Hadron masses and power corrections to event shapes

核能专业英语试题（A卷）考试时间：90分钟姓名：班级：学号：The most elementary concept is that matter is composed of individual particles – atoms – that retain their identity as elements in ordinary physical and chemical interactions. Thus a collection of helium atoms that forms a gas has a total weight that is the sum of the weights of the individual atoms. Also, when two elements combine to form a compound, the total weight of the new substance is the sum of the origin elements.1.公认的物质的概念是：物质是由单个粒子——原子组成，在普通的化学和物理反应中原子保持了元素的特性。

因此，因此一团由氦原子组成的气体的重量就是其中每一个原子重量的总和。

同样，当两种元素结合成化合物时，新物质的总重量是原先的元素的质量之和。

Bohr assumed that the atom consists of a single electron moving at constant speed in a circular orbit about a nucleus --the proton--as sketched in Fig. X.X. Each particle has an electric charge of l.6×l0-l9 coulombs, but the proton has a mass that is 1836 times that of the electron.2.波尔假设（氢）原子由一个单独的电子绕着一个核子——质子，以圆形轨道作恒定速度的移动——见图X.X，每个粒子有l.6×l0-l9库伦的电量，质子的质量是电子质量的1836倍。

小学下册英语第三单元自测题英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The children are ______ in the playground. (laughing)2.My mom loves to plant ______ in the garden.3.Plants can produce _______ for us to eat.4.Certain plants can ______ (促进) sustainable practices.5. A dilute solution contains a small amount of ______.6.I like to explore the ______ (海滩) and look for beautiful ______ (贝壳).7.We have a ______ in our backyard.8.What is the name of the famous American author known for "Beloved"?A. Toni MorrisonB. Alice WalkerC. Zora Neale HurstonD. Maya AngelouA9.What is the main purpose of a compass?A. To measure distanceB. To find directionC. To show timeD. To calculate speed10.The main component of the human body is ______.11.What is the name of the famous canyon in Arizona?A. Grand CanyonB. Antelope CanyonC. Zion CanyonD. Bryce CanyonA Grand Canyon12.What is the first letter of the alphabet?A. AB. BC. CD. D13.I have a _____ (plan) for the weekend.14.What do you call the study of weather?A. BiologyB. MeteorologyC. AstronomyD. GeologyB15.The _______ plays a role in the life cycle of plants.16.What do we call a girl who plays sports?A. PlayerB. AthleteC. DancerD. SingerB17.What do you call a large body of saltwater?A. LakeB. SeaC. OceanD. River18.What do we call the act of drawing a conclusion based on evidence?A. InferenceB. InductionC. DeductionD. AnalysisA19. A _____ (小丑鱼) swims in the sea.20.The ______ (海豹) barks loudly on the rocks.21._____ (gardening) teaches responsibility.22.What is the name of the large African animal with a long trunk?A. RhinoB. HippopotamusC. ElephantD. Giraffe23.What is the name of the current U.S. president?A. George W. BushB. Barack ObamaC. Joe BidenD. Donald TrumpC24.Hydrogen bonds are weak attractions between _____ (polar molecules).25.The __________ were ancient monuments built by the Mayans. (金字塔)26.What is the capital of Finland?A. HelsinkiB. StockholmC. OsloD. TallinnA27.What is the hardest natural substance on Earth?A. GoldB. IronC. DiamondD. QuartzC28.The _______ (Protestant Reformation) began with Martin Luther’s 95 Theses.29.The ______ helps with the digestion of food in the stomach.30.What is the name of the largest volcano in the solar system?A. Olympus MonsB. Mount EverestC. Mauna KeaD. Kilauea31. A ______ is a tool used for measuring temperature.32.小鸟) builds its nest in the tree. The ___33.The ______ (雨水收集) can benefit garden plants.34.My friend loves __________ (探索新的领域).35.My mom enjoys __________ (参加) local events.36. A prism can separate light into different ______.37.The ______ (种植方式) can vary based on the plant type.38.An acid has a pH value less than _______.39.The chameleon can blend into its _________ (环境).40.在中国，________ (traditions) 如端午节和中秋节有着深厚的文化意义。

深圳2024年小学六年级下册英语第五单元暑期作业(含答案)考试时间：90分钟（总分:100）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题共100分)1. 填空题：I want to _______ my dreams come true.2. ts can ______ (净化) air pollutants. 填空题：Some pla3. 听力填空题：I think everyone should have a hobby. Hobbies help us relax and express ourselves. My favorite hobby is __________, and I find it very enjoyable.4. 听力题：A molecule of carbon dioxide consists of one carbon and _______ oxygen atoms.5. 选择题：Which instrument is known for its strings and bow?A. PianoB. ViolinC. FluteD. Trumpet答案: B6. 选择题：What is the capital of Qatar?A. DohaB. Al RayyanC. Al KhorD. Lusail7. 听力题：She has a ________ (passion) for art.My uncle gave me a toy ____ that spins. (玩具名称)9. 选择题：What do you call a person who studies the mind?A. PsychologistB. PsychiatristC. TherapistD. All of the above答案:D10. 填空题：The ancient Romans were known for their _____ and engineering.11. 听力题：I like to _____ (跳) rope.12. 选择题：What do you call the process of water falling from the sky?A. EvaporationB. CondensationC. PrecipitationD. Transpiration答案:C13. 听力题：The __________ is a large area of land that consists of sand.14. 听力题：A _______ is a measure of how much solute is present relative to the solvent.15. 填空题：I enjoy exploring new _______ (领域) of knowledge. There’s always something new to learn.16. 填空题：The coach inspires the _____ (运动员) to do their best.17. 听力题：The chemical formula for ammonium thiocyanate is _______.18. 填空题：My _______ (猫) loves to chase after strings.The chemical formula for sodium sulfate is ______.20. 填空题：A __________ day is great for going to the park. (晴朗的)21. 填空题：The first modern democracy was established in ________ (雅典).22. 填空题：My friend has a ________ that can sing.23. 填空题：I can ______ (明确) my goals and aspirations.24. 听力题：The flowers are ______ (beautiful).25. 听力题：A chemical reaction can release _____ as a product.26. 选择题：Which country is known for the kangaroo?A. CanadaB. AustraliaC. IndiaD. South Africa答案:B27. 填空题：The __________ (历史的真实) can be difficult to face.28. 听力题：The puppy is ___ around. (running)29. 选择题：What do we call the place where you can see wild animals?A. ZooB. ParkC. FarmD. Aquarium答案: A30. 选择题：What do you use to measure time?A. ScaleB. ClockC. RulerD. Thermometer31. 选择题：What do we call the study of the heart and its functions?A. CardiologyB. NeurologyC. HematologyD. Endocrinology32. 选择题：What is the capital city of South Africa?A. PretoriaB. Cape TownC. JohannesburgD. Durban33. 填空题：The pumpkin grows on a ______.34. 选择题：What is the term for a baby cow?A. CalfB. FoalC. LambD. Kid答案:A35. 选择题：What is the first month of the year?A. JanuaryB. FebruaryC. MarchD. April答案:A36. 填空题：A _____ (54) is a large group of islands.37. 填空题：We have a ______ (美丽的) garden full of flowers.38. 听力题：A ____ can be found in many farms and says "moo."I saw a _______ (小鳄鱼) at the zoo.40. 听力题：My dad _____ a big dinner on Sundays. (cooks)41. 听力题：Astronomers study ______ to learn about the universe.42. 听力题：The butterfly is _____ on the flower. (resting)43. 选择题：What is the capital of Croatia?A. ZagrebB. SplitC. RijekaD. Dubrovnik答案: A44. 听力题：The dog is _____ the ball. (chasing)45. 选择题：Which season comes after summer?A. WinterB. FallC. SpringD. Rainy答案:B46. 选择题：What do you call a person who studies plants?A. BotanistB. ZoologistC. BiologistD. Geologist答案:A47. 选择题：What is the name of the famous Egyptian queen?A. CleopatraB. NefertitiC. HatshepsutD. Tutankhamun答案：AThe ________ (果蔬种植) is rewarding.49. 填空题：The _____ (mountain) is home to unique plants.50. 选择题：What is the process called when a caterpillar becomes a butterfly?A. MetamorphosisB. EvolutionC. TransformationD. Development答案:A51. 填空题：The first female Prime Minister of the UK was ________ (玛格丽特·撒切尔).52. 填空题：Certain plants are known for their capacity to store ______ in their leaves. (某些植物因其在叶子中储存水分的能力而著称。

a r X i v :a s t r o -p h /0109026v 1 3 S e p 2001CERN-TH 2001-239Extensive Air Showers from Ultra High Energy Gluinos V.Berezinsky 1,M.Kachelrieß2,and S.Ostapchenko 3,41INFN,Lab.Naz.del Gran Sasso,I–67010Assergi (AQ)2TH Division,CERN,CH–1211Geneva 233Forschungszentrum Karlsruhe,Institut f¨u r Kernphysik,D–76021Karlsruhe,Germany 4Moscow State University,Institute of Nuclear Physics,199899Moscow,Russia August 31,2001Abstract We study the proposal that the cosmic ray primaries above the Greisen-Zatsepin-Kuzmin (GZK)cutoffare gluino-containing hadrons (˜g -hadrons).We describe the interaction of ˜g -hadrons with nucleons in the framework of the Gribov-Regge ap-proach using a modified version of the hadronic interaction model QGSJET for the generations of Extensive Air Showers (EAS).There are two mass windows marginally allowed for gluinos:m ˜g <∼3GeV and 25<∼m ˜g <∼35GeV.Gluino-containing hadrons corresponding to the second window produce EAS very differentfrom the observed ones.Light ˜g -hadrons corresponding to the first gluino windowproduce EAS similar to those initiated by protons,and only future detectors canmarginally distinguish them.We propose a beam-dump accelerator experiment tosearch for ˜g -hadrons in this mass window.We emphasize the importance of thisexperiment:it can discover (or exclude)the light gluino and its role as a cosmic rayprimary at ultra high energies.PACS numbers:98.70.Sa,14.80.-j1IntroductionSince long time light gluinos have attracted attention as a possible carrier of the very high energy signal in the universe.In the80s,they were studied as a possible primary particle from Cyg X-3[1,2],now as a primary particle of the observed Ultra High Energy Cosmic Rays(UHECR)[3,4].The observations of UHECR with energies above1020eV impose a serious problem (see[5]for recent reviews).The data show the presence of a new,nearly isotropic component in the UHECRflux above the energy E∼1019eV[5].Since the arrival directions of the UHECR show no correlation with the galactic plane and the galactic magneticfield cannot isotropize par-ticles of such energies,this component is thought to be extragalactic.On the other hand, the signature of extragalactic protons,the Greisen-Zatsepin-Kuzmin(GZK)cutoff[6]at E≃6·1019eV,is not found.The other natural UHE primaries,nuclei and photons, must also suffer a similar cutoff.Meanwhile,four different UHECR experiments[5]do not show the presence of such a cutoff.The two highest energy events are detected by AGASA[7]and Fly’s Eye[8]at energy2·1020eV and3·1020eV,respectively.The total number of events with energy higher than1·1020eV is about30,17of which are detected by AGASA[9].The accuracy of the energy determination is estimated to be better than 20–30%.The energies of the two highest energy events[7]and[8]are determined very reliably.To resolve this puzzle,it seems that new ideas in astrophysics or particle physics are required.The proposals involving particle physics include UHE particles from superheavy dark matter[10]and topological defects[11],the resonant interaction of UHE neutrinos with dark matter neutrinos[12],strongly interacting neutrinos[13],new particles as UHE primaries[3,4,14]and such a radical possibility as Lorentz invariance violation[15].(For more references see also the reviews cited in[5].)In this paper,we shall consider a gluino-containing hadron(˜g-hadron)as a carrier of the cosmic UHE signal,being inspired by the correlation between AGN and arrival directions of UHE particles suggested by the analyses in Refs.[4,16].This correlation implies that the signal carrier is neutral and is not absorbed by the CMBR.The light gluino is a suitable candidate for such a primary:it can be efficiently produced in pp-interactions in astrophysical sources,it is not strongly absorbed by CMBR(see below) and it produces EAS in the atmosphere very similar to those observed.Heavy gluinos are naturally produced in decays of superheavy particles[17].We shall study here the interaction of both light and heavy gluinos with nucleons at UHE.In most interesting applications gluinos must be light(see below).To be a suitable primary of UHECR,the˜g-hadron should satisfy three conditions:1.The longitudinal shower profile of Fly’s Eye highest energy event with E=3·1020eVis wellfitted by a proton[18,19],though Fly’s Eye collaboration does not exclude a photon as a primary[8].Therefore,˜g-hadrons should essentially mimic proton(or photon)induced air showers.2.To shift the GZK cutoffto higher energies,the new hadron should have a massin excess of the proton mass:the threshold energy for any energy-loss reaction on microwave photons increases with increasing primary mass,while the fraction of energy lost per scattering decreases.Moreover,it is desirable that its cross-section for interactions with CMBR photons is smaller than the proton’s one.This can be achieved if,e.g.,the mass of thefirst resonance X that can be excited in the reaction˜g-hadron+γCMBR→X is relatively large.3.The primary has to be stable or quasi-stable with lifetimeτ>∼106s(m/GeV)(L/Gpc)in order to survive its travel from a source(e.g.AGN)at distance L∼100–1000Mpc to the Earth.In principle gluino-containing hadrons(˜g-hadrons)could satisfy the above require-ments.Below we shall shortly review the status of˜g-hadrons as UHECR signal carrier.To satisfy the third condition,the gluino should be the Lightest Supersymmetric Particle(LSP),or have a very small mass difference with the LSP.It also can be the second lightest supersymmetric particle,if the LSP is the gravitino;in this case the gluino decays gravitationally and its lifetime can be long enough.Theoretically the best motivated candidates for the LSP are the neutralino and gravitino.While in minimal supergravity models the LSP is the lightest neutralino(in some part of the parameter space it is the sneutrino),in models with gauge-mediated SUSY the LSP is normally the gravitino.In Farrar’s model[20],the gluino is the LSP because the dimension-three SUSY breaking terms are set to zero.A theoretically more appealing scenario containing a light gluino was developed in Refs.[21,22].There,the gluino with mass1–100GeV was found in a SO(10)model with gauge-mediated SUSY breaking and Higgs-messenger mixing.In this model either the gluino or the gravitino is the LSP.In the latter case,the gluino can decay but has a sufficiently long lifetime to be a viable UHECR primary,τ∼100yr.In a physical state,the gluino is bound into colourless hadrons.What is the lightest state of gluino-containing hadrons?In the80s(see[2]),it was argued on the basis of QCD sum rules that the glueballino ˜g g is the lightest˜g-hadron.The lightest baryonic state,gluebarino,was demonstrated to be the¯g uud-hadron[23].Gluebarino is a long-lived particle because its decay needs either violation of baryon number or R-parity[23].More recently,Farrar proposed[20]the neutral hadron S0,a˜g uds bound-state,as the lightest˜g-hadron(see also the calculations in the MIT bag model of Ref.[24]).There is some controversy if a light gluino,with a mass of a few GeV,is allowed.As it stands,the Farrar model[20]is in conflict with searches for glueballino decays[25,26,27] as well as for decays of other unstable˜g-hadrons[28].However,these searches had been restricted to a narrow band of lifetimes and masses,and their results are not valid in the context of more generic models.The existence of a light gluino(m˜g<∼5GeV)can be(dis-)proved due to its contribu-tion to the running ofαs and to QCD colour coefficients in a practically model-independent way.The authors of Ref.[29]used the ratio R between the hadronic and the¯µµproduc-tion cross-section in e+e−annihilation at different energies to constrain the light gluino scenario.They excluded light gluinos with mass m˜g=3(5)GeV with93(91)%CL,whilethe mass range≤1.5GeV remained essentially bining these results with the determination of QCD colour coefficients from the analysis of multi-jet events in[30],the conclusions of[29]became much stronger:light gluinos with mass≤5GeV were excluded with at least99.89%CL.The analysis of multi-jet events relied however on the use of Monte Carlo simulations which parameters are tuned to QCD without light gluinos.Moreover,the multi-jet analysis was based on a tree-level calculation with rather large scale ambiguities.The assessment of these uncertainties is difficult,thus preventing the definite exclusion of a very light gluino by this argument[31,32].Direct accelerator limits for the gluino as LSP were discussed recently in Refs.[22,33, 34]:The authors of Ref.[33]concluded that the range3GeV<∼m˜g<∼130–150GeV can be excluded at95%C.L.based on currently available OPAL and CDF data.Their results are sensitive to the details of the hadronic interactions of˜g-hadrons and,for certain choices of the parameters,a window in the intermediate mass region23GeV<∼m˜g<∼50GeV remains open.Meanwhile,Ref.[22]noted that these limits could be weakened if squarks are not very heavy and contribute to the jet+missing energy signal,while Ref.[34] confirmed an open window for a gluino with25GeV<∼m˜g<∼35GeV.We also mention here that cosmological constraints do not exclude both light and heavy gluinos of interest[17,35].The Gustafson experiment[37]does not exclude˜g-hadrons(see section5).Till now we discussed the limits on the gluino mass m˜g.The lightest˜g-hadron with mass M˜g is heavier than the gluino by the mass of its constituent gluon or quarks,which are expected to be less than1GeV.Light˜g-hadrons with M˜g∼1.5GeV have a spectrum with the GZK cutoffbeyond the currently observed energy range(see[17]and Fig.12of the present paper).Together with the accelerator limits on gluino masses this leaves a narrow band of allowed masses for the light˜g-hadrons at1.5<∼M˜g<∼4GeV.But this window is closed if,as argued in[23],the charged gluebarino˜g uud is lighter than the neutral˜g uds.Indeed,production of charged gluebarinos in the Earth atmosphere by cosmic rays and their accumulation in the ocean results in too high abundance of“wild hydrogen”in contradiction with observational data.In Refs.[20,24],however,it is argued that the lightest gluebarino is the neutral flavour singlet˜g uds,due to strong quark attraction in this state.But even in this case the restriction[23]might work,if˜g uds-gluebarino and proton are bound into anomalous deuterium.In conclusion,a light gluino—although being disfavoured by various arguments—is not excluded.We are studying here the interactions of gluinos,being inspired by a possible correlation between AGN and the arrival directions of UHECR[4,16]and by the recent suggestion[3,38],that Extensive Air Showers(EAS)observed at the highest energies could be produced by˜g-hadrons.The authors of Ref.[38]performed a detailed simulation of EAS induced by˜g-hadrons,using however a phenomenological description for the˜g-hadron-nucleon interaction which is not self-consistent.They found that masses as high as50GeV are compatible with presently available data.In contrast,it was argued in Ref.[17],using kinematical arguments,that the observed shower characteristics exclude any strongly interacting particle much heavier than a few GeV.The purpose of the present work is to study EAS produced by˜g-hadrons and to restrictthe mass range in which the˜g-hadron is a viable UHE primary using a self-consistent interaction model.We have used for the simulation of air showers initiated by˜g-hadrons a suitably modified version of the QGSJET model[39,40]which is known to describe successfully proton air showers[39,41].Specifically,we have considered the glueballino as the˜g-hadron but we expect that our results apply to all˜g-hadrons.We paid special attention to consistent calculations of glueballino-hadron interaction cross-sections and of cascade particle production in the atmosphere.We have found that the development of showers initiated by˜g-hadrons with masses above5GeV differs substantially from proton-initiated showers and is inconsistent with the current experimental data.In the window of masses1.5–4GeV,where a˜g-hadron can be allowed,glueballino-induced showers do not contradict the available data.Future observations by the detectors HiRes and Auger can either confirm or exclude˜g-hadrons as the dominant primary combining the information from shower profiles and energy spectrum.However,the best way to test this hypothesis is a modified Gustafson experiment(see Section5).In the case of the discovery of light˜g-hadrons in such an experiment we shall reliably know their properties,thus enabling us to calculate the production of these particles in astrophysical sources and their detection in the Earth atmosphere.Their absence will preclude further discussion of this hypothesis. 2Glueballino–proton(nucleus)interaction2.1QGSJET frameworkQGSJET,a Monte Carlo generator of hadron-hadron,hadron-nucleus,and nucleus-nucleus interactions[39,40],was developed in the framework of the Gribov-Regge approach and is based on the quark-gluon string model of the supercritical Pomeron[42].Hadronic interactions are described as a superposition of elementary rescattering processes between the partonic constituents of the projectile and target nucleons(hadrons),resulting in the production of colour neutral strings,which further fragment into secondary hadrons.The key parameters of the model are the intercepts and the slopes of the Regge trajectories of the Pomeron and of secondary Reggeons.These parameters govern the formation of different interaction configurations,how the energy-momentum is shared in elementary interactions,and also the string hadronization.The model was generalized to hadron-nucleus and nucleus-nucleus interactions in the framework of the Glauber-Gribov ap-proach[43,44],taking into account low mass diffraction and inelastic screening processes [45].Hard QCD processes were included into the Gribov-Regge formalism via the concept of a”semihard Pomeron”,which is a t-channel iteration of the soft Pomeron and a QCD parton ladder contribution[40,46].QGSJET describes hadron-hadron interaction amplitudes as a sum of two contribu-tions,namely soft and semihard rescatterings[40].The soft contributions are of purely nonperturbative nature and correspond to the case of a parton cascade with virtualities smaller than some cutoffQ20.Below this cutoff,perturbative QCD is not applicable and the interaction is described by phenomenological soft Pomeron exchange.The amplitudef ac for Pomeron exchange between two hadrons a and c is given by[42]f ac(s,b)=γaγc exp(∆y)4λac(y) (1)λac(y)=R2a+R2c+α′y,(2) where y=ln s is the rapidity size of the Pomeron,s is the squared center-of-mass energy for the interaction,b is the impact parameter between the two hadrons,and the parametersγa(c),R2a(c)are the vertices and slopes for the Pomeron-hadron a(c)coupling,respectively.Finally,∆andα′are the parameters describing the overcriticality and the slope of the soft Pomeron trajectory.Contrary to soft rescatterings,semi-hard ones correspond to the case when at least a part of the parton cascade develops in the region of parton virtualities q2>Q20and, therefore,can be described on the basis of QCD techniques.The complete semi-hard con-tribution is represented by a QCD parton ladder sandwiched between two soft Pomerons [46].For the Pomeron,the formulas(1-2)can still be used.However,since it is now coupled to a hadron a(c)on one side but to a parton ladder on the other side,the slopeR2c(a)and the couplingγc(a)have to be replaced by the slope R2lad and the coupling V lad ofthe Pomeron-ladder.The latter is parameterised asV lad(y)=r[1−exp(−y)]β,(3) where the parameters r andβdescribe the momentum distribution of a parton(sea quark or gluon)in the soft ing R2lad≃1/Q20≪R2a(b)+α′y,the slope R2ladcan be neglected.To complete the description of soft and semihard contributions,the momentum distri-bution function N a for soft Pomeron emission by a hadron of type a has to be specified. It is parameterised in the formN a x± ∼ x± α 1−x± βa,(4) where thefirst factor does not depend on the hadron type and describes the probability to slow down the hadron constituents to which the Pomeron is connected.In QGSJET, the Pomeron is connected to a(dressed)quark-antiquark ing Regge asymptotics [42],i.e.αq¯q≃0.5as the intercept of the Regge q¯q-trajectory for light quarks,it followsα=1−2αq¯q≃0.(5)Similar,the second factor in Eq.(4)describes the probability to slow down the”leading”hadron state configuration;the parameterβa is expressed via the interceptαa¯a of the corresponding Regge trajectory asβa=−αa¯a.The semihard contribution described above corresponds to the case that gluons or sea quarks of the hadron start the interaction at the initial scale Q20.Additionally,valence quarks can interact with q2≥Q20.Then the only nonperturbative input needed are the valence quark momentum distributions q v(x,Q20)at the initial scale Q20.2.2Extension for glueballinoThe nucleon-glueballino interaction can be treated in the QGSJET model in the same framework as the one for usual hadrons [39].The main difficulty is to connect the unknownphysical parameters (coupling γ˜G ,slope R 2˜G and momentum distribution N ˜G )describingthe interactions of glueballinos with the corresponding quantities of usual hadrons.We use simple scaling arguments to derive the glueballino parameters from those of the pion:1.The coupling γa of a hadron a to the Pomeron depends essentially on its size and,consequently,on its reduced mass M a .If r a denotes the radius of the hadron awith the reduced mass M a ,then γa ∼r 2a ∼M −2a ,where we have neglected a factorαs (M 2a )in the last step.Thus,the Pomeron-glueballino vertex γ˜G can be expressed via the Pomeron-pion vertex γπasγ˜G =γπ M πm ˜g +m g ,(7)where m ˜g is the mass of the gluino and m g ≃0.7GeV is the constituent mass of the gluon.Similar,we use for the pion M π=m q /2with m q ≃0.35GeV as quark constituent mass.Note that Eq.(6)does not take into account the different colour factors of quarks and gluon/gluinos because we consider an effective Pomeron coupling to the hadron as a whole,not to individual parton constituents.2.The slope R 2˜G for the Pomeron-glueballino coupling is also inverse proportional toM 2˜G .Therefore,R 2˜G is small compared to R 2p and R 2=α′y and can be neglected in the formulas (1-2),λ˜Gp (y )≃R 2p +α′y.(8)3.The momentum distribution for Pomeron emission is again given by Eq.(4),N ˜G ∼(x ±)α(1−x ±)β˜G .Now the ”leading”configuration consists of a valence gluon and gluino,β˜G =1+β˜g +βg .(9)Assuming that a valence gluon behaves similar to a valence q ¯q -pair in the low x -limit gives βg ≃1−2αq ¯q ≃0.The remaining unknown parameter β˜g can be found from the momentum distribution between the valence constituents of the ing as ansatz for the momentum distribution ρ˜G ˜g of the gluinoρ˜G ˜g (x ˜g )∼x β˜g ˜g (1−x ˜g )βg (10)and assuming that the energy is shared according to the constituent masses of the valence partons,we obtain for the average momentum fraction carried by the gluinox ˜g =m ˜g βg +β˜g +2.(11)This results inβ˜g=m˜gm g−1.(12)Havingfixed the free parameters describing the Pomeron-glueballino interactions us-ing essentially only one simple,physically well-motivated scaling argument,the soft and semi-hard contributions are determined.These two contributions to the total nucleon-glueballino interaction are referred below as the contribution due to the soft coupling, because they are both caused by soft Pomeron emission of the glueballino.To complete the formalism,we need to define the momentum distributions of the valence gluon or gluino inside the glueballino probed at the initial scale Q20,when they are involved into hard interactions.We shall refer to this contribution below as the the contribution due to the direct coupling.Parton emission by a gluino in the s-channel is strongly suppressed kinematically in the nonperturbative region q2<Q20by its mass:the virtuality q2of the process˜g→g+˜g is determined by the off-shellness q2˜g−M2˜g of the produced t-channel gluino,q2˜g→˜g= q2˜g−M2˜g =p2⊥2.3Numerical resultsThe model developed in the last subsection allows both to calculate the cross-sections for glueballino-nucleon interactions and to treat consistently particle production in these reactions.Some quantities characterising the glueballino-nucleon interactions are given in Table1for E lab=100GeV and in Table2for E lab=1012GeV.We present both total and inelastic cross-sections as well as the partial contributions arising due to thesoft(σs−coupl.tot )and direct(σd−coupl.tot)coupling of the glueballino1.At low energies,thesoft coupling strongly dominates the˜G-proton interaction for all M˜G being governed bynonperturbative soft interactions,while the direct coupling can be neglected.At high energies,this picture changes considerably.The soft coupling becomes more and moresuppressed for large M˜G .By contrast,the direct contribution,which is purely perturbativeon the glueballino side,is nearly independent of M˜G .This important difference fromthe usual hadron case is due to the very asymmetric energy partition between partonconstituents of the glueballino.For large M˜G ,the valence gluino carries almost the wholeinitial energy of the particle(88%for M˜g=5GeV and99%for M˜g=50GeV)–Eqs. (10-11),(14),thus leaving just a small part of it to other partons,to which Pomerons areconnected.Therefore,the glueballino behaves in the limit of large M˜G essentially as aperturbative object,as one expects from kinematical considerations[17].Finally,the last raw of the tables shows the inelasticity coefficient K inel as another important quantity which distinguishes proton-proton and˜G-proton interactions.Although at energies of interest for UHECR the total cross-section for˜G-proton interactions is rather large,a heavy glueballino behaves like a penetrating particle in the atmosphere loosing only a small part of its energy in one interaction.This conclusion was already reached in Ref.[17] from semiqualitative considerations.The reason for this effect is twofold.On one side, as discussed above,gluinos of larger masses carry a larger fraction of the initial particle energy,leaving a smaller part of it for the sea constituents((anti-)quarks and gluons)and thus reducing the average number of multiple interactions in˜G-proton(nucleus)collisions. On the other hand,the relative weight of the”direct hard”process increases for heavier gluinos,where the valence gluino loses typically only a small part of its energy,as a large longitudinal momentum transfer is strongly suppressed in that case by the process virtuality q2˜g→g,q2˜g→g=p2⊥1−z,(16)with p⊥and z being the transverse momentum and the light cone momentum fraction for the t-channel gluon emitted of the initial valence gluino which mediates the gluino hard interaction with the target proton(nucleus).We show also in Figs.1and2the total and inelastic cross-sections as function of theinteraction energy E lab for glueballino masses M˜G =2,5and50GeV.The fast increase ofthe direct contribution with E lab produces an interesting effect:the total interaction cross-section for the largest glueballino mass considered,M˜G=50GeV,which is dominated bythe direct contribution,overshoots the ones for smaller glueballino masses in the energy range104−109GeV.3Extensive air showers(EAS)In this section,we present some results of our simulations for the glueballino-initiated EAS.Shower profiles and distributions of shower maxima are shown in Figs.3–8for three different initial energies,E0=1017,1019and1020eV,for the glueballino as primary with different choices of the gluino mass.For comparison,the case of a primary proton is also shown.At the highest energy considered,E0=1020eV,the longitudinal shower profiles (Fig.3)and the distribution of the shower maxima X max(Fig.4)of glueballino-induced EAS are comparable with those induced by protons in the case of glueballino masses smaller than5GeV.As the glueballino mass increases,the shower develops deeper in the atmosphere with a less pronounced maximum.Thefluctuations in X max increase also for larger glueballino masses.The main reason for both effects is the competition between the large glueballino-nucleus cross-section and the small inelasticity of the interactions:a heavy glueballino injects in one interaction only a small part of its energy into secondary hadronic and electromagnetic cascades,while interactions with a large momentum transfer are rare and increase only thefluctuations.Figure4clearly shows that the glueballino-induced EAS drastically differ from the proton-induced showers for glueballino masses larger than5GeV,and hence these showers can be distinguished even in case of lowstatistics.In case of a lighter glueballino with M˜G =2GeV,a larger statistics is necessaryto distinguish glueballino from proton,when only X max measurements are used.The same conclusions can be drawn comparing the shape of the calculated profiles for individual p-and˜G-induced EAS of energy E0=3.2·1020eV with the corresponding measurements of the Fly’s Eye collaboration[48],cf.Fig.9.In doing so we choose only those showers which reach their maxima near the measured value X max=815±50g/cm2.Then we average the obtained profiles and shift them to the same position of the shower maximum,X max=815 g/cm2.It is easy to see that for gluino masses larger than5GeV the shape of the calculated profile strongly disagrees with the experimental observations.The account for the LPM effect results in only5%reduction of the electron number in the shower maximum for proton-induced EAS[19]and has an even smaller influence on the˜G-induced showers due to much softerπ0-spectrum in the glueballino interactions.The calculated lateral distribution functions(LDFs)for electrons and muons(Eµ>1 GeV)at the AKENO observation level(900g/cm2)are shown in Figs.10and11for the proton and glueballinos with masses2and5GeV.The plotted values are the LDFs of electrons and muonsρe(R),ρµ(R)at different distances R from the shower core.Although these distributions are substantially different for showers initiated by glueballinos and protons,they hardly can be used to search for the light glueballino on the basis of existing data,e.g.,of AGASA.An adequate tool for the glueballino search is thefluctuation of the muon density at distances R>∼300m from the core.This method allows in principle to discriminate showers initiated even by light glueballinos with M˜G≈2GeV from proton-initiated EAS(see Table4).Finally,we shall compare our results with those of Albuquerque,Farrar and Kolb (AFK)[38].AFK have modified the event generator SIBYLL including the ˜g -hadron (˜G )as a new particle.The interaction properties of ˜g -hadronwere taken ad hoc .Two assumptions were used for the total cross-section:σtot (˜Gp )≈σtot (πp )(the favouritechoice)and σtot (˜Gp )≈0.1σtot (πp ).The mean energy fraction transferred from the ˜g -hadron to the shower per interaction was modeled by a Peterson fragmentation function.Hard interactions with the production of minijets by the incident ˜g -hadron were neglected.It is easy to see that these modifications are notself-consistent.Indeed,on one handthe authors assume a large ˜Gp cross-section,while on the other hand they neglect thehardprocesses (production of minijets),which give the dominant contribution to the˜Gp cross-section and make it large.In fact,our calculations explicitly show that at ultra-high energies the ˜Gp cross-section and particle production are dominated by hard interactions for both light and heavy gluinos.For light gluinos,valence gluon and sea partons have enough momenta for hard interactions.For heavy gluinos,its own (”direct”)hard interaction dominates.Soft interactions without the production of parton jets are negligible in both cases.To elucidate the reason for the failure of the AFK approach,wehave calculated thetotal ˜G -nucleon cross-section switching offthe hard interaction (cf.5th entry,σAFK ,in Table 1and 2):At energies relevant for UHECR,the interactions considered by AFK are only subdominant and result in much smaller total cross-sections as compared with ours or those assumed by AFK.4Energy losses of glueballinos on CMBR photonsand glueballino energy spectrumAlthough both valence constituents of the glueballino are electrically neutral,UHE glue-ballinos loose energy due to scattering on CMBR photons.The value of the cutoffin its energy spectrum is determined by the transition from adiabaticenergy losses (redshift)to rapidly increasing energy losses due to the reaction ˜G +γ→˜G +π0at higher en-ergies.This process cannot occur due to π0exchange in the t -channel.The dominant contribution is given by the resonant formation of ˜g ¯q q states in the s -channel.The mass spectrum of ˜g ¯q q states was calculated as function of the gluino mass in Ref.[49]in the MIT bag model.The lowest ˜g ¯q q state found was the spin-1/2state ˜ρ1/2;its mass difference to the glueballino ishowever,except for m˜G <1.2GeV,too small as to allow the decay˜ρ1/2→˜G +π0,cf.Table 6.We assume therefore that the first resonance in the s -channel isan excited ˜ρ∗1/2state;for its mass m (˜ρ∗1/2)we use m (˜ρ∗1/2)=m (˜ρ1/2)+730MeV guided bythe mass difference between the ρ(770)andthe ρ(1400).The Breit-Wigner cross-sectionfor the reaction ˜G +γ→˜ρ1/2→˜G +π0is [32]σ(s )=2π(s −m 2˜ρ)2+(m ˜ρΓtot )2,(17)where p cm and √。

a r X i v :h e p -p h /9711228v 1 4 N o v 1997hep-ph/9711228October 1997O (α)QED Corrections to Polarized Elastic µe and Deep Inelastic lN ScatteringDima Bardin a,b,c ,Johannes Bl¨u mlein a ,Penka Christova a,d ,and Lida Kalinovskaya a,caDESY–Zeuthen,Platanenallee 6,D–15735Zeuthen,GermanybINFN,Sezione di Torino,Torino,ItalycJINR,ul.Joliot-Curie 6,RU–141980Dubna,RussiadBishop Konstantin Preslavsky University of Shoumen,9700Shoumen,BulgariaAbstractTwo computer codes relevant for the description of deep inelastic scattering offpolarized targets are discussed.The code µe la deals with radiative corrections to elastic µe scattering,one method applied for muon beam polarimetry.The code HECTOR allows to calculate both the radiative corrections for unpolarized and polarized deep inelastic scattering,including higher order QED corrections.1IntroductionThe exact knowledge of QED,QCD,and electroweak (EW)radiative corrections (RC)to the deep inelastic scattering (DIS)processes is necessary for a precise determination of the nucleon structure functions.The present and forthcoming high statistics measurements of polarized structure functions in the SLAC experiments,by HERMES,and later by COMPASS require the knowledge of the RC to the DIS polarized cross-sections at the percent level.Several codes based on different approaches for the calculation of the RC to DIS experiments,mainly for non-polarized DIS,were developped and thoroughly compared in the past,cf.[1].Later on the radiative corrections for a vast amount of experimentally relevant sets of kinematic variables were calculated [2],including also semi-inclusive situations as the RC’s in the case of tagged photons [3].Furthermore the radiative corrections to elastic µ-e scattering,a process to monitor (polarized)muon beams,were calculated [4].The corresponding codes are :•HECTOR 1.00,(1994-1995)[5],by the Dubna-Zeuthen Group.It calculates QED,QCD and EW corrections for variety of measuremets for unpolarized DIS.•µe la 1.00,(March 1996)[4],calculates O (α)QED correction for polarized µe elastic scattering.•HECTOR1.11,(1996)extends HECTOR1.00including the radiative corrections for polarized DIS[6],and for DIS with tagged photons[3].The beta-version of the code is available from http://www.ifh.de/.2The Programµe laMuon beams may be monitored using the processes ofµdecay andµe scattering in case of atomic targets.Both processes were used by the SMC experiment.Similar techniques will be used by the COMPASS experiment.For the cross section measurement the radiative corrections to these processes have to be known at high precision.For this purpose a renewed calculation of the radiative corrections toσ(µe→µe)was performed[4].The differential cross-section of polarized elasticµe scattering in the Born approximation reads,cf.[7],dσBORNm e Eµ (Y−y)2(1−P e Pµ) ,(1)where y=yµ=1−E′µ/Eµ=E′e/Eµ=y e,Y=(1+mµ/2/Eµ)−1=y max,mµ,m e–muon and electron masses,Eµ,E′µ,E′e the energies of the incoming and outgoing muon,and outgoing electron respectively,in the laboratory frame.Pµand P e denote the longitudinal polarizations of muon beam and electron target.At Born level yµand y e agree.However,both quantities are different under inclusion of radiative corrections due to bremsstrahlung.The correction factors may be rather different depending on which variables(yµor y e)are used.In the SMC analysis the yµ-distribution was used to measure the electron spin-flip asymmetry A expµe.Since previous calculations,[8,9],referred to y e,and only ref.[9]took polarizations into account,a new calculation was performed,including the complete O(α)QED correction for the yµ-distribution,longitudinal polarizations for both leptons,theµ-mass effects,and neglecting m e wherever possible.Furthermore the present calculation allows for cuts on the electron re-coil energy(35GeV),the energy balance(40GeV),and angular cuts for both outgoing leptons (1mrad).The default values are given in parentheses.Up to order O(α3),14Feynman graphs contribute to the cross-section forµ-e scattering, which may be subdivided into12=2×6pieces,which are separately gauge invariantdσQEDdyµ.(2) One may express(2)also asdσQEDdyµ+P e Pµdσpol kk=1−Born cross-section,k=b;2−RC for the muonic current:vertex+bremsstrahlung,k=µµ;3−amm contribution from muonic current,k=amm;4−RC for the electronic current:vertex+bremsstrahlung,k=ee;5−µe interference:two-photon exchange+muon-electron bremsstrahlung interference,k=µe;6−vacuum polarization correction,runningα,k=vp.The FORTRAN code for the scattering cross section(2)µe la was used in a recent analysis of the SMC collaboration.The RC,δA yµ,to the asymmetry A QEDµeshown infigures1and2is defined asδA yµ=A QEDµedσunpol.(4)The results may be summarized as follows.The O(α)QED RC to polarized elasticµe scattering were calculated for thefirst time using the variable yµ.A rather general FORTRAN codeµe la for this process was created allowing for the inclusion of kinematic cuts.Since under the conditions of the SMC experiment the corrections turn out to be small our calculation justifies their neglection. 3Program HECTOR3.1Different approaches to RC for DISThe radiative corrections to deep inelastic scattering are treated using two basic approaches. One possibility consists in generating events on the basis of matrix elements including the RC’s. This approach is suited for detector simulations,but requests a very hughe number of events to obtain the corrections at a high precision.Alternatively,semi-analytic codes allow a fast and very precise evaluation,even including a series of basic cuts andflexible adjustment to specific phase space requirements,which may be caused by the way kinematic variables are experimentally measured,cf.[2,5].Recently,a third approach,the so-called deterministic approach,was followed,cf.[10].It treats the RC’s completely exclusively combining features of fast computing with the possibility to apply any cuts.Some elements of this approach were used inµe la and in the branch of HECTOR1.11,in which DIS with tagged photons is calculated.Concerning the theoretical treatment three approaches are in use to calculate the radiative corrections:1)the model-independent approach(MI);2)the leading-log approximation(LLA); and3)an approach based on the quark-parton model(QPM)in evaluating the radiative correc-tions to the scattering cross-section.In the model-independent approach the QED corrections are only evaluated for the leptonic tensor.Strictly it applies only for neutral current processes.The hadronic tensor can be dealt with in its most general form on the Lorentz-level.Both lepton-hadron corrections as well as pure hadronic corrections are neglected.This is justified in a series of cases in which these corrections turn out to be very small.The leading logarithmic approximation is one of the semi-analytic treatments in which the different collinear singularities of O((αln(Q2/m2l))n)are evaluated and other corrections are neglected.The QPM-approach deals with the full set of diagrams on the quark level.Within this method,any corrections(lepton-hadron interference, EW)can be included.However,it has limited precision too,now due to use of QPM-model itself. Details on the realization of these approaches within the code HECTOR are given in ref.[5,11].3.2O (α)QED Corrections for Polarized Deep Inelastic ScatteringTo introduce basic notation,we show the Born diagramr rr r j r r r r l ∓( k 1,m )l ∓( k 2,m )X ( p ′,M h )p ( p ,M )γ,Z ¨¨¨¨B ¨¨¨¨£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡z r r r r r r r r r r r r r rr ¨¨¨¨B ¨¨¨¨r r r r j r r r r and the Born cross-section,which is presented as the product of the leptonic and hadronic tensordσBorn =2πα2p.k 1,x =Q 2q 2F 1(x,Q 2)+p µ p ν2p.qF 3(x,Q 2)+ie µνλσq λs σ(p.q )2G 2(x,Q 2)+p µ s ν+ s µ p νp.q1(p.q )2G 4(x,Q 2)+−g µν+q µq νp.qG 5(x,Q 2),(8)wherep µ=p µ−p.qq 2q µ,and s is the four vector of nucleon polarization,which is given by s =λp M (0, n )in the nucleonrest frame.The combined structure functions in eq.(8)F1,2(x,Q2)=Q2e Fγγ1,2(x,Q2)+2|Q e|(v l−p eλl a l)χ(Q2)FγZ1,2(x,Q2)+ v2l+a2l−2p eλl v l a l χ2(Q2)F ZZ1,2(x,Q2),F3(x,Q2)=2|Q e|(p e a l−λl v l)χ(Q2)FγZ3(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)F ZZ3(x,Q2),G1,2(x,Q2)=−Q2eλl gγγ1,2(x,Q2)+2|Q e|(p e a l−λl v l)χ(Q2)gγZ1,2(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)g ZZ1,2(x,Q2),G3,4,5(x,Q2)=2|Q e|(v l−p eλl a l)χ(Q2)gγZ3,4,5(x,Q2),+ v2l+a2l−2p eλl v l a l χ2(Q2)g ZZ3,4,5(x,Q2),(9) are expressed via the hadronic structure functions,the Z-boson-lepton couplings v l,a l,and the ratio of the propagators for the photon and Z-bosonχ(Q2)=Gµ2M2ZQ2+M2Z.(10)Furthermore we use the parameter p e for which p e=1for a scattered lepton and p e=−1for a scattered antilepton.The hadronic structure functions can be expressed in terms of parton densities accounting for the twist-2contributions only,see[12].Here,a series of relations between the different structure functions are used in leading order QCD.The DIS cross-section on the Born-leveld2σBorndxdy +d2σpol Borndxdy =2πα2S ,S U3(y,Q2)=x 1−(1−y)2 ,(13) and the polarized partdσpol BornQ4λp N f p S5i=1S p gi(x,y)G i(x,Q2).(14)Here,S p gi(x,y)are functions,similar to(13),and may be found in[6].Furthermore we used the abbrevationsf L=1, n L=λp N k 12πSy 1−y−M2xy2π1−yThe O(α)DIS cross-section readsd2σQED,1πδVRd2σBorndx l dy l=d2σunpolQED,1dx l dy l.(16)All partial cross-sections have a form similar to the Born cross-section and are expressed in terms of kinematic functions and combinations of structure functions.In the O(α)approximation the measured cross-section,σrad,is define asd2σraddx l dy l +d2σQED,1dx l dy l+d2σpol radd2σBorn−1.(18)The radiative corrections calculated for leptonic variables grow towards high y and smaller values of x.Thefigures compare the results obtained in LLA,accounting for initial(i)andfinal state (f)radiation,as well as the Compton contribution(c2)with the result of the complete calculation of the leptonic corrections.In most of the phase space the LLA correction provides an excellent description,except of extreme kinematic ranges.A comparison of the radiative corrections for polarized deep inelastic scattering between the codes HECTOR and POLRAD[17]was carried out.It had to be performed under simplified conditions due to the restrictions of POLRAD.Corresponding results may be found in[11,13,14].3.3ConclusionsFor the evaluation of the QED radiative corrections to deep inelastic scattering of polarized targets two codes HECTOR and POLRAD exist.The code HECTOR allows a completely general study of the radiative corrections in the model independent approach in O(α)for neutral current reac-tions including Z-boson exchange.Furthermore,the LLA corrections are available in1st and2nd order,including soft-photon resummation and for charged current reactions.POLRAD contains a branch which may be used for some semi-inclusive DIS processes.The initial state radia-tive corrections(to2nd order in LLA+soft photon exponentiation)to these(and many more processes)can be calculated in detail with the code HECTOR,if the corresponding user-supplied routine USRBRN is used together with this package.This applies both for neutral and charged current processes as well as a large variety of different measurements of kinematic variables. Aside the leptonic corrections,which were studied in detail already,further investigations may concern QED corrections to the hadronic tensor as well as the interference terms. References[1]Proceedings of the Workshop on Physics at HERA,1991Hamburg(DESY,Hamburg,1992),W.Buchm¨u ller and G.Ingelman(eds.).[2]J.Bl¨u mlein,Z.Phys.C65(1995)293.[3]D.Bardin,L.Kalinovskaya and T.Riemann,DESY96–213,Z.Phys.C in print.[4]D.Bardin and L.Kalinovskaya,µe la,version1.00,March1996.The source code is availablefrom http://www.ifh.de/~bardin.[5]A.Arbuzov,D.Bardin,J.Bl¨u mlein,L.Kalinovskaya and T.Riemann,Comput.Phys.Commun.94(1996)128,hep-ph/9510410[6]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,DESY96–189,hep-ph/9612435,Nucl.Phys.B in print.[7]SMC collaboration,D.Adams et al.,Phys.Lett.B396(1997)338;Phys.Rev.D56(1997)5330,and references therein.[8]A.I.Nikischov,Sov.J.Exp.Theor.Phys.Lett.9(1960)757;P.van Nieuwenhuizen,Nucl.Phys.B28(1971)429;D.Bardin and N.Shumeiko,Nucl.Phys.B127(1977)242.[9]T.V.Kukhto,N.M.Shumeiko and S.I.Timoshin,J.Phys.G13(1987)725.[10]G.Passarino,mun.97(1996)261.[11]D.Bardin,J.Bl¨u mlein,P.Christova,L.Kalinovskaya,and T.Riemann,Acta Phys.PolonicaB28(1997)511.[12]J.Bl¨u mlein and N.Kochelev,Phys.Lett.B381(1996)296;Nucl.Phys.B498(1997)285.[13]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,Preprint DESY96–198,hep-ph/9609399,in:Proceedings of the Workshop‘Future Physics at HERA’,G.Ingelman,A.De Roeck,R.Klanner(eds.),Vol.1,p.13;hep-ph/9609399.[14]D.Bardin,Contribution to the Proceedings of the International Conference on High EnergyPhysics,Warsaw,August1996.[15]M.Gl¨u ck,E.Reya,M.Stratmann and W.Vogelsang,Phys.Rev.D53(1996)4775.[16]S.Wandzura and F.Wilczek,Phys.Lett.B72(1977)195.[17]I.Akushevich,A.Il’ichev,N.Shumeiko,A.Soroko and A.Tolkachev,hep-ph/9706516.-20-18-16-14-12-10-8-6-4-200.10.20.30.40.50.60.70.80.91elaFigure 1:The QED radiative corrections to asymmetry without experimental cuts.-1-0.8-0.6-0.4-0.200.20.40.60.810.10.20.30.40.50.60.70.80.91elaFigure 2:The QED radiative corrections to asymmetry with experimental cuts.-50-40-30-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 3:A comparison of complete and LLA RC’s in the kinematic regime of HERMES for neutral current longitudinally polarized DIS in leptonic variables.The polarized parton densities [15]are used.The structure function g 2is calculated using the Wandzura–Wilczek relation.c 2stands for the Compton contribution,see [6]for details.-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 4:The same as in fig.3,but for energies in the range of the SMC-experiment.-20-10010203040500.10.20.30.40.50.60.70.80.91HectorFigure 5:The same as in fig.4for x =10−3.-200-150-100-5005010015020000.10.20.30.40.50.60.70.80.91HectorFigure 6:A comparison of complete and LLA RC’s at HERA collider kinematic regime for neutral current deep inelastic scattering offa longitudinally polarized target measuring the kinematic variables at the leptonic vertex.。

a rXi v :h e p -p h /9704448v 1 30 A p r 1997DESY 97-079IFT-96-29PM–97/04April 1997HDECAY:a Program for Higgs Boson Decaysin the Standard Model and its Supersymmetric ExtensionA.Djouadi 1,J.Kalinowski 2and M.Spira 31Laboratoire de Physique Math´e matique et Th´e orique,UPRES–A 5032,Universit´e de Montpellier II,F–34095Montpellier Cedex 5,France.2Deutsches Elektronen–Synchrotron,DESY,D–22603Hamburg,Germany,Institute of Theoretical Physics,Warsaw University,PL–00681Warsaw,Poland.3Theory Division,CERN,CH–1211,Geneva 23,Switzerland.Abstract We describe the Fortran code HDECAY †,which calculates the decay widths and the branching ratios of the Standard Model Higgs boson,and of the neutral and charged Higgs particles of the Minimal Supersymmetric extension of the Standard Model.The program is self-contained (with all subroutines included),easy to run,fast and calculates the decay widths and branching ratios according to the current theoretical knowledge.:f1IntroductionThe experimental observation of scalar Higgs particles is crucial for our present under-standing of the mechanism of electroweak symmetry breaking.Thus the search for Higgs bosons is one of the main entries in the LEP2agenda,and will be one of the major goals of future colliders such as the Large Hadron Collider LHC and the future Linear e+e−Collider LC.Once the Higgs boson is found,it will be of utmost importance to perform a detailed investigation of its fundamental properties,a crucial requirement to establish the Higgs mechanism as the basic way to generate the masses of the known particles.To this end,a very precise prediction of the production cross sections and of the branching ratios for the main decay channels is mandatory.In the Standard Model(SM),one doublet of scalarfields is needed for the electroweak symmetry breaking,leading to the existence of one neutral scalar particle H0[1].Once M H0isfixed,the profile of the Higgs boson is uniquely determined at tree level:the couplings to fermions and gauge bosons are set by their masses and all production cross sections,decay widths and branching ratios can be calculated unambiguously[2].Unfor-tunately,M H0is a free parameter.From the direct search at LEP1and LEP2we know that it should be larger than about71GeV[3].Triviality restricts the Higgs particle to be lighter than about1TeV;theoretical arguments based on Grand Unification at a scale ∼1016GeV suggest however,that the preferred mass region will be100GeV<∼M H0<∼200GeV;for a recent summary,see Ref.[4].In supersymmetric(SUSY)theories,the Higgs sector is extended to contain at least two isodoublets of scalarfields.In the Minimal Supersymmetric Standard Model(MSSM) this leads to the existence offive physical Higgs particles:two CP-even Higgs bosons h and H,one CP-odd or pseudoscalar Higgs boson A,and two charged Higgs particles H±[1].Besides the four masses,two additional parameters are needed:the ratio of the two vacuum expectation values,tgβ,and a mixing angleαin the CP-even sector. However,only two of these parameters are independent:choosing the pseudoscalar mass M A and tgβas inputs,the structure of the MSSM Higgs sector is entirely determined at lowest order.However,large SUSY radiative corrections[5]affect the Higgs masses and couplings,introducing new[soft SUSY-breaking]parameters in the Higgs sector. If in addition relatively light genuine supersymmetric particles are allowed,the whole set of SUSY parameters will be needed to describe the MSSM Higgs boson properties unambiguously.In this report we describe the program HDECAY1,which calculates the decay widths and branching ratios of Higgs bosons in the SM and the MSSM.It includes:•All decay channels that are kinematically allowed and which have branching ratios larger than10−4,y compris the loop mediated,the most important three body decay modes,and in the MSSM the cascade and the supersymmetric decay channels.•All relevant higher-order QCD corrections to the decays into quark pairs and to the quark loop mediated decays into gluons are incorporated in the most complete form[7].The largest part of the corrections to the heavy quark pair decay modes aremapped into running masses which have to be evaluated at the scale of the Higgs mass.The small leading electroweak corrections are also included.They become sizeable only in the large Higgs mass regime due to the enhanced self-interactions of the Higgs bosons.•Double off-shell decays of the CP-even Higgs bosons into massive gauge bosons which then decay into four massless fermions[8].These decays are important for masses close to M W or M Z.For larger masses,it is a sufficient approximation to switch offthese decays[which are CPU time consuming]and to allow for one on-shell gauge boson only.•All important below-threshold[three-body]decays:with off-shell heavy top quarks H0,H,A→t¯t∗→t¯bW−and H+→t∗¯b→b¯bW+;with one off-shell gauge boson H→W±∗H∓,H→Z∗A,A→Z∗h and H±→W±∗A,W±∗h;as well as the decays of H with one off-shell Higgs boson H→hh∗,AA∗.These three body decays can be rather important,especially in the MSSM[9](see also[10]).•In the MSSM,the complete radiative corrections in the effective potential approach with full mixing in the stop and sbottom sectors;it uses the renormalization group improved values of the Higgs masses and couplings,and the relevant leading next-to-leading-order corrections are also implemented[11].•In the MSSM,all the decays into SUSY particles when they are kinematically al-lowed.The decays into charginos and neutralinos are included in the most general case,and the decays to sleptons and squark pairs with sfermion mixing in the third generation sector[12].•In the MSSM,all SUSY particles are included in the loop mediatedγγand gg decay channels:charged Higgs bosons,chargino,slepton and squark[including mixing] loops in h,H→γγdecays,chargino loops in A→γγand squark loops in h,H→gg.In the gluonic decay modes the large QCD corrections for quark[13,14]and squark loops[15]are also included.The basic input parameters,fermion and gauge boson masses and their total widths, coupling constants and in the MSSM,soft SUSY-breaking parameters can be chosen from an inputfile.In thisfile severalflags allow to switch on/offor change some options[e.g. choose a particular Higgs boson,include/exclude the multi-body or SUSY decays,or include/exclude specific higher-order QCD corrections].The results for the many decay branching ratios and the total decay widths are written into several outputfiles with headers indicating the processes and giving the input parameters.The program is written in FORTRAN and has been tested on several machines:VAX stations under the operating system VMS and work stations running under UNIX.All the3necessary subroutines[e.g.for integration]are included.The program is lengthy[more than5000FORTRAN lines]but rather fast,especially if some options[as decays into double off-shell gauge bosons]are switched off.The rest of this report is organized as follows.In the next section we discuss the physical decay processes included in the program.We describe the parameters of the inputfile in Section3.In Section4,we present examples of outputfiles.Some comments and conclusions are given in Section5.2Decay Modes2.1Standard Modela)Decays to quarks and leptonsThe Higgs boson partial width for decays to massless quarks,directly coupled to the SM Higgs particle,is calculated including the O(α3s)QCD radiative corrections[16,17] in them Q(M H)and the strong coupling constantαs(M H)both defined at the scale of the Higgs boson mass.The quark masses can be neglected in the phase space and in the matrix element except for decays in the threshold region,where the next-to-leading-order QCD corrections are given in terms of the quark pole mass M Q[16].The relation between the perturbative pole quark mass(M Q)and the running m Q)at the scale of the pole mass can be expressed as[18]1+4π+K Q αs(M Q)MS massm Q(M Q)are adopted as starting points,because these are directly determined from QCD spectral sum rules[19]for the b and c quarks.Theflag NNLO(I)determines whether(I=1)the input running mass is related to the pole mass according to the eq.(1) or(I=0)using the simplified version with the K Q term neglected[in this case we denotethe pole mass by M pt2Q ].The input pole mass values and corresponding running massesare presented in Table1.The evolution from M Q upwards to a renormalization scaleµis given bym Q(M Q)c[αs(µ)/π]Q M pt2Q1.41GeV4.62GeV175.0GeVMS mass and the two different definitions of the pole masses.The strong coupling has been chosen asαs(M Z)=0.118and the bottom and charm mass values are taken from Ref.[19].with[20]c(x)= 99[1+0.895x+1.371x2]for M s<µ<M cc(x)= 2525[1+1.014x+1.389x2]for M c<µ<M bc(x)= 2323[1+1.175x+1.501x2]for M b<µ<M tc(x)= 77[1+1.398x+1.793x2]for M t<µFor the charm quark mass the evolution is determined by eq.(2)up to the scaleµ=M b, while for scales above the bottom mass the evolution must be restarted at M Q=M b. The values of the running b,c masses at the scaleµ=100GeV,characteristic for theHiggs mass,are typically35%(60%)smaller than the bottom(charm)pole masses M pt2b (M pt2).cThe program HDECAY includes the full massive NLO corrections close to the thresh-olds as well as the massless O(α3s)corrections far above the thresholds.The transition between both regions is provided by a linear interpolation as shown in Fig.1.Thus the result is optimized for the description of the mass effects in the threshold region and for the renormalization group improved large Higgs mass regime.The electroweak corrections to heavy quark and lepton decays in the intermediate Higgs mass range are small[21]and could thus be neglected,but the bulk of the effect [22]is included in the program.For large Higgs masses the electroweak corrections due to the enhanced self-coupling of the Higgs bosons are included,which however turn out to be small[23].In the case of t¯t decays of the Standard Higgs boson,the O(αs)QCD corrections are included according to[16].Below-threshold(three-body)decays H→t¯t∗→t¯bW−into off-shell top quarks may be sizeable[9]and thus are implemented.5Γ(H → bb) [MeV ]_M b = 4.62 GeV NLO massiveNNNLO (RG)M H [GeV ]8102030507010010-210-1110Figure 1:Interpolation between the full massive NLO expression (dashed line)for the b ¯b decay width of the Standard Higgs boson and the renormalization group improved NNNLO result (dotted line).The interpolated curve is presented by the full line.b)Decays to gluonsThe decay of the Higgs boson to gluons is mediated by heavy quark loops in the Standard Model;the partial decay width in lowest order is given in [24].QCD radiative corrections [13,14]are built up by the exchange of virtual gluons,gluon radiation from the internal quark loop and the splitting of a gluon into unresolved two gluons or a quark-antiquark pair.The radiative corrections are very large,nearly doubling the partial width.Since b quarks,and eventually c quarks,can in principle be tagged experimentally,it is physically meaningful to include gluon splitting g ∗→b c )in H →gg ∗→gb c )decays to the inclusive decay probabilities Γ(H →b ¯b +...)etc.[7].Separating this contribution generates large logarithms,which can be effectively absorbed by defining the number of active flavors in the gluonic decay mode in the input file of HDECAY by specifying the NF-GG parameter.The contributions of the subtracted flavors will automatically be added to the corresponding heavy quark decay modes.c)Decays to γγand ZγThe decay of the Higgs boson to two photons and to a photon and a Z boson,medi-ated by W and heavy fermion loops,are implemented according to [25].QCD radiative corrections are rather small [13,26]and thus neglected in the program.6d)Decays to W W/ZZ bosonsAbove the W W and ZZ decay thresholds the partial decay widths into pairs of on-shell massive gauge bosons are given in[27].Electroweak corrections are small in the intermediate mass range[28]and thus neglected in the program HDECAY.Higher order corrections due to the self-couplings of the Higgs particles are sizeable[29]for M H>∼400 GeV and are taken into account.Below the W W/ZZ threshold,the decay modes into off-shell gauge bosons are im-portant.With the input parameter ON-SH-WZ=1the program includes decays with one on-shell and one off-shell gauge boson[30],while for ON-SH-WZ=0decays with both off-shell are also calculated[8].The branching ratios for the latter reach the percent level for Higgs masses above about100(110)GeV for both W(Z)boson pairs off-shell.For higher masses,it is sufficient to allow for one off-shell gauge boson only,especially because the two virtual gauge boson option is CPU time consuming.2.2The Minimal Supersymmetric Standard ModelThe MSSM Higgs sector is implemented in HDECAY including the complete radiative corrections due to top/bottom quark and squark loops within the effective potential ap-proach.Next-to-leading order QCD corrections and the full mixing in the stop and sbottom sectors are incorporated.The Higgs boson mass spectrum,the mixing angles and Higgs boson couplings are calculated using the approximate formulae of M.Carena, M.Quiros and C.E.M.Wagner[11].The basic parameters describing the effective Higgs potential at higher orders are specified in the inputfile.The formulae for the decay widths at tree-level have been derived in Ref.[31].a)Decays to quarks and leptonsThe calculation of the partial decay widths of scalar neutral Higgs bosons h and H to fermions in the MSSM is performed using the same approximations and options as in the Standard Model case with properly modified Higgs boson couplings.For massless quarks the QCD corrections for scalar,pseudoscalar and charged Higgs boson decays are implemented analogously to the SM case[16,17],i.e.the Yukawa and QCD couplings are evaluated at the scale of the Higgs boson mass.In the threshold regions mass effects play a significant role,in particular for the pseu-doscalar Higgs boson,which has an S-wave behavior∝βas compared with the P–wave suppression∝β3for CP-even Higgs bosons[β=(1−4m2f/M2Φ)1/2is the velocity of the decay fermions].The QCD corrections to the partial decay width of the CP-odd Higgs boson A into heavy quark pairs are taken from Ref.[16],and for the charged Higgs par-ticles from Ref.[32].The transition from the threshold region,involving mass effects, to the renormalization group improved large Higgs mass regime is provided by a smooth linear interpolation analogous to the SM case.7Below the t¯t threshold,decays of the neutral Higgs bosons into off-shell top quarks are sizeable,thus modifying the profile of the Higgs particles significantly.Off-shell pseu-doscalar branching ratios reach a level of a few percent for masses above about300GeV for small tgβvalues.Similarly,below the t¯b threshold,off-shell decays H+→t∗¯b→b¯bW+ are important,reaching the percent level for charged Higgs boson masses above about100 GeV for small tgβvalues.These decays are incorporated according to the expressions from Ref.[9].b)Decays to gluonsSince the b quark couplings to the Higgs bosons may be strongly enhanced and the t quark couplings suppressed in the MSSM,b loops can contribute significantly to the Higgs-gg couplings so that the approximation M2Q≫M2H cannot be applied any more for MΦ<∼150GeV,where this decay mode is important.Nevertheless,it turns out a posteriori that this is an excellent approximation for the QCD corrections in the range, where these decay modes are relevant.The LO width for h,H→gg is generated by quark and squark loops with the latter contributing significantly for Higgs masses below about 400GeV[15].The partial decay widths are calculated according to Ref.[13,14].The bottom and charmfinal states from gluon splitting can be added to the corresponding b¯b and c¯c decay modes,as in the SM case,by defining NF-GG=3in the inputfile.c)Decays intoγγand ZγThe decays of the neutral Higgs bosons to two photons and a photon plus a Z boson are mediated by W and heavy fermion loops,as in the Standard Model,and in addition by charged Higgs,sfermion and chargino loops;the partial decay widths are calculated according to Ref.[13].QCD corrections to the quark and squark loop contributions are small[13,26]and thus neglected in the program.d)Decays to W W/ZZ gauge bosonsThe partial widths of the CP-even neutral MSSM Higgs bosons into W and Z boson pairs are obtained from the SM Higgs decay widths by rescaling with the corresponding MSSM couplings.They are strongly suppressed[due to kinematics in the case of h and reduced couplings for the heavy H],thus not playing a dominant role as in the SM case.e)Decays to Higgs boson pairsThe heavy CP-even Higgs particle can decay into a pair of light scalars as well to a pair of pseudoscalar Higgs bosons,H→hh and H→AA.While the former is the dominant decay mode of H in the mass range2M h<M H<2m t for small values of tgβ,the latter mode occurs only in a marginal area of the MSSM parameter space.For large values of tgβ,these decays occur only if M A∼M h<∼M H/2,corresponding to the lower end of the heavy Higgs mass range,and have branching ratios of50%each.Since the Hb¯b Yukawa coupling is strongly enhanced for large tgβ,below threshold decays H→hh∗,AA∗with A,h→b¯b are included[9].The lightest CP-even Higgs particle h can also decay into8pseudoscalar Higgs pairs for values tgβ∼1and M h<50GeV;however this area of the parameter space is already ruled out by present data[3].f)Decays to W/Z and Higgs bosonsThe Higgs bosons can also decay into a gauge boson and a lighter Higgs boson.The branching ratios for the two body decays A→hZ and H+→W+h may be sizeable in specific regions of the MSSM parameter space[small values of tgβand below the tt/tb thresholds for neutral/charged Higgs bosons].The expressions of the decay widths are given in e.g.Ref.[9].Below-threshold decays into a Higgs particle and an off-shell gauge boson turned out to be rather important for the heavy Higgs bosons of the MSSM.Off-shell A→hZ∗decays are important for the pseudoscalar Higgs boson for masses above about130GeV for small tgβ.The decay modes H±→hW∗,AW∗reach branching ratios of several tens of percent and lead to a significant reduction of the dominant branching ratio intoτνfinal states to a level of60%to70%for small tgβ.In addition,three-body H→AZ∗and H→H+W−∗,which are kinematically forbidden at the two-body level,can be sizeable for small M A values.The partial decay widths for these three-body decays are calculated according to the formulae given in Ref.[9].g)Decays to charginos and neutralinosThe lightest charginos and neutralinos are expected to have masses of the order of the Z boson mass.The heavy CP-even,CP-odd and charged Higgs bosons of the MSSM can therefore decay into these states[31].Present experimental bounds on the SUSY particle masses,do not allow decays for SUSY decay modes of the lightest CP-even Higgs boson h,except maybe for the decays into a pair of the lightest neutralinos.These decays,the partial widths of which can be found in Ref.[12],are included in the program.The masses of charginos and neutralinos as well as their couplings to the Higgs bosons depend on three extra parameters[in addition to those describing the Higgs sector at the tree-level]:the Higgs-Higgsino mass parameterµ[which also enters the radiative correc-tions in the Higgs sector],the Bino and Wino mass parameters M1and M2.Assuming a common gaugino mass at the unification scale,the parameter M1is related to M2by the GUT relation M1=5lead to very large decay widths.The sfermions masses and couplings to Higgs bosons will depend on three extra pa-rameters[in addition to tgβand M A]for each generation:the left-and right-handedsoft SUSY-breaking mass parameters M˜f L and M˜f R,the Higgs mass parameterµandthe trilinear coupling A f.The trilinear couplings are important only in the case of the third generation sfermions,and only A t,A b and Aτneed to be introduced.The latter couplings[at least A t and A b]also contribute to the radiative corrections to the Higgs sector.For the SUSY breaking scalar masses,we assumed degeneracy in thefirst and second generation and treated the third generation separately2.While the masses of the left-and right-handed1st/2nd generation sfermions correspond to the physical sfermion masses,in the third generation mixing between thesefields needs to be included to obtain the physical eigenstates[35].The masses of the sfermions,as well as their couplings to Higgs bosons,including the mixing in the generation are calculated in the subroutine SFERMION.The decay widths are calculated in the main subroutine using the formulae given in Ref.[12].The QCD corrections to squark decays[in particular stop and sbottom decays]have been calculated in Ref.[37]but are not yet implemented in the program.3How to Run HDECAY:Input FileThe HDECAY program is self-contained with all necessary subroutines included.In addition to the source code of the program HDECAY,an inputfile,defined as unit98, is needed from which the program reads the input parameters.The name of this input file can be specified in thefirst OPEN statement of HDECAY.It should be noted that the input numbers must not start before the equality signs in each corresponding line. The inputfile contains the following parameters[all non-integer parameters are in double precision and the mass parameters as well as the decay widths and the trilinear couplings are in GeV]:HIGGS:ratio of the vacuum expectation values in the MSSM,tgβ,the second basic input of the model;the program is suitable only for values tgβ>∼1.:end value of the Higgs mass in GeVNMA:strong coupling constant at the scale M Z:αS(M Z)MSBAR(1)MS mass of the strange quark at the scale Q=1GeVMC:bottom quark pole massMT:τlepton massMMUON:inverse QED coupling constant:α−1(0)GF:total decay width of the W bosonGAMZ:Z boson massMW:CKM parameter V usVCB:ratio of the CKM parameters V ub/V cb.MU:SUSY breaking gaugino mass parameter M2MSL1:SUSY breaking mass parameter for1st/2nd generation right-handed charged sleptons,M˜eRMSQ1:SUSY breaking mass parameter for1st/2nd generation right-handed down-type squarks,M˜d RMSL:SUSY breaking mass parameter for3rd generation right-handed sleptons,M˜τR MSQ:SUSY breaking mass parameter for right-handed stops,M˜tRMDR:SUSY breaking trilinear coupling forτsleptons,AτAU:SUSY breaking trilinear coupling for sbottoms,A bNNLO(M)MS masses=1:use O(α2s)formula for the quark pole masses→:integer=0:include three-body decays with off-shell tops,Higgs and gauge bosons=1:exclude three-body decays with off-shell tops,Higgs and gauge bosonsON-SH-WZ:integer=0:calculate:integer=0:include decays into and loops of supersymmetric particles=1:exclude decays into and loops of supersymmetric particlesINDIDECintegernumber of lightflavors included in the decaysΦ→gg∗→gq¯q(NF-GG=3,4or5).12The current values of the SM parameters[fermion masses,gauge boson masses and total widths,coupling constants,CKM angles]are given in Tab.2,where an example of the inputfile is displayed.The entire Higgs sector of the MSSM isfixed once the parameterstgβ,M A,µ,M2,the masses M˜L L ,M˜E R,M˜U L,M˜U R,M˜D Rand the trilinear couplings Aτ,A tand A b are specified.Some examples for these values are shown in Tab.2.4Results of Test Run:Output FilesThe output is written to severalfiles.Only the outputfiles of the chosen HIGGS bo-son(s)are printed,and they contain all decay branching ratios and the total decay width, except for the decays to SUSY particles[if OFF-SUSY=0]where only the sums of the branching ratios into charginos,neutralinos,sleptons and squarks are printed,if theflag INDIDEC=0;only for INDIDEC=1all individual branching ratios are printed in addi-tional outputfiles.For convenience,an outputfile br.input is printed in which the input parameters are given.Below we will describe the outputfiles in the SM and the MSSM [also with the option for SUSY decays switched on]and list all the decay channels which we have considered for the various Higgs bosons.4.1Standard Model Higgs bosonFor the SM Higgs boson,in addition to thefile br.input for the input parameters,two outputfiles are printed in which the total decay width and the following11branching ratios are given[notice that we have put the decays into fermions and gauge bosons into two differentfiles]br.sm1:M H0,BR(b¯b),BR(τ+τ−),BR(µ+µ−),BR(s¯s),BR(c¯c),BR(t¯t) br.sm2:M H0,BR(gg),BR(γγ),BR(γZ),BR(W W),BR(ZZ),Γtot H0For the example of inputfile shown in Tab.2,one obtains the two outputs given in Tab.3. The various branching ratios and the total decay width are shown in Fig.2.4.2MSSM without SUSY decaysAs discussed earlier,the two basic inputs of the program for the MSSM Higgs sector are tgβand M A.Once these parameters arefixed,all the other Higgs masses and couplings are determined at tree-level.However,subleading effects due to squark mixing[mainly the parameters A t,b andµ]will alter these values.For the lightest MSSM Higgs boson hHIGGS=0TGBET= 1.5D0MABEG=100.D0MAEND=500.D0NMA=5ALS(MZ)=0.118D0MSBAR(1)=0.190D0MC= 1.42D0MB= 4.62D0MT=175.D0MTAU= 1.7771D0MMUON=0.105658389D01/ALPHA=137.0359895D0GF= 1.16639D-5GAMW= 2.080D0GAMZ= 2.490D0MZ=91.187D0MW=80.33D0VUS=0.2205D0VCB=0.04D0VUB/VCB=0.08D0MU=300.D0M2=200.D0MSL1=500.D0MER1=500.D0MQL1=500.D0MUR1=500.D0MDR1=500.D0MSL=500.D0MER=500.D0MSQ=500.D0MUR=500.D0MDR=500.D0AL=1500.D0AU=1500.D0AD=1500.D0NNLO(M)=0ON-SHELL=0ON-SH-WZ=0IPOLE=0OFF-SUSY=1INDIDEC=0NF-GG=5Table2:Example of the inputfile.14Γ(H) [GeV ]M H [GeV ]50100200500100010-310-210-1110102BR(H)bb _τ+τ−cc _ggWW ZZtt-γγZ γM H [GeV ]50100200500100010-310-210-11Figure 2:Total decay width Γ(H )in GeV and the main branching ratios BR (H )of the Standard Model Higgs decay channels,using the inputs of Tab.2.15MHSM BB TAU TAU MU MU SS CC TT___________________________________________________________________________100.0000.81190.7926E-010.2752E-030.6048E-030.3698E-010. 200.0000.2596E-020.2884E-030.1000E-050.1928E-050.1177E-030. 300.0000.6082E-030.7274E-040.2521E-060.4513E-060.2754E-040.5293E-04 400.0000.2283E-030.2869E-040.9940E-070.1694E-060.1033E-040.1376 500.0000.1183E-030.1542E-040.5342E-070.8772E-070.5347E-050.1936MHSM GG GAM GAM Z GAM WW ZZ WIDTH___________________________________________________________________________100.0000.5807E-010.1532E-020.4654E-040.1025E-010.1046E-020.2598E-02 200.0000.8219E-030.5241E-040.1753E-030.73500.2609 1.428 300.0000.5674E-030.1289E-040.5670E-040.69130.30738.510 400.0000.7532E-030.3192E-050.1935E-040.58720.274128.89 500.0000.5476E-030.4897E-060.7666E-050.54500.260767.53 Table3:The two outputfiles in the SM with the inputs of Tab.2.For the heavy CP-even MSSM Higgs boson H,there are less possibilities than for the H bo-son:due to CP-invariance,the pseudoscalar A does not couple to gauge and Higgs boson pairs.The10decay channels are printed in the outputfiles as followsbr.a1:M A,BR(b¯b),BR(τ+τ−),BR(µ+µ−),BR(s¯s),BR(c¯c),BR(t¯t) br.a2:M A,BR(gg),BR(γγ),BR(γZ),BR(hZ),Γtot AFor the charged MSSM Higgs bosons H±。