to particularly enhance y b over y t .Then,since m t ≫m b ,only the top quark couples significantly to the Higgs boson H ,and we can ignore the coupling to the bottom quark.On the other hand,in the purely scalar sector,tree level amplitudes do not depend on the parameters ξ′,λ3,λ4,etc.The leading one-loop corrections to W L W L scattering and the Higgs boson decay width were computed in Ref.[5,6]and,for phenomenological purposes,they can be incorporated in the effective definition of ξ.We now proceed to investigate the phenomenology of the model presented above.63PhenomenologyIn this section,we explore the phenomenology of a nonstandard Higgs boson at the LHC. We shall only consider Higgs boson masses larger than the ZZ threshold.In this mass range,the Higgs boson decays primarily to gauge boson pairs and thus can be most effectively searched for in the“gold-plated”channelH→ZZ→l+l−l+l−(14)where l is an electron or a muon.This process has been discussed at great length in the literature2,and it is expected that a Standard Higgs boson with mass m H≤500GeV (800GeV)will be discovered at the LHC at an integrated luminosity of10fb−1(100fb−1). The main question we try to answer in the analysis that follows is whether a nonstandard Higgs boson of given mass m H and couplingsξand y t can be detected at the LHC and distinguished from a SM Higgs boson of the same mass.We present results for integrated luminosities of10fb−1and100fb−1,while the center-of-mass energy is assumed to be √4παs(m H).(17)9An irreducible ZZ background also arises from gluon fusion through a quark loop(the ‘box’diagram)gg→ZZ.(18)In fact,this process interferes with the resonant Higgs boson exchange processgg→H→ZZ(19)where the Higgs boson is produced through a top quark loop.An exact calculation for the SM[20]has shown that the effect of the interference is rather small,for most of the range of masses we consider.Towards the upper end of this range,however,(that is m H≈800GeV)the increase in the cross-section caused by the interference term may become sizeable(it is constructive interference).We ignored this effect,and thus ourestimates of the signal rate are somewhat conservative for large masses.We did take into account,however,the contribution of the‘box’diagram to the background,which amounts to approximately50%of the Born process(15),by scaling the cross-section of the latter by1.5.There are also reducible four-lepton backgrounds,primarily from t¯t production.It has been argued[15,21]that,with appropriate isolation cuts and the expected Z mass resolution capability at the LHC,these backgrounds can be reduced to well below the irreducible background levels.We shall therefore ignore them in this study.However,we have taken into account a10%loss of signal rate due to these cuts[21].The main mechanism for Z-boson pair production through a Higgs boson is the process (19).The rate for this process depends on the top quark mass,which is chosen here to be m t=170GeV[22],and also on the nonstandard Yukawa coupling y t.In the Standard Model,for such a top-quark mass,the gluon fusion is the dominant production mechanism for all Higgs boson masses up to1TeV.Leading QCD corrections to this process have been included by multiplying the cross section by another“K-factor”[23,24,25]K=1+ 11π.(20)A second production mechanism for Z pairs through a Higgs boson is gauge boson fusionqq→qqH→qqZZ.(21) We computed the cross-section for this process by using the effective-W approximation [26,27].The scattering amplitudes are calculated at tree-level in the gauge theory from the Lagrangian of Section2.The cross-section is obtained by folding the amplitudes with8the luminosities of the W’s and Z’s inside a quark.Both transverse and longitudinal polarizations are included using the distribution functions of Ref.[28](see also[29]). (The subleading terms in the expressions for these functions depend on the characteristic energy scale of the process under consideration,taken here to be Q2=m2ZZ/4.)The contribution from W L W L(Z L Z L)fusion,which is the least affected by the choice of Q2, is dominant for energies around the peak,since this amplitude is most sensitive to the existence of the Higgs resonance,while the W L W T+W T W T fusion prevails outside this region.The contribution to the cross-section from the interaction of the gauge bosons that does not involve the exchange of the Higgs resonance should in fact be considered as a background[30].We have calculated this background in the effective theory with ξ=0,and subtracted it from the cross-section of the process(21)in our estimates for the signal.We should also remark that in the calculation of both processes(21)and(19),the s-channel Higgs boson exchange diagram is unitarized by including the“running”Higgs boson decay width3in the propagator.This prescription(which can be justified only in the resonance region)differs from other ones,such as including a constant width,by effects which are formally of higher order inλ≡m2H/2v2.However,for W W scattering, it was shown[31]that it is better to use an energy dependent width,because partial wave amplitudes stay closer to the unitarity circle.In terms of event rates,we found that,for gluon fusion,the two prescriptions differ by at most10%for a heavy and wide resonance (see also Ref.[32]).In Tables1–6we present our results for the event rates and the statistical significance of Higgs boson signals for various values ofξand y t.The resonance will have an effective widthΓeff determined by the physical Higgs boson width and by the mass resolution of the detector:Γeff=3The running width is obtained through the relation ImΠH(s)=−√resonance peak occurs,in general,at a lower energy than the nominal Higgs boson mass m H,due to the interference with the non-resonant terms,the energy dependence of the (running)width and the effect of the falling distribution functions.For example,if m H= 800(600)GeV andξ=y t=1,the maximum of the signal cross-section occurs at approximately730(585)GeV.In our results,the Higgs boson mass quoted refers to m H rather than the resonance mass.The results presented for the event rates at the high luminosity(100fb−1)were obtained from those at low luminosity(10fb−1)by scaling by a factor of10.This is not,strictly speaking,a correct procedure,because of the problems a higher luminosity environment may pose(such as deterioration in the energy resolution)[16,33].A full detector simulation is needed in order to assess the magnitude of these effects.Consequently,our results for a luminosity of100fb−1should be regarded as rather optimistic.From these tables it can be seen that a nonstandard Higgs resonance may be distin-guished in principle from the SM Higgs boson by a comparison of its width and total cross-section to the Standard Model predictions.Before we decide whether this can be achieved in practice,we need to know the expected accuracy of a width measurement,as well as the theoretical uncertainties in the calculation of the width and the cross-section. There are few theoretical uncertainties in the calculation of the SM Higgs boson width. Higher order corrections to both gauge boson and fermion decay modes have been com-puted[34,35]and have been found to increase the full width by approximately15%.We chose here not to include this correction,but this does not alter our conclusions.(It will simply change the effective SM value ofξand y t to a value slightly different from1.)For the purposes of deciding whether an observed resonance is consistent with the Standard Model predictions,what matters is to know the latter precisely enough,which we do. Similarly,we have chosen not to include radiative corrections to the width of a nonstan-dard Higgs boson since these can be incorporated into the definition forξand y t[6].In contrast,the accuracy of the cross-section calculation is compromised by the imprecise knowledge of structure functions(amounting to perhaps30%for Higgs boson production [16]),our various approximations(such as the effective-W scheme or the neglect of the interference effects of the‘box’diagram in ZZ production)as well as further corrections beyond the included QCD effects.Consequently,if a Higgs-like resonance is discovered, a comparison of its width to the Standard Model prediction offers the best way to probe its nature.The systematic uncertainty in the measurement of the width arising from smear-10ing may be corrected for by using eq.(22).This will be an accurate procedure only if ΓH>∼∆m H.The statistical error involved in the measurement of the width warrants a more detailed discussion:Suppose that a Higgs resonance is observed at a mass m H and its width measured and found to differ from the expected Standard Model valueΓSM.We wish to attach a statistical significance to this deviation.This statistical significance can be derived from the probability density function according to which the possible measure-ments of the Standard Higgs boson width are distributed.(Any measured quantity is a statistical variable and,as such,obeys some probability distribution function.)To obtain the probability distribution we performed a large number of numerical experiments sim-ulating the possible outcomes of an actual experiment.The procedure adopted was the following:the ZZ invariant-mass range of interest was divided in4-GeV bins.In each of them the total number of events was generated according to a Poisson distribution with mean N S+N B,where N S,N B are the SM signal and background events respectively, expected in that bin.Assuming that the continuum background is known(e.g.from independent experiments)we subtracted the expected background N B in each bin.The resulting distribution represents the signal with an additional noise due to background fluctuations.The mass and the width were obtained byfitting this data with a function of the formm4(E2−m2)2+m2Γ2(23) where E is the invariant mass of the Z pair and m,Γare the parameters of thefit.The exponential encodes the effect of the falling parton distribution functions,while in the expression for the cross-section,factors other than the propagator have a rough m4/E dependence.The value of the constant E0wasfixed from the exact(lowest-order)cross-section for the processpp(gg)→H→ZZ(24) The bestfit occurs for E0=283.8GeV.Repeating this experiment a large number of times,we were able to obtain the proba-bility density,the mean<Γeff>and the standard deviationδΓeff.As mentioned earlier, the physical Higgs boson width can be recovered from the measured,or“effective”,width Γeff through eq.(22).In particular,the spreadδΓSM that corresponds to one standarddeviationδΓeff is given byδΓSM=δΓeff11−(∆m H/Γeff)2(25)Thus,if a resonance of(physical)widthΓH=ΓSM is observed,the statistical significance S associated with this discrepancy is given by the number of standard deviations thatΓH lies away fromΓSM:S=|ΓH−ΓSM|Γeff =cN(27)In the limit of large N and negligible background,c is a constant4.In general,though,c is a function of both the signal N and the background B(and,as can be expected,increases with increasing B or decreasing N).For poor statistics and wide objects(for instance in the case m H=800GeV),the width can hardly be measured,even if a statistically significant signal can be obtained.In Tables7–8we display,for various masses and three representative values of y t, namely y2t=0.5,1and2,the range of values ofξfor which the nonstandard Higgs boson is observable and distinguishable from the SM Higgs.Results are presented for integrated luminosities of10fb−1and100fb−1.The criteria used in compiling these tables are the following:For a signal to be declared“observable”we require that it consists of at least10 events and that its statistical significance is greater than5σ.For it to be distinguishable from the SM Higgs boson,we require that its widthΓH differ from the Standard Model value by at least three standard deviations as defined by eq.(25).If this criterion is not satisfied,one could in principle examine the signal event rate.However,given the large uncertainty in the theoretical calculation,we opted not to use this information.4ConclusionsOur conclusions are consistent with the expectation that a SM Higgs boson will be de-tected at the LHC in this channel provided its mass is less than about500GeV(at 10fb−1)or800GeV(at100fb−1).As y t becomes smaller or larger than unity,this mass range will shrink or expand.For example,at y2t=0.5andξ=1the respective mass ranges at the low and high luminosity options considered are330GeV<∼m H<∼430GeV and2M Z<∼m H<∼680GeV respectively.We observe further that at10fb−1,only modelswith relatively largeξcan be differentiated from the Standard Model.This is primarily due to the low statistics and the consequent imprecision in the width measurement.It might be possible,however,to improve the statistics by a less strict set of cuts on the final state leptons(or Z’s).The situation is considerably better at100fb−1,as can be seen from Table8.In certain cases whereξis small,the nonstandard Higgs boson is too narrow to be resolved,even though a SM Higgs of the same mass is not.In this case one could tell that the Higgs boson is nonstandard by comparing the detector resolution to the expected SM width,but it is not possible to determine a value forξ.As we emphasized earlier,the deviation of the values of the parametersξand y t from unity is a measure of the cutoffΛ,which can be thought of as an upper bound to the scale of new physics.Precise relations,however,are model-dependent.In the context of specific models,the results presented in Tables7-8reveal the energy scale that the LHC will be able to probe.For example,if m H=500GeV,where the sensitivity of the LHC to the measurement ofξis about30%(see Table8),the scale probed isΛ=4.3TeV in the SU(3)L×SU(3)R/SU(3)V model of Ref.[8]whereξ2=1−v2/f2,Λ=2.2TeV in the SU(5)/SO(5)model[9]whereξ2=1−(v2/4f2),andfinallyΛ=16TeV in the SU(4)/SU(2)×SU(2)model[10]in whichξ2=1−(4v2/f2).In the above,Λ=4πf is the compositeness scale of the underlying new strong dynamics and v=246GeV,while we have assumed y t=1in all of these cases.In a general Two-Higgs-Doublet model where a gap exists between the mass m H of the lightest neutral state and that of the heavier (nearly degenerate)scalars(M,say),the parameterξgenerally approaches its SM value faster:ξ2=1−O(m4H/M4);our results indicate that,in this case,it will be very hard to determine the existence of a non-minimal scalar sector solely from a measurement of the width of the observed resonance(see also Ref.[36]).AcknowledgementsWe thank R.S.Chivukula,M.Golden,ne and B.Zhou for useful conversations. This work was supported in part under NSF contract PHY-9057173and DOE contract DE-FG02-91ER40676.m H=350GeVξWidth Width Width39(5.6)26(7.6) 3.70.500.36 4.0224.242(6.0)34(9.0)14(5.2)1.00 1.4115.363.349(6.9)43(9.3)18(5.0)1.50 3.1834.012859(8.2)45(8.2)22(4.4)2.00 5.6560.3219Table1:Event rates and decay widths for various Higgs boson masses m H andξat the LHC at a luminosity of10fb−1for standard top Yukawa coupling and m t=170GeV. The statistical significance is also shown for signals consisting of more than10events.m H=400GeV m H=800GeV Ev.(Sg.)Ev.(Sg.)Ev.(Sg.)Ev.(Sg.)0.250.09 4.8525.148.6403(18.5)205(22.9)50(9.3)14(4.0)0.750.8017.072.4167446(20.2)340(28.1)82(10.1)28(4.0)1.252.2141.2167403535(23.7)368(24.6)111(8.6)44(2.8)1.75 4.3277.63092.00 5.65100398m H=350GeVξWidth Width Width20(3.0)15(4.9) 3.10.500.36 3.8918.622(3.3)18(5.4)8.81.00 1.4115.157.628(4.2)25(6.0)11(3.4)1.50 3.1833.912339(5.7)28(5.6)14(3.1)2.00 5.6560.1214SM 1.4115.363.3Table3:Event rates and decay widths for various masses andξat the LHC at a luminosity of10fb−1for nonstandard top Yukawa coupling y2t=0.5and m t=170GeV.The statistical significance is also shown for signals consisting of more than10events.m H=400GeV m H=800GeV Ev.(Sg.)Ev.(Sg.)Ev.(Sg.)Ev.(Sg.)0.250.09 3.1815.531.7204(9.9)126(15.5)35(7.4)10(3.0)0.750.8015.362.8150245(11.7)190(18.3)50(7.0)18(2.9)1.252.2139.5158386334(15.6)220(16.6)74(6.5)32(2.2)1.75 4.3275.92992.00 5.6598.6388446(20.2)340(28.1)82(10.1)28(4.0)m H=350GeVξWidth Width Width75(9.9)42(11.1) 4.90.500.36 4.2935.582(10.7)64(14.5)21(6.8)1.00 1.4115.574.589(11.5)78(14.8)29(7.2)1.50 3.1834.314099(12.6)77(12.7)35(6.5)2.00 5.6560.5231SM 1.4115.363.3Table5:Event rates and decay widths for various masses andξat the LHC at a luminosity of10fb−1for nonstandard Higgs-top Yukawa coupling y2t=2and m t=170GeV.The statistical significance is also shown for signals consisting of more than10events.m H=400GeV m H=800GeV Ev.(Sg.)Ev.(Sg.)Ev.(Sg.)Ev.(Sg.)0.250.098.1944.282.4795(33.3)301(28.9)65(10.4)20(4.8)0.750.8020.391.5201846(35.0)546(40.3)131(14.0)44(5.7)1.252.2144.5186437936(38.1)636(37.4)178(12.7)67(3.9)1.75 4.3280.13282.00 5.65104417446(20.2)340(28.1)82(10.1)28(4.0)m H(GeV)y2t=1300–350ξ>∼1.70400ξ>∼1.60450ξ>∼1.70500–Range ofξy2t=0.5y2t=2––ξ>∼1.40ξ>∼1.400.20<∼ξ<∼0.45ξ>∼1.15ξ>∼1.205000.20<∼ξ<∼0.60ξ>∼1.35ξ>∼1.20ξ>∼1.45ξ>∼1.35–ξ>∼1.55––Table8:Range of values of the parameterξfor which the nonstandard Higgs boson resonance is both observable and distinguishable from the Standard Higgs at100fb−1of luminosity and three values of the nonstandard Yukawa coupling y t.The range0<ξ≤2.0 has been explored.References[1]ALEPH Collaboration,D.Decamp et al.,Phys.Rev.216(1992)253;DELPHI Collaboration,P.Abreu et al.,Nucl.Phys.B373(1992)3;L3Collaboration,O.Adriani et al.,Phys.Lett.B303(1993)391;OPAL Collaboration,M.Akrawy et al.,Phys.Lett.B253(1991)511.[2]R.Dashen and H.Neuberger,Phys.Rev.Lett.50(1983)1897.[3]B.W.Lee,C.Quigg and H.Thacker,Phys.Rev.D16(1977)1519.[4]G.’t Hooft,in:Recent Developments in Gauge Theories,edited by G.’t Hooft(Plenum Press,New York,1980).[5]R.S.Chivukula and V.Koulovassilopoulos,Phys.Lett.B309(1993)371.[6]V.Koulovassilopoulos and R.S.Chivukula,Phys.Rev.D50(1994)3218.[7]D.B.Kaplan and H.Georgi,Phys.Lett.B136(1984)183;D.B.Kaplan,S.Dimopoulos and H.Georgi,Phys.Lett.B136(1984)187.[8]T.Banks,Nucl.Phys.B243(1984)125.[9]H.Georgi and D.B.Kaplan,Phys.Lett.B145(1984)216;M.J.Dugan,H.Georgi and D.B.Kaplan,Nucl.Phys.B254(1985)299.[10]D.A.Kosower,in Physics of the Superconducting Supercollider,Proceedings of the1986Summer Study on the Physics of the SSC,Snowmass1986,edited by R.Don-aldson and J.Marx.[11]Y.Nambu,Enrico Fermi Institute Preprint EFI88-39;V.A.Miransky,M.Tanabashi,and K.Yamawaki,Phys.Lett.B221(1989)177;Mod.Phys.Lett.A4(1989)1043;W.A.Bardeen,C.T.Hill,and M.Lindner,Phys.Rev.D41(1990)1647.[12]S.Coleman,J.Wess and B.Zumino,Phys.Rev.177(1969)2239;C.G.Callan,S.Coleman,J.Wess and B.Zumino,Phys.Rev.177(1969)2247.[13]R.S.Chivukula,M.Dugan and M.Golden,Phys.Lett.B336(1994)62.。

a r X i v:071.3109v 1 [h e p -p h ] 16 O c t 2007Heavy MSSM Higgs Bosons at CMS:“LHC wedge”and Higgs-Mass PrecisionS.Heinemeyer 1a ,A.Nikitenko 2,and G.Weiglein 3b1Instituto de Fisica de Cantabria (CSIC-UC),Santander,Spain2Imperial College,London,UK;on leave from ITEP,Moscow,Russia 3IPPP,University of Durham,Durham DH13LE,UKAbstract.The search for MSSM Higgs bosons will be an important goal at the LHC.In order to analyze the search reach of the CMS experiment for the heavy neutral MSSM Higgs bosons,we combine the latest results for the CMS experimental sensitivities based on full simulation studies with state-of-the-art theoretical predictions of MSSM Higgs-boson properties.The experimental analyses are done assuming an integrated luminosity of 30or 60fb −1.The results are interpreted as 5σdiscovery contours in MSSM M A –tan βbenchmark scenarios.Special emphasis is put on the variation of the Higgs mixing parameter µ.While the variation of µcan shift the prospective dis-covery reach (and correspondingly the “LHC wedge”region)by about ∆tan β=10,the discovery reach is rather stable with respect to the impact of other supersymmetric parameters.Within the discovery region we analyze the accuracy with which the masses of the heavy neutral Higgs bosons can be determined.An accuracy of 1–4%should be achievable,depending on M A and tan β.PACS.14.80.Cp Non-standard-model Higgs bosons –12.60.Jv Supersymmetric models1IntroductionIdentifying the mechanism of electroweak symmetry breaking will be one of the main goals of the LHC.The most popular models are the Higgs mechanism within the Standard Model (SM)and within the Minimal Su-persymmetric Standard Model (MSSM)[1].Contrary to the case of the SM,in the MSSM two Higgs doublets are required.This results in five physical Higgs bosons instead of the single Higgs boson of the SM.These are the light and heavy CP -even Higgs bosons,h and H ,the CP -odd Higgs boson,A ,and the charged Higgs bo-son,H ±.The Higgs sector of the MSSM can be spec-ified at lowest order in terms of the gauge couplings,the ratio of the two Higgs vacuum expectation val-ues,tan β≡v 2/v 1,and the mass of the CP -odd Higgs boson,M A .Consequently,the masses of the CP -even neutral Higgs bosons and the charged Higgs boson are dependent quantities that can be predicted in terms of the Higgs-sector parameters.Higgs-phenomenology in the MSSM is strongly affected by higher-order correc-tions,in particular from the sector of the third gener-ation quarks and squarks,so that the dependencies on various other MSSM parameters can be important.The current exclusion bounds within the MSSM [2,3,4]and the prospective sensitivities at the LHC are usually displayed in terms of the parameters M A and tan βthat characterize the MSSM Higgs sector at low-1In our analysis we do not consider diffractive Higgs production,pp →p ⊕H ⊕p [11].For a detailed discussion of the search reach for the heavy neutral MSSM Higgs bosons in diffractive Higgs production we refer to Ref.[12].Colliders-Higgs Phenomenology Contributed Talk500N S63172.4×10−3R Mφ0.1760.1872.8300N S72.932.86.4×10−3R Mφ0.2160.2303.2500572.0×10−20.2002.6Table 3.Required number of signal events,N S,with L=30fb−1for a5σdiscovery in the channelφ→τ+τ−→µ+jet.The other quantities are defined as in Tab.1.The results quoted in Tabs.1–3for the required number of signal events depend only on the Higgs-boson mass,i.e.the event kinematics,but are indepen-dent of any specific MSSM scenario.In order to deter-mine the5σdiscovery contours in the M A–tanβplane these results have to be confronted with the MSSM predictions.The number of signal events,N ev,for a given parameter point is evaluated viaN ev=L×σb¯bφ×BR(φ→τ+τ−)×BRττ×εexp.(4)Here L denotes the luminosity collected with the CMS detector,σb¯bφis the Higgs-boson production cross sec-tion,BR(φ→τ+τ−)is the branching ratio of the Higgs boson toτleptons,BRττis the product of the branching ratios of the twoτleptons into their respec-tivefinal state,BR(τ→jet+X)≈0.65,(5) BR(τ→µ+X)≈BR(τ→e+X)≈0.175,(6)andεexp denotes the total experimental selection effi-ciency for the respective process(as given in Tabs.1–3).For our numerical predictions of total cross sections (see Ref.[18]and references therein)and branching ra-tions of the MSSM Higgs bosons we use the program FeynHiggs[19,20,21,22].We take into account effects from higher-order corrections and from decays of the heavy Higgs bosons into supersymmetric particles.In spite of the escaping neutrinos,the Higgs-boson mass can be reconstructed in the H,A→ττchannel from the visibleτmomenta(τjets)and the missing transverse energy,E missT,using the collinearity approx-imation for neutrinos from highly boostedτ’s.In the investigated region of M A and tanβthe two states A and H are nearly mass-degenerate.For most values of the other MSSM parameters the mass difference of A and H is much smaller than the achievable mass resolution,and the difference in reconstructing the A or the H will have no relevant effect on the achiev-able accuracy in the mass determination.The preci-sion∆Mφ/Mφshown in Tabs.1–3is derived for the border of the parameter space in which a5σdiscov-ery can be claimed,i.e.with N S observed Higgs events. The statistical accuracy of the mass measurement has been evaluated via∆Mφ/Mφ=R Mφ/S.Heinemeyer,A.Nikitenko,G.Weiglein Heavy MSSM Higgs Bosons at CMS...2A corresponding analysis in benchmark scenariosfulfilling cold dark matter constraints can be found in Ref.[23].3Since the results of the experimental simulation for this channel are available only for two M A values,the interpo-lation is a straight line.This may result in a slightly larger uncertainty of the results compared to the other two chan-nels.Fig.1.Variation of the5σdiscovery contours obtained in the m maxhscenario for different values ofµfrom the channels b¯bφ,φ→τ+τ−→jets(top),→e+jet(middle),→µ+jet(bottom).4Numerical results for the Higgs-boson mass precisionThe expected statistical precision of the heavy Higgs-boson masses is evaluated according to eq.(7).In Fig.2 we show the expected precision for the mass measure-ment achievable from the channel b¯bφ,φ→τ+τ−using thefinal stateτ+τ−→jets.Within the5σdiscovery region we have indicated contour lines corresponding to different values of the expected precision,∆M/M.Colliders-Higgs Phenomenology Contributed Talk。

a r X i v :0709.4408v 1 [h e p -p h ] 27 S e p 2007SUSY HIGGS BOSONS AT THE LHC G.WEIGLEIN IPPP,Department of Physics,University of Durham,South Road,Durham DH13LE,UK Recent results on MSSM Higgs physics at the LHC are reviewed.The dependence of the LHC discovery reach in theb ¯bH/A,H/A →τ+τ−channel on the underlying SUSY scenario is analysed.This is done by combining the latest results for the prospective CMS experimen-tal sensitivities for an integrated luminosity of 30or 60fb −1with state-of-the-art theoretical predictions of MSSM Higgs-boson properties.The results are interpreted in terms of the parameters governing the MSSM Higgs sector at lowest order,M A and tan β.While the higgsino mass parameter µhas a significant impact on the prospective discovery reach (and correspondingly the “LHC wedge”region),it is found that the discovery reach is rather stable with respect to variations of other supersymmetric parameters.Within the discovery region a determination of the masses of the heavy neutral Higgs bosons with an accuracy of 1–4%seems feasible.It is furthermore shown that Higgs-boson production in central exclusive diffractive channels can provide important information on the properties of the neutral MSSM Higgs bosons.1Introduction Signatures of an extended Higgs sector would provide unique evidence for physics beyond the Standard Model (SM).While models with an extended Higgs sector often give rise to a relatively light SM-like Higgs boson over a large part of their parameter space,detecting heavy states of anextended Higgs sector and studying their properties will be of utmost importance for revealing the underlying physics.2Dependence of the LHC discovery reach on the SUSY scenarioIn Ref.1the reach of the CMS experiment with 30or 60fb −1for the heavy neutral MSSM Higgs bosons has been analysed focusing on the channel b ¯bH/A,H/A →τ+τ−with the τ’s subsequently decaying to jets and/or leptons.The experimental analysis,yielding the number of events needed for a 5σdiscovery (depending on the mass of the Higgs boson)was performed with full CMS detector simulation and reconstruction for the final states of di-τ-lepton decays 2.The events for the signal and background processes were generated using PYTHIA 3.The experimental analysis has been combined with predictions for the Higgs-boson masses,produc-tion processes and decay channels obtained with the code FeynHiggs 4,taking into account all relevant higher-order corrections as well as possible decays of the heavy Higgs bosons into su-persymmetric particles.The results have been interpreted in terms of the two parameters tan β,the ratio of the vacuum expectation values of the two Higgs doublets of the MSSM,and M A ,the mass of the CP-odd Higgs boson.The variation of the discovery contours in the M A–tanβplane indicates the dependence of the“LHC wedge”region,i.e.the region in which only the light CP-even MSSM Higgs bosoncan be detected at the LHC at the5σlevel,on the details of the supersymmetric theory.See Ref.5for previous analyses.Figure1:Variation of the5σdiscovery contours obtained from the channel b¯bφ,φ→τ+τ−→jets in the m maxh benchmark scenario for different values ofµ(left plot).The right plot shows the result in the case where no decays of the heavy Higgs bosons into supersymmetric particles are taken into account.Fig.1shows the variation of the5σdiscovery contours obtained from the channel b¯bφ,φ→τ+τ−→jets in the m maxhbenchmark scenario6for various values of the higgsino mass parameter µ.The parameterµenters via higher-order corrections affecting in particular the bottom Yukawa coupling as well as via its kinematic effect in Higgs decays into charginos and neutralinos.Both effects can be seen in Fig.1.While the left plot shows the full result,in the right plot no decays of the Higgs bosons into supersymmetric particles are taken into account,so that the right plot purely displays the effect of higher-order parison of the two plots shows that in the region of large tanβ(corresponding to larger values of M A on the discovery contours)the dominant effect arises from higher-order corrections.For lower values of tanβ,on the other hand, the modification of the Higgs branching ratio as a consequence of decays into supersymmetric particles yields the dominant effect on the5σdiscovery contours.The largest shift in the5σdiscovery contours amounts up to about∆tanβ=10.The discovery contours have been shown to be rather stable with respect to the impact of other supersymmetric contributions1.Figure2:The statistical precision of the Higgs-boson mass measurement achievable from the channel b¯bφ,φ→τ+τ−→jets in the m maxhbenchmark scenario forµ=−200GeV(left)andµ=+200GeV(right)is showntogether with the5σdiscovery contour.The prospective accuracy of the mass measurement of the heavy neutral MSSM Higgs bosonsin the channel b¯bH/A,H/A→τ+τ−is analysed in Fig.2.The statistical accuracy of the mass measurement has been evaluated via∆Mφ√the M A–tanβplane of the MSSM(using the m maxbenchmark scenario6)for different luminos-hity scenarios.It is found that the CED Higgs-boson production channel can cover an interesting part of the MSSM parameter space at the5σlevel if the CED channel can be utilised at high in-stantaneous luminosity(which requires in particular to bring pile-up background under control). For an effective luminosity of600fb−1×2(see Ref.8)the discovery of a heavy CP-even Higgs boson with a mass of about140GeV will be possible for all values of tanβ.This is of particular interest in view of the“wedge region”left uncovered by the conventional search channels for heavy MSSM Higgs bosons(see above).In the high-tanβregion the discovery reach extends beyond M H=200GeV at the5-σlevel.If the Higgs bosons h and/or H have been detected in the conventional search channels,a lower statistical significance may be sufficient for the CED production of h and H,corresponding to a larger coverage in the M A–tanβplane.The CED Higgs-boson production channel will provide in this case important information on the Higgs-boson properties and may even allow a direct measurement of the Higgs-boson width8.AcknowledgmentsThe author gratefully acknowledges the collaboration with S.Gennai,S.Heinemeyer,A.Kali-nowski,V.A.Khoze,R.Kinnunen,S.Lehti,A.Nikitenko,M.G.Ryskin,W.J.Stirling and M.Tasevsky on the results presented in this paper.He also thanks the organisers of the42nd Rencontres de Moriond for the kind invitation and the pleasant atmosphere at the meeting.References1.S.Gennai,S.Heinemeyer,A.Kalinowski,R.Kinnunen,S.Lehti,A.Nikitenko andG.Weiglein,arXiv:0704.0619[hep-ph],to appear in Eur.Phys.J.C.2.CMS Physics Technical Design Report,Volume2.CERN/LHCC2006-021,see:cmsdoc.cern.ch/cms/cpt/tdr/.3.T.Sjostrand et al.,mun.135(2001)238.4.S.Heinemeyer,W.Hollik,G.Weiglein,mun.124(2000)76;hep-ph/0002213;Eur.Phys.J.C9(1999)343;G.Degrassi,S.Heinemeyer,W.Hollik, P.Slavich,G.Weiglein,Eur.Phys.J.C28(2003)133;M.Frank,T.Hahn,S.Heine-meyer,W.Hollik,H.Rzehak,G.Weiglein,JHEP02(2007)047;see:www.feynhiggs.de.5.ATLAS Collaboration,Detector and Physics Performance Technical Design Report,CERN/LHCC/99-15(1999);R.Kinnunen and A.Nikitenko,CMS note2003/006;J.Thomas,ATL-PHYS-2003-003;D.Cavalli and D.Negri,ATL-PHYS-2003-009;S.Ab-dullin et al.,Eur.Phys.J.C39S2(2005)41;M.Carena,S.Heinemeyer,C.Wagner andG.Weiglein,Eur.Phys.J.C45(2006)797.6.M.Carena,S.Heinemeyer,C.Wagner and G.Weiglein,Eur.Phys.J.C26(2003)601.7.V.A.Khoze,A.D.Martin and M.Ryskin,hep-ph/0006005;Eur.Phys.J.C19(2001)477[Erratum-ibid.C20(2001)599].8.S.Heinemeyer,V.A.Khoze,M.G.Ryskin,W.J.Stirling,M.Tasevsky and G.Weiglein,arXiv:0708.3052[hep-ph].9.A.Kaidalov,V.A.Khoze,A.D.Martin,M.Ryskin,Eur.Phys.J.C33(2004)261;M.Boonekamp,J.Cammin,vignac,R.Peschanski,C.Royon,Phys.Rev.D73 (2006)115011;J.Ellis,J.Lee,A.Pilaftsis,Phys.Rev.D70(2004)075010;Phys.Rev.D71(2005)075007;V.A.Khoze,A.D.Martin,M.Ryskin,Eur.Phys.J.C34(2004) 327;B.Cox,F.Loebinger and A.Pilkington,arXiv:0709.3035[hep-ph].。

Adsorption of heavy metal ion from aqueous single metal solutionby chemically modified sugarcane bagasseOsvaldo Karnitz Jr.a ,Leandro Vinicius Alves Gurgel a ,Ju´lio Ce ´sar Perin de Melo a ,Vagner Roberto Botaro a ,Taˆnia Ma ´rcia Sacramento Melo a ,Rossimiriam Pereira de Freitas Gil b ,Laurent Fre´de ´ric Gil a,*aDepartamento de Quı´mica,Instituto de Cie ˆncias Exatas e Biolo ´gicas,Universidade Federal de Ouro Preto,35400-000Ouro Preto,Minas Gerais,BrazilbDepartamento de Quı´mica,Instituto de Cie ˆncias Exatas,Universidade Federal de Minas Gerais,31270-901Belo Horizonte,Minas Gerais,BrazilReceived 22November 2005;received in revised form 28April 2006;accepted 2May 2006Available online 14July 2006AbstractThis work describes the preparation of new chelating materials derived from sugarcane bagasse for adsorption of heavy metal ions in aqueous solution.The first part of this report deals with the chemical modification of sugarcane bagasse with succinic anhydride.The carboxylic acid functions introduced into the material were used to anchor polyamines,which resulted in two yet unpublished modified sugarcane bagasse materials.The obtained materials were characterized by elemental analysis and infrared spectroscopy (IR).The sec-ond part of this reports features the comparative evaluation of the adsorption capacity of the modified sugarcane bagasse materials for Cu 2+,Cd 2+,and Pb 2+ions in aqueous single metal solution by classical titration.Adsorption isotherms were studied by the Freundlich and Langmuir models.Ó2006Elsevier Ltd.All rights reserved.Keywords:Adsorption;Modified sugarcane bagasse;Polyamines;Isotherm;Heavy metals1.IntroductionWater pollution is a major environmental problem faced by modern society (Baird,1995)that leads to eco-logical disequilibrium and health hazards (Kelter et al.,1997).Heavy metal ions such as copper,cadmium,lead,nickel,and chromium,often found in industrial waste-water,present acute toxicity to aquatic and terrestrial life,including humans.Thus,the discharge of effluents into the environment is a chief concern.The methods commonly used to remove toxic heavy metal from municipal and industrial wastewater are based on the adsorption of ions onto insoluble compounds and the separation of the sed-iments formed.Many efforts have been made recently tofind cheaper pollution control methods and materials(Panday et al.,1985;Ali and Bishtawi,1997;Acemiog˘lu and Alma,2001).The new material world trends point to the importance of using industrial and agricultural residues as production starting materials.Reusing and recycling these residues can minimize the environmental problems associated with their build-up and reduce the use of noble starting materi-als.This trend has contributed to the reconsideration of the use of traditional biomaterials such as natural lignocellu-losic fibers to substitute synthetic polymers,for example,since in many cases they have a better performance.Brazil is the world leading producer of sugarcane for both the alcohol and the sugar industries.These industries produce a large amount of sugarcane bagasse and although it is burned to produce energy for sugar mills,leftovers are still significant.Thus,on account of the importance of0960-8524/$-see front matter Ó2006Elsevier Ltd.All rights reserved.doi:10.1016/j.biortech.2006.05.013*Corresponding author.Tel.:+553135591717;fax:+55315511707.E-mail address:laurent@iceb.ufop.br (L.F.Gil).Bioresource Technology 98(2007)1291–1297bagasse sugar as an industrial waste,there is a great interest in developing chemical methods for recycling it.Sugarcane bagasse has around50%cellulose,27%polyoses,and23% lignin(Caraschi et al.,1996).These three biological poly-mers have many hydroxyl and/or phenolic functions that can be chemically reacted to produce materials with new properties(Xiao et al.,2001;Navarro et al.,1996).Despite the many studies of the chemical modification of cellulose published around the world in this area(Gurnani et al.,2003;Gellerested and Gatenholm,1999),only a few have investigated the modification of bagasse sugar(Krish-nan and Anirudhan,2002;Orlando et al.,2002).This work describes the preparation and the evaluation of new chelating materials from sugarcane bagasse to adsorb heavy metal ions in aqueous solution.In a prelimin-ary study,it has been chosen to study the adsorption of Cu2+,Cd2+,and Pb2+.Thefirst part of this work describes the modification of sugarcane bagasse with succinic an-hydride to introduce carboxylic functions to sugarcane bagasse and the chemical introduction of commercial linear polyamine via the formation of amide functions.It is well known that polyamines have powerful chelating properties, mainly towards ions such as Cu2+,Zn2+,and Pb2+(Bian-chi et al.,1991;Martell and Hancock,1996).The second part of this work evaluates the adsorption of Cu2+,Cd2+,and Pb2+onto three modified sugarcane bag-asses(MSBs)from aqueous single metal ion solutions by classical titration.The results were analyzed by the Lang-muir and Freundlich models(Ho et al.,2005).2.Methods2.1.MaterialsPolyamines ethylenediamine3and triethylenetetramine 4were used in this work.Succinic anhydride,1,3-diiso-propylcarbodiimide(DIC),and triethylenetetramine,from Aldrich,were used without purification.Ethylenediamine and dimethylformamide were distilled before use.Pyridine was refluxed with NaOH and distilled.2.2.Sugarcane bagasse preparationSugarcane bagasse was dried at100°C in an oven for approximately24h and nextfiber size was reduced to pow-der by milling with tungsten ring.The resulting material was sieved with a4-sieve system(10,30,45,and60mesh). Then,the material was washed with distilled water under stirring at65°C for1h and dried at100°C.Finally,it was washed anew in a sohxlet system with n-hexane/ ethanol(1:1)as solvent for4h.2.3.Synthesis of MSBs1and2Washed and dried sugarcane bagasse(5.02g)was trea-ted with succinic anhydride(12.56g)under pyridine reflux (120mL)for18h.The solid material wasfiltered,washed in sequence with1M solution of acetic acid in CH2Cl2, 0.1M solution of HCl,ethanol95%,distilled water,and finally with ethanol95%.After drying at100°C in an oven for30min and in a desiccator overnight,MSB1(7.699g) was obtained with a mass gain of53.4%.MSB2was obtained by treatment of1with saturated NaHCO3solu-tion for30min and afterwards byfiltering using sintered filter and washing with distilled water and ethanol.2.4.Synthesis of MSBs5and6The process used to introduce amine functions was the same as that used to prepare MSB5and6.MSB1was trea-ted with5equiv of1,3-diisopropylcarbodiimide(DIC)and 6equiv of polyamine in anhydrous DMF at room tempera-ture for22h under stirring.Afterfiltration,the materials were washed with DMF,a saturated solution of NaHCO3, distilled water,andfinally with ethanol.Next,they were dried at80°C in an oven for30min and in a desiccator overnight.2.5.Kinetic study of metal ion adsorption of MSBs2,5,and6Experiments with each material and metal ion were per-formed to determine the adsorption equilibrium time from 10to90min in10min intervals.The amount of100mg MSB was placed in a250-mL Erlenmeyer with100.0mL metal ion solution with concentration of200mg/L under stirring.The experiments were done at pHs5.8for Cu2+, 7.0for Cd2+,and6.2for Pb2+,optimal values to obtain the best adsorption.To adjust pH values,was added NaOH solution(0.01mol/L)into metal solutions with MSB.Afterfiltration,metal ion concentration was deter-mined by EDTA titration.2.6.pH study of metal ion adsorption of MSBs2,5,and6Experiments with each material and metal ion were per-formed to determine the effect of pH on ion adsorption.An amount of100mg MSB was placed into a250-mL Erlen-meyer with100.0mL of metal ion solution200mg/L under stirring.pH was calibrated with HCl or NaOH solutions (0.1–1.0mol/L).The reaction times used were30min (MSB2)or40min(MSB5and6)for Cu2+and Cd2+, and40min(MSB2)or50min(MSB5and6)for Pb2+. Metal ion concentration was determined afterfiltration by EDTA titration.No significative variation of pH was observed at the end of each experiment.2.7.Adsorption isotherms of MSBs2,5,and6Experiments were performed for each material and metal ion to determine adsorption isotherms.In each experiment,100mg of MSB was placed into a250-mL Erlenmeyer with100.0mL of metal ion solution in specific concentrations(between200mg/L and400mg/L)under stirring.Each experiment was performed at the pH of1292O.Karnitz Jr.et al./Bioresource Technology98(2007)1291–1297larger ion adsorption during the time necessary for equilib-rium (Tables 3and 4).After filtration,the metal ion con-centration was determined by EDTA titration.2.8.Characterization of the new obtained materials MSB 1,2,5,and 6were characterized by IR spectro-scopy in a Nicolet Impact 410equipment with KBr.Elemental analyses were accomplished in Analyzer 2400CHNS/O Perkin Elemer Series II.3.Results and discussion3.1.Synthesis of MSBs 1,2,5,and 6The synthesis route used to prepare MSBs 1,2,5,and 6are presented in Scheme 1.Prewashed sugarcane bagasse was succinylated for various periods of time.The degree of succinylation of the bagasse fibers was determined by measuring the quantity of acid function.The results are shown in Fig.1.The concentration of carboxylic functions per mg of bagasse was determined by retro titration.For this,MSB 1was initially treated with an excess solution of NaOH (0.01mol/L)for 30min.Soon afterwards the material was filtered and the obtained solution was titrated with an HCl solution (0.01mol/L).The highest degree of succinylation was reached after 18-h ing this reaction time,sugarcane bagasse was succinylated to pro-duce MSB 1,which presented a weight gain of 54%and a concentration of carboxylic acid function per mg of 3.83·10À6mol.Next,MSB 1was treated with a saturated NaHCO 3solution to produce MSB 2.Starting from MSB 1,two polyamines were introduced:ethylenediamine 3and triethylenetetramine 4.The method-ology used to introduce the polyamines was the same for the two MSBs 5and 6,as shown in Scheme 1.Concentra-tions of 2.4·10À6mol (5)and 2.6·10À6mol (6)of amine function per mg of material were determined by back titra-tion with excess HCl solution.The introduction of the amine functions was also verified by IR spectroscopy (Table 1)and elemental analysis (Table 2).3.2.Characterization of MSBs 1,5,and 6Characterization of carboxylated MSB 1was accom-plished by IR spectroscopy.The spectrum of unmodified sugarcane bagasse and MSB 1are presented in Fig.2.The spectrum of MSB 1displayed two strong bands at 1740and 1726cm À1in relation to that of unmodified sug-arcane bagasse.This demonstrated the presence of two types of carbonyl functions,one relative to carboxylic acid and another relative to the ester.The acid and ester IR bands indicate that succinic anhydride acylated theO.Karnitz Jr.et al./Bioresource Technology 98(2007)1291–12971293hydroxy group of bagasse to generate an ester bond with consequent release of a carboxylic acid functional group.The spectra of MSBs5and6(Figs.3and4,respectively) showed three new strong bands at1550–1650cmÀ1(see data in Table1)corresponding to the presence of amide and amine functions,and one band at1060cmÀ1 corresponding to C–N stretch.The bands at1635and 1650cmÀ1(Fig.3)correspond to the axial deformation of the carbonyl of the amide function and the angular deformation of the N–H bond of the amine function.The band at1575cmÀ1corresponds to the angular deformation of the N–H bond of the amide function.The band at 1159cmÀ1(Fig.4)corresponds to the asymmetric stretch of C–N–C bond.The main bands observed in all MSBs are presented in Table1.MSB elemental analysis data presented in Table2show a modification in the carbon and hydrogen composition of MSB1and a larger proportion of nitrogen as the number of amine functions in the used polyamine increases.3.3.Study of adsorption of Cu2+,Cd2+and Pb2+on MSBs2,5,and6The study of the MSB adsorption properties was accom-plished for each material and metal ion.A kinetic study and an adsorption study as a function of pH werefirst carried out.3.3.1.Effect of contact timeThe kinetic study of MSB2with Cu2+,Cd2+,and Pb2+ ions in aqueous solution is presented in Fig.5.Adsorption equilibrium was reached after20min for Cd2+ions.A time of30min was chosen for all studies of MSB2with Cd2+. The adsorption equilibrium times chosen for pH and con-centration dependent experiments are presented in Table3.Similar studies were accomplished for MSBs5and6for Cu2+,Cd2+,and Pb2+.The results are presented in Table3.3.3.2.pH EffectThe removal of metal ions from aqueous solutions by adsorption is dependent on solution pH as it affects adsor-Table1Main IR spectrum bands observed in MSBs1,5,and6MSB Main bands observed(cmÀ1)11740,172651745,1650,1635,1575,1423,1060 61738,1651,1635,1560,1400,1159,1060 Table2Elemental analysis of MSBs1,2,5,and6C(%)H(%)N(%) Sugarcane bagasse43.98 6.020.13MSB145.41 5.620.10MSB238.04 5.140.01MSB544.01 6.51 2.21MSB646.88 6.65 3.431294O.Karnitz Jr.et al./Bioresource Technology98(2007)1291–1297bent surface charge,the degree of ionization,and the species of adsorbates.The study of adsorption of Cd 2+,Cd 2+,and Pb 2+on MSB 2as a function of pH was accom-plished with the reaction times given in Table 3;the results are presented in Fig.6.The adsorption of the three metal ions increases with the increase in pH.Maximum removal of Cd 2+was observed above pH 6and in the case of Pb 2+and Cu 2,above pH 5and 5.5.Similar studies were accomplished for MSBs 5and 6and Cu 2+,Cd 2+and Pb 2+with similar results,as shown in Table 4.3.3.3.Adsorption isothermsThe Langmuir (Ho et al.,2005)(Eq.(1))and Freundlich (Eq.(2))isotherms were evaluated by adsorption experi-ments as a function of the initial metal ion concentrations in aqueous solution under equilibrium time and pH condi-tions given in Tables 3and 4.The results of each material and metal ion are presented in Fig.7(Langmuir)and Fig.8(Freundlich)and Table 5.c q ¼1Q max Âb þc Q maxð1Þln q ¼ln k þ1nln cð2ÞTable 3Adsorption equilibrium times of MSBs 2,5and 6MSB Equilibrium time (min)Cu 2+Cd 2+Pb 2+230304054040506404050Table 4pH of largest adsorption of MSBs 2,5and 6MSB pH of largest adsorption Cu 2+Cd 2+Pb 2+2 5.5–6.0 6.5–7.5 5.0–6.05 5.5–6.0 6.5–7.5 5.0–6.065.5–6.06.5–7.55.0–6.0O.Karnitz Jr.et al./Bioresource Technology 98(2007)1291–12971295where q(mg/g)is the concentration of adsorbed metal ions per gram of adsorbent,c(mg/L)is the concentration of metal ion in aqueous solution at equilibrium,Q max and b are the Langmuir equation parameters and k and n are the Freundlich equation parameters.High correlation coefficients of linearized Langmuir and Freundlich equations indicate that these models can explain metal ion adsorption by the materials satisfactorily. Therefore,both models explained metal ion adsorption by MSBs2,5,and6as can be observed in Table5,with the exception of the Freundlich model for Pb2+adsorption by MSB2.The Langmuir isotherm parameter Q max indicates the maximum adsorption capacity of the material,in other words,the adsorption of metal ions at high concentrations. It can be observed in Table5that MSB5presents the larg-est Cu2+adsorption capacity while MSB6adsorbs Cd2+ and Pb2+the ngmuir parameter b indicates the bond energy of the complexation reaction of the material with the metal ion.It can be observed that MSB2presents the largest bond energy for Cu2+and Cd2+,while three materials do not differ significantly for Pb2.The Freundlich isotherm parameter k indicates the adsorption capacity when the concentration of the metal ion in equilibrium is unitary,in our case1mg/L.This parameter is useful in the evaluation of the adsorption capacity of metal ions in dilute solutions,a case closer to the characteristics of industrial effluents.The values of k of MSB2and5are much similar for Cu2+and Cd2+ and much higher than that for MSB6.This shows the superiority of both materials in the adsorption of these metal ions in low concentrations.MSB5has a higher k value for Pb2+when compared to those of the other materials.These results were compared with those of Vaughan et al.(2001)for a commercial macroreticular chelating resin with thiol functional groups,Duolite GT-73.The Q max of Duolite GT-73for Cu2+,Cd2+,and Pb2+were 62mg/g,106mg/g,and122mg/g,respectively.Duolite GT-73exhibited Q max lower than those of MSBs(Table5).4.ConclusionsThrough a fast,effective,and cheap methodology,it was possible to devise a strategy to introduce chelating func-tions(carboxylic acid and amine)to sugarcane bagasse. Modified sugarcane bagasses presented a good adsorption capacity for Cu2+,Cd2+,and Pb2+ions with maximum adsorption capacity observed for MSB6.It has been dem-onstrated that metal ion adsorption efficiency is propor-tional to the number of amine functions introduced into the material.MSB2,which contained only carboxylate functions,showed an efficiency similar to that of MSB5, a material of much more complex synthesis. AcknowledgementsWe thank FAPEMIG forfinancial support,CAPES and UFOP.Table5The Langmuir and Freundlich parameters for Cu2+,Cd2+and Pb2+ adsorptionMetalion MSB Langmuir FreundlichQ max (mg/g)b(L/mg)r2k(mg/g)n r2Cu2+21140.431191.623.90.919351390.1730.999898.315.80.906161330.0140.992722.8 3.640.9635Cd2+21960.1030.993459.4 4.160.977351640.0680.995762.8 5.490.983463130.0040.9528 5.15 1.630.9856Pb2+21890.1100.994566.0 4.660.757951890.1250.999914724.510.98163130.1210.9994121 5.210.8771296O.Karnitz Jr.et al./Bioresource Technology98(2007)1291–1297ReferencesAcemiog˘lu,B.,Alma,M.H.,2001.Equilibrium studies on adsorption of Cu(II)from aqueous solution onto cellulose.Journal of Colloid and Interface Science243,81–83.Ali,A.A.,Bishtawi,R.,1997.Removal of lead and nickel ions using zeolite tuff.Journal of Chemical Technology and Biotechnology69, 27–34.Baird,C.,1995.Environmental Chemistry.W.H.Freeman and Company, New York.Bianchi,A.,Micheloni,M.,Paoletti,P.,1991.Thermodynamic aspects of the polyazacycloalkane complexes with cations and anions.Coordi-nation Chemistry Reviews110,17–113.Caraschi,J.C.,Campana,S.P.,Curvelo, A.A.S.,1996.Preparac¸a˜o e Caracterizac¸a˜o de Polpas Obtidas a Partir de Bagac¸o de Cana de Ac¸u´car.Polı´meros:Cieˆncia e Tecnologia3,24–29.Gellerested,F.,Gatenholm,P.,1999.Surface properties of lignocellulosic fibers bearing carboxylic groups.Cellulose6,103–121.Gurnani,V.,Singh,A.K.,Venkataramani,B.,2003.2,3-Dihydroxypyri-dine-loaded cellulose:a new macromolecular chelator for metal enrichment prior to their determination by atomic absorption spectrometry.Analytical and Bioanalytical Chemistry377,1079–1086. Ho,Y.S.,Chiu,W.T.,Wang,C.C.,2005.Regression analysis for the sorption isotherms of basic dyes on sugarcane dust.Bioresource Technology96,1285–1291.Kelter,P.B.,Grundman,J.,Hage,D.S.,Carr,J.D.,Castro-Acun˜a,C.M., 1997.A discussion of water pollution in the United States and Mexico;with High School Laboratory Activities for the analysis of lead, atrazine,and nitrate.Journal of Chemical Education74,1413–1421. Krishnan,K.A.,Anirudhan,T.S.,2002.Removal of mercury(II)from aqueous solutions and chlor-alkali industry effluent by steam activated and sulphurised activated carbons prepared from bagasse pith:kinetics and equilibrium studies.Journal of Hazardous Materials92,161–183. Martell, A.E.,Hancock,R.D.,1996.Metal complexes in aqueous solutions.Plenum,New York.Navarro,R.R.,Sumi,K.,Fujii,N.,Matsumura,M.,1996.Mercury removal from wastewater using porous cellulose carrier modified with polyethyleneimine.Water Research30,2488–2494.Orlando,U.S.,Baes,A.U.,Nishijima,W.,Okada,M.,2002.Preparation of chelating agents from sugarcane bagasse by microwave radiation as an alternative ecologically benign procedure.Green Chemistry4,555–557.Panday,K.K.,Gur,P.,Singh,V.N.,1985.Copper(II)removal from aqueous solutions byfly ash.Water Research19,869–873. Vaughan,T.,Seo,C.W.,Marshall,W.E.,2001.Removal of selected metal ions from aqueous solution using modified corncobs.Bioresource Technology78,133–139.Xiao,B.,Sun,X.F.,Sun,R.,2001.The chemical modification of lignins with succinic anhydride in aqueous systems.Polymer Degradation and Stability71,223–231.O.Karnitz Jr.et al./Bioresource Technology98(2007)1291–12971297。

a rXiv:h ep-e x /5596v13Ma y25Measurement of the Higgs Boson Mass with a Linear e +e −Collider P .Garcia-Abia,CIEMAT,Madrid W.Lohmann and A.Raspereza DESY February 5,2008Abstract The potential of a linear e +e −collider operated at a centre-of-mass energy of 350GeV is studied for the measurement of the Higgs boson mass.An integrated luminosity of 500fb −1is assumed.For Higgs boson masses of 120,150and 180GeV the uncertainty on the Higgs boson mass measurement is estimated to be 40,65and 70MeV ,re-spectively.The effects of beam related systematics,namely a bias in the beam energy measurement,the beam energy spread and the luminosity spectrum due to beamstrahlung,on the precision of the Higgs boson mass measurement are investigated.In order to keep the systematic uncertainty on the Higgs boson mass well below thelevel of the statistical error,the beam energy measurement must be controlled with a relative precision better than 10−4.1IntroductionIn the Standard Model [1]particles acquire mass due to spontaneous sym-metry breaking by introducing a doublet of complex scalar fields.This so called Higgs mechanism [2]leads to one scalar particle,the Higgs boson.The mass of the Higgs boson is a free parameter of the Standard Model and of fundamental nature.If the Higgs boson exists,the Large Hadron Collider at CERN will be able to discover it [3].Precision measurements of the Higgs boson parameters and the exploration of the complete Higgs boson profile will be one of the central tasks at a future linear e +e −collider.In this article we study the potential of a future e +e −collider for the measurement of the mass of a relatively light Higgs boson,in the massrange from120to180GeV,and investigate possible systematic effects in-fluencing the precision of this measurement.The analysis presented ex-tends previous studies on the measurement of the mass of a light Higgs boson[4]and complements recent studies on the determination of reso-nance parameters of the Higgs boson with the mass in the range from200 to320GeV at a future linear e+e−collider[5].2Experimental Conditions and Detector Simu-lationsThe study is performed for a linear collider operated at a centre-of-mass energy,√p t=7·10−5·p t,(1) where p t is the transverse momentum in GeV/c.The energy resolutions of the electromagnetic and hadron calorimeters are:σE e√Eh =50%E h⊕4%,(2)where E e and E h are the energies of electrons and hadrons in GeV.Thepolar angular coverage of the central tracker maintaining the resolution is|cosθ|<0.85,above this range the tracking resolution deteriorates.The electromagnetic and hadron calorimeters cover|cosθ|<0.996maintain-ing the resolution over the whole angular range.The simulation of the detector is done using the SIMDET[7]package.The event reconstruction is done in terms of particleflow objects.First,tracks are measured with the tracking system and associated to calorime-ter clusters to define charged particleflow objects of electrons,muons and charged hadrons.Since the momentum measurement by the tracking sys-tem is much more accurate than the angular and energy measurements with calorimeters,the tracking information is used for the determination of the four-momentum of charged particles.Calorimetric clusters with no associated track are regarded as neutral particleflow objects originatingfrom photons and neutral hadrons.Measurements of the four-momentum of neutral objects are solely based on the calorimetric information.3Physics Processes√At a centre-of-mass energy oftopology150GeVZH→ℓ+ℓ−q¯q,ZH→ℓ+ℓ−gg8.80.06 ZH→q¯q q′¯q′,ZH→q¯q gg91.90.62 ZH→ℓ+ℓ−WW,W→q¯q′0.6 2.6ZH→q¯q WW,W→q¯q′ 6.026.6 ZH→ℓ+ℓ−ZZ,Z→q¯q0.080.17 ZH→q¯q ZZ,Z→q¯q0.82 1.73123.7s=350GeV.Also given is the total cross section for e+e−→ZH.The cross sections are calculated with PYTHIA taking into account initial state radiation.For background estimations events are generated with PYTHIA for the processes e+e−→q¯q(γ),e+e−→W+W−,e+e−→Z(γ∗)Z(γ∗)and e+e−→γ∗γ∗e+e−→f¯fe+e−.Six fermionfinal states resulting from the triple gauge boson production are generated with the WHIZARD package[9].The cross sections of the main background reactions are given in Table2.The numbers of events generated for each background channel as well as the number of generated signal events correspond to an integrated luminosity of500fb−1.Initial state radiation is simulated by PYTHIA.Beamstrahlung is taken into account using the CIRCE program[10].background process events4.0×1062.7×1041.3×1041.0×10313.20.48sinθ.(3)The resolutions of the jet energies and angular measurements are obtained from a Monte Carlo study using the sub-detector resolutions from Equa-tions(1)and(2).They are parameterized as:σE/E=30%E,σθ=15mrad,σφ=σθsignal and background distributions.The shape of the signal distribution is derived from a high statistics Monte Carlo sample of signal events andkeptfix in thefit.Free parameters are the peak value and the normalisa-tion factor of the signal distribution.4.1The ZH→ℓ+ℓ−q¯q and ZH→q¯q q′¯q′Final StatesThesefinal states are characterized by two isolated leptons and two jetsor by four jets and have the full energy deposited in the detector.Hence, events where the total energy visible in the detector is less that80%of thecentre-of-mass energy are rejected.Global event characteristics are used for the signal selection.For the channel ZH→ℓ+ℓ−q¯q,the number of reconstructed particlesmust be greater than20,the event thrust,T,must be less than0.85and the absolute value of the cosine of the polar angle of the thrust vector,cosθT,must be less than0.9.Electrons are identified as energy deposits in the electromagnetic calorimeter whose shape is compatible with the expecta-tion for an electromagnetic shower and with a matched track in the centraltracker.The measured track momentum and shower energy must be in agreement within5%and the shower leakage into the hadron calorimetermust be less than2GeV.Muons are tracks pointing to energy depositsin the calorimeters which are consistent with the expectation for a mini-mum ionizing particle.A pair of electrons or muons with opposite chargeis required.Both electrons and muons must have momenta larger than 10GeV/c and fulfill the polar angle cut|cosθℓ|<0.9.Leptons must satisfy isolation criteria,meaning that there are no other particles reconstructedwithin a15o cone with respect to the lepton momentum vector.The in-variant mass of a pair of leptons must be compatible with the mass of theZ boson within10GeV.These criteria reduce the backgrounds listed in Table2in the selected sample to the level of a few%with the exception of the process e+e−→ZZ.A cut on the polar angle of the momentum vector of the di-electron or di-muon system,|cosθℓℓ|<0.9,further suppresses the ZZ background.The signal selection efficiency is about45%.All recon-structed particles,except the two isolated leptons,are grouped into two jets using the Durham[11]jet clustering algorithm.Event selection for the ZH→q¯q q′¯q′channel is performed by requiringthe number of reconstructed particles to be larger than40,T<0.85and |cosθT|<0.8.No isolated leptons with an energy greater than10GeV are allowed.Reconstructed particles are grouped into four jets using the Durham jet clustering algorithm.Events are retained if the jet resolution parameter,for which the event is resolved from the four-to three-jet topol-ogy,y34,fulfill the relation log(y34)>−5.The selected events of bothfinal states are subject to a kinematicfit[12] imposing energy and momentum conservation.The kinematicfit is per-formed by varying the lepton momenta and angles within their resolu-tions given by Equations(1)and(3),respectively.The jet energies and an-gles are varied within the corresponding resolutions given by Equations(4).For events selected as ZH→ℓ+ℓ−q¯q,energy and momentum conserva-tion results in four constraints(4Cfit).Since the experimental resolutionin the invariant mass of the di-lepton system is much smaller than the nat-ural width of the Z boson,no constraint is applied in the kinematicfit to force the di-lepton mass to m Z.The di-jet invariant mass spectra after the4Cfit are shown in Figure1for m H=120GeV and150GeV,respectively. Clear signals are seen on top of the remaining smooth background frome+e−→ZZ.Also shown are the contributions from H→WW and H→ZZ decays to the signal.These are negligible for m H=120GeV but amount to 62%and5%,respectively,of the signal for m H=150GeV.The masses obtained from thefits equal the generated Higgs boson masses and have errors of85MeV for m H=120GeV and100MeV for m H =150GeV.For the4-jetfinal states,in addition to the four constraints from energy and momentum conservation,the invariant mass of the two jets assigned to the Z boson decay is constrained to m Z.Hence,a5Cfit is performed for all possible di-jet pairings.The pairing with the minimalχ2is chosen. In addition,thisχ2must be less than70.The signal selection efficiency is about25%,however the remaining event sample contains consider-able background from e+e−→ZZ,e+e−→W+W−and e+e−→q¯q(γ).The signal-to-background ratio is enhanced using the identification of b-quark jets.The ZVTOP[13]topological vertexfinder adapted for the pixel micro-vertex detector[6]is used to search for secondary vertices inside jets and determine mass,momentum and decay length of the vertex.In addition, the impact parameter joint probability[14]and the two highest impact pa-rameter significances are used as input into neural networks trained with jets containing no,one and more than one secondary vertices.A jet b-tag variable is defined[15]as function of the neural network output x asf b(x)B(x)=boson mass is performed.As an example,the di-jet invariant mass distri-bution and thefitted function of the signal is shown in Figure3.The results for the Higgs boson masses are equal to the generated masses. The statistical errors are45MeV at m H=120GeV and170MeV at m H=150GeV.4.2The ZH→ℓ+ℓ−WW and ZH→q¯q WW Final StatesWe consider W-boson decays into two quarks,hence the topologies ofthesefinal states are two isolated leptons accompanied by four jets or six jets,respectively.The requirements for electron and muon identificationare the same as in the previous section.Although event selection is opti-mized specifically for the ZH→ℓ+ℓ−WW and ZH→q¯q WWfinal states, contributions from the ZH→ℓ+ℓ−ZZ and ZH→q¯q ZZ channels are alsotaken into account.Events are selected with an energy deposited in the detector of morethan80%of the centre-of-mass energy and a number of the reconstructed particles larger than40.Events of thefinal state ZH→ℓ+ℓ−WW must contain a pair of isolatedelectrons or muons with opposite charges.Furthermore,the event thrust and the polar angle of the thrust vector are used to suppress the dominant background from the WW and ZZfinal states.The values of the cuts areT<0.95and|cosθT|<0.95.Since the two leptons of ZH→ℓ+ℓ−WW originate from the Z decay,their invariant mass is required to be equalwithin10GeV to m Z.A cut on the polar angle of the di-lepton momentum vector,|cosθℓℓ|<0.9,further suppresses the ZZ background.Tracks and calorimetric energy deposits not stemming from the leptons are grouped into four jets using the Durham algorithm.The jet resolution parameter y34must satisfy log(y34)>−6.0.Then a4C kinematicfit is performed imposing energy and momentumconservation.Only events for which theχ2of the4Cfit is less than50are retained in the selected sample.The signal selection efficiency amounts to50%at m H=150GeV and60%at m H=180GeV.The4-jet invariant mass distributions after the kinematicfit are shown in Figure4for m H= 150GeV and180GeV.Thefit of the mass spectra in Figure4again results in mass values for the Higgs boson equal to the generated ones.The uncertainties of the masses amount to90and80MeV for m H=150GeV and m H=180GeV, respectively.The small background in this channel comes mainly from the semilep-tonic decays of pair produced Z bosons and triple gauge boson produc-tion,ZWW,with a leptonic Z decay.Events of the process ZH→ℓ+ℓ−ZZ constitute13%and6%of the signal in the selected sample for m H=150 and180GeV,respectively.The ZH→q¯q WW channel is selected by requiring T<0.9and|cosθT|<0.95.There must be no isolated leptons with an energy greater than 10GeV.The reconstructed particles are grouped into six jets using Durham jet algorithm.The jet resolution parameter,for which an event is resolved from the6-to5-jet topology,y56,must satisfy log(y56)>−8.Then a likeli-hood discriminant,L HZ,is defined using as input the number of particles reconstructed in an event,the polar angle of the thrust vector and the jet resolution parameters y34and y56.Events are accepted when the value ofthis discriminant is larger than0.9.As an example,Figure5shows the dis-tribution of L HZ for the signal events for m H=180GeV and the backgroundprocesses.The six jets are now grouped in three di-jet pairs following crite-ria which depend on the mass of the Higgs boson.For m H<2m W usually only one W is expected to be on the mass shell,while the other is producedwith a mass close to the difference between m H and m W.The quantity χ2=(m ij−m Z)2/σ2Z+(m kl−m W)2/σ2W+(m mn−m klmn+m W)2/σ2W∗is calculated for all possible di-jet combinations,where m ij is the invariantmass of the two jets assigned to the Z boson,m kl the invariant mass of two jets assigned to the on-shell W boson,m mn the invariant mass of two jets assigned to the off-shell W boson and m klmn the invariant mass of thefour jets assigned to decay H→WW∗.The quantitiesσ2Z,σ2W andσ2W∗are obtained from Monte Carlo studies as the convolution of the bosonicwidths and the mass resolutions and are estimated to be6,9and15GeV, respectively.For m H>2m W both W bosons are on shell.Hence all di-jet combinations are taken and the quantityχ2=(m ij−m Z)2/σ2Z+(m kl−m W)2/σ2W+(m mn−m W)2/σ2Wis calculated.The jet pairing with the smallest value ofχ2is chosen and subject of a kinematicfit imposing energy-momentum conservation andconstraining the mass of the two jets assigned to the Z boson to m Z.Events are selected into thefinal sample if theχ2of the5Cfit is less than30.In addition,thefitted mass of the jets originating from the on-shell W decaymust be equal to m W within20GeV in the event sample selected for m H= 150GeV.For m H=180GeV,the sum and the difference of thefitted masses of the two jet pairs assigned to a W decay must be between125GeV and185GeV and−20and20GeV,respectively.The signal selection efficiency amounts to about20%.The sample selected for m H=150GeV also contains5%signal from the ZH→q¯q q′¯q′final state.The distribution of the invariant mass of the4-jet system is shown in Figure6for m H=150GeV and180GeV,respectively.From thefit ap-proximating the signal by a Gaussian the uncertainties of the masses are 100MeV and150MeV for m H=150GeV and180GeV,respectively.The background in this channel originates from e+e−→W+W−,e+e−→ZZ and e+e−→q¯q(γ)final states,and from triple gauge boson production processes.Events of the process ZH→q¯q ZZ constitute9%and5%of thesignal in the selected sample for m H=150and180GeV,respectively.4.3Combined ResultsTable3summarizes the statistical accuracy on the determination of m H for the differentfinal states and their combination.It should be noted that considerable overlap exists in the selected samples of the ZH→ℓ+ℓ−q¯q and ZH→ℓ+ℓ−WW channels and of the ZH→q¯q q′¯q′and ZH→q¯q WW channels.Hence,the combination is performed only for the non-overlapping topologies which gives a minimal combined error on the Higgs boson mass.This is done using the formula:1,∆2i(m H)where∆is the combined error,whereas∆i is the error obtained in the i th channel.Decay mode150ZH→ℓ+ℓ−q¯q10045–ZH→ℓ+ℓ−WW90–1504070Table3:Uncertainties on the determination of the Higgs boson mass for m H=120,150and180GeV.The ZH→ℓ+ℓ−WW and ZH→q¯q WW chan-nels are used for the combination at m H=150GeV.5Beam Related Systematic EffectsWe have investigated the effect of a bias in the beam energy measurement, of the beam energy spread and of an uncertainty in the differential lumi-nosity spectrum on the measurement of the Higgs boson mass.The impact of a bias in the beam energy measurement is estimated bygenerating signal samples with both positron and electron beam energies√shifted with respect to the nominal value ofs=350GeV,the shift in the beam energy is expected to result in a shift in the measured Higgs boson mass.As an example Figure7shows the distributions offitted values of m H in the ZH→ℓ+ℓ−q¯q channel for shifts in the beam energies of+25MeV, zero MeV and−25MeV.In each of the three considered cases the distribu-tion of m H is obtained from200statistically independent signal samples.The shift obtained in thefit of m H corresponds roughly to the shift of the beam energy with opposite sign.In the range of beam energy shifts from -100to100MeV the shift in the Higgs boson mass is found to depend lin-early on the shift in the beam energy:δm H=−α·δE b,(5) withα=0.85for the ZH→q¯q q′¯q′channel,0.80for the ZH→q¯q WW chan-nel,and1.04for the ZH→ℓ+ℓ−q¯q and ZH→ℓ+ℓ−WW channels.Hence, in order to keep the systematic bias in m H well below its statistical error, the beam energy measurement must be controlled with a precision better than10−4.To estimate the impact of a beam energy spread,a Gaussian distribu-tion of the beam energy has been used for the generation of signal events. As an example,Figure8shows the reconstructed Higgs boson mass spec-trum for a sample of ZH→q¯q q′¯q′events for a1%energy spread for both electron and positron beams and the same distribution for afix beam en-√ergy ofin Figure9for nominal values of the parameters a i and for the parameter a0shifted by±10%from its nominal value.Figure10presents the corre-sponding Higgs boson mass spectra a the sample of ZH→ℓ+ℓ−q¯q events. An uncertainty of10%in the determination of the parameters a0results in a systematic uncertainty of about10MeV on the Higgs boson mass in the ZH→ℓ+ℓ−q¯q and ZH→q¯q q′¯q′channels.The same result is obtained for the other parameters.The uncertainty is reduced to about1MeV if the parameters a i are measured with an accuracy of1%.The same result is obtained for the study of the ZH→ℓ+ℓ−WW and ZH→q¯q WW channels. 6ConclusionThe potential of the future linear e+e−collider for the measurement of the Higgs boson mass is evaluated.Assuming an integrated luminosity of500 fb−1,the Higgs boson mass can be measured with a statistical accuracy ranging from40MeV to70MeV for m H between120GeV and180GeV.In order to keep the systematic uncertainty due to a bias of the beam energy measurement well below the statistical uncertainty,the beam energy mea-surement has to be controlled with a precision better than10−4.Under operational conditions envisaged for the TESLA machine,the beam en-ergy spread and uncertainty in the differential luminosity spectrum are found to have negligible effect on the Higgs boson mass measurement.7AcknowledgmentsWe would like to thank Prof.K.Desch for many helpful discussions and his continuous interest and support.References[1]S.L.Glashow,Nucl.Phys.22(1961)579;S.Weinberg,Phys.Rev.Lett.19(1967)1264;A.Salam,Elementary Particle Theory,edited by N.Svartholm(Almqvist and Wiksell,Stockholm,1968),p.367. [2]P.W.Higgs,Phys.Lett.12(1964)132,Phys.Rev.Lett.13(1964)508andPhys.Rev.145(1966)1156;F.Englert and R.Brout,Phys.Rev.Lett.13 (1964)321;G.S.Guralnik,C.R.Hagen and T.W.B.Kibble,Phys.Rev.Lett.13(1964)585.[3]ATLAS Collaboration,”ATLAS:Detector and Physics Performance Tech-nical Design Report,Volume2”,CERN-LHCC-99-15,ATLAS-TDR-15 (1999);CMS Collaboration,”CMS Technical Proposal”,CERN/LHCC/94-38 (1994).[4]P.Garcia-Abia and W.Lohmann,EPJdirect C2(2000)1,A.Juste,hep-ex/9912041.[5]N.Meyer and K.Desch,Eur.Phys.J.C35(2004)171.[6]F.Richard,J.R.Schneider,D.Trines and A.Wagner,”TESLA:TechnicalDesign Report”,DESY2001-01,ECFA2001-209,TESLA Report2001-023,TESLA-FEL2001-05(2001).[7]SIMDET V3.2,M.Pohl and H.J.Schreiber,DESY-99-030(1999).[8]PYTHIA V6.136,T.Sj¨ostrand,m.82(1994)74.[9]W.Kilian,WHIZARD1.24,LC Note LC-TOOL-2001-039(2001).[10]CIRCE V6,T.Ohl,m.94(1996)53.[11]S.Catani et al.,Phys.Lett.B269(1991)432;S.Bethke et al.,Nucl.Phys.B370(1992)310.[12]V.Blobel,”Constrained Least Squares and Error Propagation”,Ham-burg(1997).[13]T.Kuhl,Nucl.Instr.and Meth.A511(2003)221;D.Jackson,Nucl.Instr.and Meth.A388(1997)247.[14]R.Barate et al.,Phys.Lett.B401(1997)150.[15]K.Desch et al.,LC Note LC-PHSM-2004-006(2004).[16]K.M¨onig,LC Note LC-PHSM-2000-060(200).050100150200Mass of 4C fit [GeV ]E v e n t s /0.5G e V 0255075100Mass of 4C fit [GeV ]E v e n t s /0.5G e V Figure 1:The di-jet invariant mass from the ZH →ℓ+ℓ−q¯q final state after a 4C kinematic fit for m H =120GeV (top)and 150GeV (bottom).0500100015002000100110120130140150Mass of 5C fit [GeV ]E v e n t s / G e V without b-tagwith b-tagFigure 2:The distribution of the invariant mass of the two jets assigned to the Higgs boson decay in the ZH →q¯q q ′¯q ′final state without requirement on the b-tag and after requiring the values of the b-tag of two jets to be larger than 0.2.02505007501000Mass of 5C fit [GeV ]E v e n t s / G e V Figure 3:The invariant mass of the two jets assigned to the Higgs boson decay in the ZH →q¯q q ′¯q ′final state after the 5C kinematic fit for m H =020406080Mass of 4C fit [GeV ]E v e n t s /0.5G e V 020406080Mass of 4C fit [GeV ]E v e n t s /0.5G e V Figure 4:The 4-jet invariant mass from the ZH →ℓ+ℓ−WW final state after a 4C kinematic fit for m H =150GeV (top)and 180GeV (bottom).101010101010L HZE v e n t s / 0.05Figure 5:The distributions of the signal likelihood used to select H →WW →6-jet final states for m H =180GeV .Solid,dashed and dotted lines represent the background processes,ZH →q¯q WW and ZH →q¯q ZZ signals.The vertical line indicates the cut imposed on this quantity.0100200Mass of 5C fit [GeV ]E v e n t s /G e V 050100150200Mass of 5C fit [GeV ]E v e n t s /G e V Figure 6:The four jet invariant mass from the ZH →q¯q WW final state after a 5C kinematic fit for m H =150GeV (top)and m H =180GeV (bottom).m H [GeV ]E n t r i e s /0.04 G e V Figure 7:The spectrum of the fitted values of the Higgs boson mass as obtained from 200independent signal samples for the case when both electron and positron beam energies are overestimated by 25MeV (dotted histogram),when they are underestimated by 25MeV (dashed histogram)and when no shifts are introduced to the beam energies (solidhistogram).Mass of 5C fit [GeV ]E v e n t s / G e V Figure 8:Reconstructed Higgs boson mass spectrum in the sample of the ZH →q¯q q ′¯q ′events for the case of monochromatic beams (solid his-togram)and for the case of 1%Gaussian energy spread for both electron and positron beams (dashed histogram).Figure 9:The beam energy spectrum after beamstrahlung for nominal pa-rameters a i at √。