From Hadronic Parity Violation to Parity-Violating Electron Scattering and Tests of the Sta

a r X i v :h e p -p h /9608383v 2 13 J a n 1997UR-1384MADPH-96-968Parity Violation in Bottom Quark Pair Productionat Polarized Hadron CollidersChung Kao a,b ,David Atwood c and Amarjit Soni d a Department of Physics and Astronomy,University of Rochester,Rochester,NY 14627,USA b Department of Physics,University of Wisconsin,Madison,WI 53706,USA c Theory Group,CEBAF,Newport News,VA 23606,USA d Department of Physics,Brookhaven National Laboratory,Upton,NY 11973,USA Abstract Parity violation induced by the chromo-anapole form factor of the bottom quark,generated from weak corrections,is studied in polarized hadron collisions.The forward-backward asymmetry in the bottom quark pair production at polarized pp and p ¯p colliders is evaluated in the Standard Model and in a Two Higgs Doublet Model to examine the effects of parity violation.In the models studied,promising results are found for polarized p ¯p colliders.1IntroductionThe large production cross section of bottom quark pairs(b¯b)at polarized hadron col-liders[1,2]coupled with the relatively long lifetime of the b-quark,implies that detailed experimental study of the properties of the b-quark at those facilities could also be very useful.Since the CKM mixing angle V tb is close to one,the b quark couples rather readily to the virtual top quark in loop diagrams.Now the top quark is so heavy(m t∼175GeV) [3,4]that the b-quark becomes very sensitive to electroweak radiative corrections as these corrections often tend to grow with the virtual quark mass[5].Precision studies of the b’s are thus very useful in testing the Standard Model(SM)and in searching for new physics.In the hadronic environment,while the production cross sections are high,a quantitative understanding of the effects of QCD can be a very difficult challenge.For this reason,in testing the SM and in searching for clues of new physics,it is perhaps better to focus on observables that tend to be robust to QCD corrections.For that reason,in general, the production cross section is not a good observable.We propose to focus instead on signatures of parity violation in b-quark production since QCD corrections cannot generate parity violation.Parity violating asymmetries that are ratios of cross-sections should be less sensitive to QCD corrections as well as to the uncertainties in the parton distribution functions.Furthermore,in study of parity violation,one may be able to make use of polarized incident p(¯p)beams[6].We will concentrate on one type of parity violating observable,that is the forward-backward asymmetry.In its differential form,it is defined as:dσF/dM b¯b−dσB/dM b¯bδA(M b¯b)≡two sources of contributions to such a parity violating observable.These are the chromo-anapole form factor of the gb¯b vertex(note g≡gluon)and the tree level electroweak process q¯q→Z→b¯b.The latter contribution(Z exchange)is significant only when the invariant mass(M b¯b)of the b¯b pair is close to the Z mass(M Z).It can be removed,if necessary,by imposing an appropriate cut on the M b¯b.Thus,the chromo-anapole form factor is a very important contributor to the parity violating signal and consequently it is our primary focus.Recently,several suggestions have been made to study parity violation asymmetries in polarized hadron collisions for(1)the production of one jet,two jets,and two jet plus photon in the SM[7];(2)the production of W±and Z in the SM[8];and(3)the inclusive production of one jet with a new handed interaction between subconstituents of quarks [9].These works primarily deal with interference of electroweak and strong interactions on light quarks.In this Letter,we present thefirst study on parity violation generated from one loop weak corrections to bottom quark pair production at polarized hadron colliders.The key difference with the works in Refs.[7,8,9]is,as alluded to in the opening paragraph,that the b¯b pair in thefinal state in our study is a very sensitive tool of the effects of the top quark which in turn is sensitive to non-standard effects.Specifically,we will evaluate the forward-backward asymmetry in the bottom quark pair production at polarized pp and p¯p colliders in the Standard Model and in a Two Higgs Doublet Model to examine the effects of parity violation from the interactions of b¯b with spin-1and spin-0fields.2Form FactorsLet us write the gb¯b vertex as−ig s¯u(p1)T aΓµv(p2)(2)where g s=the strong coupling,T a=the SU(3)matrices,u(p1)and v(p2)are the Dirac spinors of b and¯b with outgoing momenta p1and p2and k=p1+p2is the momentum of the gluon.At the tree levelΓµ0=γµ.The1-loop vertex function can be expressed asΓµ=γµ[A(k2)−B(k2)γ5]+(p1−p2)µ[C(k2)−D(k2)γ5]+(p1+p2)µ[E(k2)−F(k2)γ5](3)Current conservation demands that E=0and B=−k2F(k2)/2m b,where k=p1+p2and k2=M2=ˆs in the b¯b center of mass(CM)frame.Applying the Gordon identities we can b¯bre-writeΓµ=F1(k2)γµ−F2(k2)iσµνkν+a(k2)γνγ5(k2gµν−kµkν)+d(k2)iσµνkνγ5(4) where F1(k2)=A(k2)+2m b C(k2),F1(0)=the chromo-charge;F2(k2)=C(k2),F2(0)= the anomalous chromo-magnetic moment;a(k2)=−B(k2)/k2=F/(2m b),a(0)=chromo-anapole moment;d(k2)=D(k2),and d(0)=the chromo-electric dipole moment.In the SM,the dominant one loop weak corrections that contribute to the chromo-anapole moment arise from diagrams with the W+and its Goldstone counterpart,the G+.In many extensions of the SM,e.g.in models which contain more than one doublets of Higgs,there are charged Higgs bosons(H±)contributing to the chromo-anapole form factor of fermions at the one-loop order.As is well known the simplest of such extensions consists of two Higgs doublets[10]φ1andφ2with vacuum expectation values(VEVs)v1 and v2.After symmetry breaking,there remainfive physical Higgs bosons[11]:a pair of singly charged Higgs bosons H±,two neutral CP-even scalars H(heavier)and h(lighter), and a neutral CP-odd pseudoscalar A.The ratio of the two VEVs is usually expressed as tanβ≡v2/v1.In our analysis,we have considered such a Two Higgs Doublet Model(THDM)with the Yukawa interactions of model II[12],which is required in the minimal supersymmetric model(MSSM)1.[11]In this model,one doublet(φ1)couples to down-type quarks and charged leptons while the other(φ2)couples to up-type quarks and neutrinos.The one loop weak corrections from diagrams with the W+,the G+and the H+,yield dominant contribution to the b quark anapole moment from the virtual top quark in the loop.In our calculations of these corrections we will set V tb=1and also we will ignore CP violating effects.We have employed the’t Hooft–Feynman gauge for loop calculations with M G±= M W.The forward-backward asymmetry in b¯b production is primarily driven by Re B(k2) which is related to the chromo-anapole form factor(a(k2))via B(k2)=−k2a(k2).There-fore,in Fig.1we present Re B(k2)coming separately from diagrams with the G±(B G),the W±(B W)and the Z as well as the total contribution in the SM.As an illustration of a beyond the SM effect,we also show Re B(k2)for THDM for M H+=200GeV and vari-ous values of tanβ.The Z boson exchange contribution to the b-chromo-anapole moment is very small since the coupling product2g b V g b A is very small.The form factor Re B(k2)is enhanced near k2∼4m2t,where k2=ˆs=M2b¯b,due to the t¯t threshold which appears in dia-grams with charged boson(i.e.W±or H±)exchanges.Since B(k2)=−k2a(k2)=−ˆs a(ˆs), its value is expected to grow with M b¯b.From Fig.1we see that numerically this increase sets in for M b¯b∼>500GeV.In the THDM,the form factor B(k2)gets an additional contribution,B H(k2),from the charged Higgs boson.Clearly B H is a function of M H+and tanβ,being proportional to cot2β{1−[(m b/m t)tan2β]2}.Therefore,it has the same sign as B G for tanβ<m t/m b.Thus the effects of parity violation areenhanced in the THDM if tan βis less than m t /m b ,the B H vanishes and the total B (k 2)becomes that of the SM.3Forward Backward AsymmetryLet us define the cross section for the sub-process,q ¯q →b ¯b ,in each helicity state of quarks in the initial state asˆσλ1λ2≡ˆσ(q λ1¯q λ2→b ¯b )(5)where λ1,2represents a right-handed (R )or a left-handed (L )helicity of the quark and the antiquark.The cross sections in the forward (0≤θ≤π)and the backward (−π≤θ≤0)directions are defined asˆσF λ1λ2≡ 10d ˆσλ1λ2dzdz ˆσλ1λ2=ˆσF λ1λ2+ˆσB λ1λ2∆ˆσλ1λ2=ˆσF λ1λ2−ˆσB λ1λ2(6)where z =cos θ,with θbeing the scattering angle of the b in the b ¯b center of mass frame,ˆσis the total cross section of the q ¯q subprocess and ∆ˆσis the difference of the cross sections in the forward and the backward directions of the subprocess.(Note that variables in the CM frame of the q ¯q subprocess are denoted with a ˆon top of them).The tree level expressions for these cross sections areˆσ0RL =ˆσ0LR=g 4ss )ˆσ0LL =ˆσ0RR =0(7)At the tree level,the difference of the cross sections in the forward and backward directions is zero in each helicity state of q ¯q because parity is conserved in QCD.The one loop weak corrections to the q¯q cross section is ˆσ1RL=ˆσ1LR=g4sˆs)+Re(C)(m b)(−1+4m2b18πˆsβ2[Re(B)](9)whereβ=dx1dx2=ˆσRL[q R(x1,ˆs)¯q L(x2,ˆs)+q R(x2,ˆs)¯q L(x1,ˆs]+ˆσLR[q L(x1,ˆs)¯q R(x2,ˆs)+q L(x2,ˆs)¯q R(x1,ˆs]+ˆσRR[q R(x1,ˆs)¯q R(x2,ˆs)+q R(x2,ˆs)¯q R(x1,ˆs]+ˆσLL[q L(x1,ˆs)¯q L(x2,ˆs)+q L(x2,ˆs)¯q L(x1,ˆs](10) where x1and x2are momentum fractions of the partons in the initial beam.Parity violation can be studied at hadron colliders by using polarized initial beams, e.g.p R p L or p R¯p L etc.Let us consider two hadron colliders with polarized beams(a)p R p L and(b)p R¯p L.With polarized pp or p¯p beams,we can define q+i(x,ˆs)[q−i(x,ˆs)]to be the probability density[13]for a quark offlavor i and momentum fraction x with a helicity of the same[opposite]sign as the helicity of the proton.The differential cross section,dσRL in polarized p R p L collisions becomedσRLdx1dx2=ˆσRL[q+(x1,ˆs)¯q+(x2,ˆs)+q−(x2,ˆs)¯q−(x1,ˆs) +q−(x1,ˆs)¯q−(x2,ˆs)+q+(x2,ˆs)¯q+(x1,ˆs)]σRL= 1x min1dx1 1x min2dx2dσRLdx1dx2=−δσLRdx1dx2(12)At high energy,parity violation from chromo-anapole form factor is expected to increase with M b¯b.It is therefore useful to examine the differential forward-backward asymmetry given in Eq.1.The numerator has contribution only from q¯q→b¯b,while the denominator has contributions from both q¯q→b¯b and gg→b¯b.Gluon fusion produces a large number of b¯b pairs,which tend to contribute significantly to the denominator of Eq.1thus reducing the signal for the parity violating asymmetry from q¯q in pp collisions.In p¯p collisions,the antiquark density is greatly enhanced,therefore,parity violation signals from q¯q→b¯b is much larger in p¯p than in pp collisions at the same energy.This differential asymmetry is presented in Figures2and3for polarized p R p L and p R¯p L collisions at several values of energy.The parity violation signal peaks at the M b¯b=2m t in the differential of forward-backward asymmetry versus M b¯b.Also shown is the same asymmetry in q¯q→Z→b¯b;it dominates if M b¯b is close to M Z,but becomes negligible for|M b¯b−M Z|>10GeV.The integrated forward-backward asymmetry is defined asA≡N F−N BσF+σBN=Lσ(13)where N F and N B are the number of b¯b pairs in the forward and the backward directions; and L is the integrated luminosity.The statistical uncertainty(∆A)and the statistical significance(N S)of the integrated asymmetry are∆A≃1N F+N B(14)N S≡A/∆A.(15) The difference(∆σ)and the total(σ)of the cross sectionsσF andσB with one loop weak corrections,as well as the integrated asymmetry(A)and its statistical significance (N S)are presented in Table1for an integrated luminosity of10fb−1and100fb−1.For √ˆs∼<2m t.In any case,it is very unlikely that the contribution to the forward backward asymmetry from such a source will cancel away the q¯q contribution for all values of M b¯b.2)It would clearly be extremely interesting to consider these parity violating effects in other extensions of the SM;in particular in the MSSM.As we noted before,in MSSM, there will be additional loop contributions not contained in a THDM that could enhance the asymmetry[14].4Conclusions√To summarize,at a hadron collider with polarized pp ands≥1000GeV and enough integrated luminosity,it might be possible to observe parity violation signals from SM weak corrections in b¯b production.In the THDM with Model II Yukawa interactions,the chromo-anapole form factor of the bottom quark generated from leading weak corrections is enhanced for tanβclose to one.It is enhanced by the factor cot2βfor tanβless than one.Therefore,the signal of parity violation in b¯b production is greatly enhanced for tanβ∼<1and M H+less than about300GeV.2The study of parity violation in b¯b production might provide a good opportunity to study new interactions between the third generation quarks and(charged)spin-0as well as spin-1 bosons.AcknowledgementsWe are grateful to Stephane Keller and JeffOwens for providing polarized parton distri-bution functions and for beneficial discussions. C.K.and D.A.would like to thank Bill Bardeen and the Theoretical Physics Department of Fermilab for hospitality where part of this research was completed. A.S.would like to thank Mike Tannenbaum for inter-esting discussions.This research was supported in part by the the U.S.Department of Energy Grant Nos.DE-FG05-87ER40319(Rochester),DE-FG02-95ER40896(Wisconsin), DE-AC05-84ER40150(CEBAF),and DE-AC-76CH00016(BNL),and in part by the Uni-versity of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation.References[1]A.P.Contougouris,S.Papadopoulas and B.Kamal,Phys.Lett.B246(1990)523.[2]M.Karliner and R.Robinett,Phys.Lett.B324(1994)209.[3]F.Abe et al.,[CDF],Phys.Rev.Lett.74(1995)2626.[4]S.Abachi et al.,[D∅],Phys.Rev.Lett.74(1995)2632.[5]See,e.g.,W.S.Hou,R.S.Willey and A.Soni,Phys.Rev.Lett.58(1987)1608.[6]G.Bunce et al.,Particle World3,1(1992);See also,Proceedings of the PolarizedCollider Workshop,Penn State University1990,edited by J.Collins,S.Heppelmann, and R.Robinett,AIP conf.Proceedings No.223(AIP,New York,1991).[7]H.-Y.Cheng,M.-L.Huang and C.F.Wai,Phys.Rev.D49(1994)1272.[8]C.Bourrely and J.Soffer,Nucl.Phys.B423(1994)329.[9]P.Taxil and J.M.Virey,Phys.Lett.B364(1995)181.[10]H.M.Georgi,Hadronic J.1(1978)155.[11]J.F.Gunion,H.E.Haber,G.L.Kane and S.Dawson,The Higgs Hunter’s Guide,Addison-Wesley,Redwood City,CA(1990)and references therein.[12]J.F.Donoghue and L.-F.Li,Phys.Rev.D19(1979)945;L.Hall and M.Wise,Nucl.Phys.B187(1981)397.[13]S.Keller and J.F.Owens Phys.Rev.D49(1994)1199.[14]D.Atwood,C.Kao and A.Soni,work in progress.[15]C.Kao,Phys.Lett.B348(1995)155.10TablesTable1.The difference(∆σ)and the total(σ)of cross sectionsσF andσB,and the asymmetry of p R¯p L→b¯b+X as defined in Eq.13generated by weak corrections in(a)√the SM and(b)the THDM with M H+=200GeV and tanβ=1,for√s=1TeV with M b¯b>200GeV and√(a)SM500-0.13012481.2-0.0630.91 2.91000-0.08122.917.2-0.20 1.3 4.12000-0.12216.633.3-0.25 1.7 5.5(b)THDM500-0.15612481.2-0.076 1.1 3.41000-0.10622.917.2-0.27 1.7 5.32000-0.16316.733.3-0.33 2.37.3FiguresFig.1.The real part of the chromo-anapole form factor B(ˆs)as a function of M b¯b from(a) the diagrams with G+(dash),the W+(dot-dash),the Z(dot)and the SM Total;and the THDM Total for tanβ=0.5,1,3,10and35,with(b)m H+=200GeV and(c)m H+=400 GeV.Note thatˆs=M b¯b.Fig.2.The differential forward-backward asymmetry(δA)defined in Eq.1versus M b¯b,in√s=1000GeV and(c)√polarized p R p L collisions for(a)√s=2000s=500GeV(b)GeV.This asymmetry has been evaluated using the(total)chromo-anapole form factor from leading weak corrections in the SM as well as in the THDM for m H+=200GeV and tanβ=0.5,1,and35.12。

高三英语统计学分析单选题60题及答案1.The average score of a class is calculated by adding all the scores and dividing by the number of students. This is an example of _____.A.meanB.medianC.modeD.range答案：A。

本题考查统计学基本概念。

A 选项mean（平均数）是通过将所有数据相加再除以数据个数得到的，符合题干描述。

B 选项median（（中位数）是将数据从小到大排列后位于中间位置的数。

C 选项mode（众数）是数据中出现次数最多的数。

D 选项range（极差）是数据中的最大值与最小值之差。

2.In a set of data, if there is a value that occurs most frequently, it is called the _____.A.meanB.medianC.modeD.range答案：C。

A 选项mean 是平均数。

B 选项median 是中位数。

C 选项mode 众数是出现次数最多的值，符合题意。

D 选项range 是极差。

3.The middle value in a sorted list of data is called the _____.A.meanB.medianC.modeD.range答案：B。

A 选项mean 是平均数。

B 选项median 中位数是排序后位于中间的数，符合题干描述。

C 选项mode 是众数。

D 选项range 是极差。

4.The difference between the highest and lowest values in a set of data is known as the _____.A.meanB.medianC.modeD.range答案：D。

a r X i v :h e p -e x /9901032v 1 22 J a n 1999SLAC-PUB-8046December 1998PHYSICS RESULTS FROM SLD USING THE CRID ∗David MullerRepresenting The SLD Collaboration ∗∗Stanford Linear Accelerator CenterStanford University,Stanford,CA 94309Abstract We review recent Z 0physics results from SLD that use the Cherenkov Ring Imaging Detector for charged particle identification.The performance of the detector and likeli-hood method are described briefly.Several hadronization measurements are presented,in-cluding identified hadron production in events of different primary flavors,leading hadron production,and new correlation studies sensitive to details of both leading and nonleading hadron production.Identified K ±have been used in conjunction with precision vertexing to study charmless and doubly charmed B -hadron decays.This combination has also been used to tag b ,¯b ,c and ¯c jets,yielding precise measurements of B 0-¯B 0mixing and of the asymmetric couplings A b and A c .Identified K ±and Λ0/¯Λ0have been used to tag s and ¯s jets,yielding a measurement of A s .The clean identified particle samples provided efficiently by the CRID allow the purities of these tags to be measured from the data,an essential ingredient for precision physics.Presented at the 3rd International Workshop on Ring Imaging Cherenkov Detectors,15–20November 1998,Ein-Gedi,Israel.∗Work supported in part by Department of Energy contract DE-AC03-76SF00515.1.IntroductionThe SLD experiment[1]studies Z0bosons produced in e+e−annihilatons at the SLAC Linear Collider(SLC).A carrier of the electroweak interaction,the Z0boson decays into a fermion-antifermion(f¯f)pair with probability predicted by the Standard Model(SM) electroweak couplings of the Z0to fermion f.The parity violation in this decay leads to an asymmetric distribution of the polar angle between the outgoing f and the incoming e−,which depends strongly on the e+and e−polarizations.The SLC electron beam is longitudinally polarized to a magnitude of∼73%with a sign determined randomly for each beam pulse.A key aspect of the SLD physics program is the measurement of total and asymmetric couplings,R f and A f,for as many of the fundamental fermions f as possible.Measuring A f requires both identifying Z0→f¯f events and determining the direction of the outgoing f(as opposed to¯f),which is challenging for the quarks,f=u,d,s,c,b,as they appear as jets of particles.Z0→b¯b and c¯c events can be identified by modern vertex detectors, using the3(1)mm averageflight distance of the leading B(D)hadron in each b(c)jet. Quantities used to distinguish b(c)from¯b(¯c)jets include the total charge of vertices or jets,and the charge of identified leptons or reconstructed D mesons.Thefirst two methods suffer from low analyzing power,and the other two from low efficiency.The charge of identified kaons is foreseen as a powerful method in futureB physics experiments,and we have recently pioneered its use for both b and c jets using our Cherenkov Ring Imaging Detector.The purity of aflavor tag can be measured from the data in e+e−annihilations using the anticorrelation between the f and¯f in the event.Lightflavor(u,d,s)jets are identifiable using their leading particles,and early work in this area is promising.We have used high-momentum strange particles to tag s and¯s jets,measured the tag purities from the data,and made a measurement of A s.We are studying ways to saparate u,¯u,d and¯d jets.The tagging of lightflavors would have a wide range of applications in high energy physics,from deep inelastic scattering,to jets from hadron-hadron collisions and studies of the decays of W-bosons,top quarks,Higgs bosons,and any new particle that is discovered.In addition,the hadronic event samples at the Z0are of unprecendented size and pu-rity,providing a unique opportunity to study the structure of hadronic jets and the decays of B and D hadrons in great detail.Jet formation is in the realm of non-perturbative QCD and is not understood quantitatively.The empirical understanding of jet structure is essential as jets are(will be)part of the signal for decays of W±bosons,t quarks(any undiscovered heavy objects),as well as the background for these and other processes. Isolated jets have been identified with partons in order to make a number of tests of perturbative QCD.QCD tests,searches for new physics,and conventional physics studies would be more sensitive if we could distinguish jets of different origins(gluons,quarks,an-tiquarks).Jet structure in terms of inclusive properties of charged tracks has been studied extensively,however more theoretical and experimental input is needed,especially in the area of identified and reconstructed particles.In particular,the study of leading particlesis needed for the development of light-flavor jet tags.Decays of B0and B+mesons have been studied extensively by experiments operating at theΥ(4S).The properties and mixture of B hadrons produced at the Z0differ consid-erably from those at theΥ(4S),providing a number of opportunities for complementary studies of B hadron decays[2],especially those involving identified particles for which the Υ(4S)experiments have limited momentum coverage.To study this wide range of physics,the SLD includes a Cherenkov Ring Imaging Detector(CRID)designed to identifyπ±,K±and p/¯p over most of the momentum range,and leptons at low momentum,complemeting the electromagnetic calorimeter and muon detectors.The CRID design and performance are summarized in sec.2.We then present a number of physics results in the areas of jet structure(sec.3)and physics withflavor-tagged jets(sec.4).Two unique studies[3]of B-hadron decays that benefit from SLD’s excellent vertexing and particle identification are described separately in these proceedings[2].2.SLD CRID PerformanceThe SLD CRID design and hardware performance are described in[4].Briefly,it is a large barrel detector covering the polar angle range|cosθ|<0.68,and comprising two radiator systems;liquid C6F14and gaseous C5F12+N2cover the lower and higher mo-mentum regions,respectively.Cherenkov photons from the liquid(gaseous)radiator are focussed by proximity(spherical mirrors)onto one of40quartz-windowed time projection chambers(TPCs)containing ethane with∼0.1%TMAE.Each single photoelectron drifts to a wire chamber where its conversion point is measured in three dimensions and used to reconstruct a Cherenkov angleθc with respect to each extrapolated track.The averageθc resolution for liquid(gas)photons was measured to be16(4.5)mrad, including errors on alignments and track extrapolation;the local resolution of13(3.8) mrad is consistent with the design value.The average number of detected photons per β=1track was16.1(10.0)inµ-pair events.In hadronic events,cuts to suppress spurious hits and cross-talk from saturating hits gave an average of12.8(9.2)accepted hits.The average reconstructedθc forβ=1tracks was675(58.6)mrad,independent of position within the CRID and¯θliq c was constant in time.Time variations in¯θgas c of up to±1.2 mrad were tracked with an online monitor and verified in the data.Tracks were identified using a likelihood technique[5].For each of the hypotheses i=e,µ,π,K,p,a likelihood L i was calculated based upon the number of detected photons and their measuredθc,the expected number and¯θc,and a background term. The background included overlapping Cherenkov radiation from other tracks in the event and a constant term normalized to the number of hits in the relevant TPC that were associated with no track.Cuts on differences between the logarithms of these likelihoods,L i=ln L i,are op-timized for each analysis.For example,in the analysis of charged hadrons(sec.3)weconsidered only the hypotheses i=π,K,p,and high purity was the primary considera-tion.We therefore applied a tight set of CRID quality cuts[6](accepting∼60%of the tracks with CRID information),and tracks with p<2.5(p>2.5)GeV/c were identified as species j if L j exceeded both of the other log-likelihoods by at least5(3)units.The matrix E of identification efficiencies is shown infig.1.The elements Eπj and E p j were determined from the data using tracks from selected K0s,τandΛ0decays.The E Kj were related to the measured elements using a detailed detector simulation.The bands infig.1 encompass the systematic errors on the efficiencies,determined from the statistics of the data test samples.The discontinuities correspond to Cherenkov thresholds in the gaseous radiator.The identification efficiencies peak near or above0.9and the pion coverage is continuous over∼0.3–35GeV/c.There is a gap in the kaon-proton separation,∼7–10 GeV/c,and the proton coverage extends to the beam momentum.Misidentification rates are typically less than0.03,with peak values of up to0.06.Many analyses required identifying K±with high efficiency and reasonable purity.A looser track selection was made(∼95%of CRID tracks)and a moderate cut,typically L K−Lπ>3,made against pions and leptons,along with a loose cut against protons, typically L K−L p>−1.The efficiency for identifying true kaons is∼70%for1<p<30 GeV/c;the pion(proton)misidentification rate depends strongly on momentum and can be as large as12%(70%).K±samples of70–90%purity are achieved.The power of this loose identification for reconstructing strange and charmed mesons is illustrated infigs.2 and3.The CRID has also been used in the identification of leptons.Alone,it provides effi-cient e-πseparation for p<4GeV/c,and combined with the electromagnetic calorimeter gave improved e±identification for p<8GeV/c.For e±from B hadron decays,adding the CRID information resulted in a doubling of the efficiency of an optimized algorithm for a given purity.Forµ±,the CRID rejectsπ±for2<p<4GeV/c,and K±,a substan-tial source of punchthrough,at all momenta.Reoptimizing the muon selection including CRID information increased the efficiency by∼10%at all p,and the purity by∼40%for 2<p<4GeV/c and5–30%at higher momenta.110110Momentum (GeV/c)1100.2True πE f f i c i e n c y t o I d e n t i f y a s :4–988400A210.40.60.81.000.040.080πpK 00.040.080.120.040.080.1200.20.40.60.800.040.080.040.080True p True K 000.20.40.60.80.040.08Figure 1:Calibrated identification efficiencies for tracks used in the charged hadronanalysis.0200040006000800010000120000.751 1.25 1.5 1.75E n t r i e s /20 M e V /c 20501001502002503003504004500.951 1.05 1.1 KK Mass GeV/c 2Kpi Mass GeV/c 2 1.15E n t r i e s /4 M e V /c 2Figure 2:Distributions of invariant mass using loosely identified kaons (see text)showing signals for the K ∗0(890)and φ(1020).1.522.5m(K π)010203040506070801.7 1.8 1.92 2.12.2m(KK π)E n t r i e s /40 M e V /c2Figure 3:Invariant mass distributions for tracks forming secondary vertices (dots)show-ing signals for the D 0,including the satellite peak,and D s mesons.The simulated (back-ground)distributions are shown as (hatched)histograms.3.Hadronization PhysicsInclusive properties of the charged tracks and photons in jets have been studied extensively in e+e−annihilations.Studies of specific identified particles at lower energies had low statistics and incomplete momentum coverage,but were able to observe the production of baryons,vector mesons and strange mesons and baryons,and to study mechanisms for strangeness and baryon number conservation through correlations.The large samples at the Z0have allowed much more detailed studies[7],including the recent observations of tensor mesons and orbitally excited baryons.We have studied the production of seven identified particle species in hadronic Z0 decays[6].Chargedπ±,K±and p/¯p identified as described in sec.2were counted as a function of momentum and these counts unfolded using the inverse of the identification efficiency matrix(fig.1)to yield production cross sections as a function of momentum. The neutral strange vector mesons K∗0andφwere reconstructed in their K+π−and K+K−modes,respectively,using the loose kaon selection(sec.2).Production cross sections were extracted fromfits to the invariant mass distributions(seefig.2).These cross sections,along with similar measurements for K0andΛ0/¯Λ0[6],are shown infig.4.These measurements cover a wide momentum range with good precision.Similar inclusive measurements have been made[7]at the Z0by DELPHI using RICH particle identification,and by ALEPH and OPAL using d E/d x.The measurements are consistent, have comparable precision and,between the two methods,cover the entire momentum range.The clean samples available from the CRID compensate for the much higher statistics at LEP,and also allow smaller systematic errors in some cases,most notably the K∗0,for which the background is high and contains large contributions from reflections of resonances decaying intoπ+π−.The CRID efficiency and purity are especially useful when the data are divided into smaller samples and additional levels of unfolding are required.We divided the hadronic events into b-,c-and light-flavor(u,d,s)samples[6],repeated the above analyses on each, and unfolded the results to yield production cross sections in these threeflavor categories. Substantial differences are observed,as expected from the known production and decay properties of the leading heavy hadrons.The results for the light-flavor sample are shown infig.5,where coverage and precision comparable to that of theflavor-inclusive sample are evident.This measurement provides a more pure way of looking at hadronization at a fundamental level.We have found these results to be consistent with the limited predictions of perturbative QCD[6],and compared them with the predictions of three hadronization models(seefig.5).All describe the data qualitatively;differences in detail include:all models are high for low-momentum kaons;the JETSET model is high for the vector mesons and protons at all momenta;the HERWIG model and,to a lesser extent, the UCLA model show excess structure at high momentum for all particle species;no model is able to reproduce the∼10%difference between K±and K0production.These discrepancies have been observed previously[7],however our measurement demonstrates unambiguously that they are in the hadronization part of the model and not in the simula-0.110.0110–310–410–110010110210–2x p 1/N d n /d x pFigure 4:Differential production cross sections per hadronic Z 0decay per unit x p for all charged particles and seven identified hadron species.0.010.1110–310–410–110–2x p 1/N d n /d x p 10101102103Figure 5:Differential production cross sections per light-flavor hadronic Z 0decay,com-pared with the predictions of three hadronization models.tion of heavy hadron production and decay.We have found additional minor discrepancies in the heavyflavor events[6].The events in the lightflavor sample can be divided further into quark hemispheres and antiquark hemispheres using the electron beam polarization,providing a unique study of leading particle effects[8,6].For events with thrust axis|cosθ|>0.2,the forward(back-ward)thrust hemisphere is tagged as the quark jet if the beam is left-(right-)polarized, and the opposite hemisphere tagged as the antiquark jet.The SM predicts a quark purity of73%.The set of hadrons in quark jets plus their respective antihadrons in antiquark jets were analyzed to yield cross sectionsσh for hadrons in light quark jets.Similarly, the remaining hadrons yielded antihadron cross sectionsσ¯h.The corrected normalized production differences D h=(σh−σ¯h)/(σh+σ¯h)are shown infig.6.At low momentum,hadron and antihadron production are consistent.At higher mo-mentum there is an excess of baryons over antibaryons,as expected from leading baryon production(a baryon contains valence quarks,not antiquarks).The large excess of pseu-doscalar and vector antikaons over kaons at high momentum is evidence both for leading kaon production,and for the dominance of s¯s events in producing leading kaons.No significant leading particle signature is visible for pions.CRID type particle identification greatly enhances studies of pairs of hadrons in the same event.We have analyzed[9]correlations in rapidity y=0.5ln((E+p )/(E−p )), where E(p )is the energy(momentum projection onto the thrust axis)of the hadron, between pairs of identifiedπ±,K±and p/¯p in light-flavor events.We compared the distribution of∆y=|y1−y2|for identified K+K−pairs with that for K+K+and K−K−pairs.The latter are expected to be uncorrelated,and the difference between the two distributions illuminates strangeness production in the hadronization process.We observe [9]a large difference at low values of∆y;this‘short range’correlation indicates that the conservation of strangeness is‘local’,that is,a strange and an antistrange particle are produced close to each other in the phase space of the jet.Similar effects for p¯p and π+π−pairs indicate local conservation of baryon number and isospin,respectively.Such effects have been observed previously,however the CRID has allowed the study of the shape and range of the correlations in detail and at many momenta,in particular we have verified the scale-invariance of the range.We have also observed short-range correlations between opposite-chargeπK,πp and K p pairs;they are relatively weak,and high purity is required to separate them from the largeππbackground.They suggest charge-ordering of all particle types along the q¯q axis and provide new tests of fragmentation models.We also expect correlations at long range due to leading particles,e.g.an s¯s event may have a leading K−in the s jet and a leading K+in the¯s jet that have a large ∆y.We have studied pairs of identified hadrons that both have p>9GeV/c.Their∆y distributions are shown infig.7;the p cut separates each distribution into two parts, one(∆y<2)comprising pairs in the same jet and the other(∆y>3)comprising pairs in opposite jets of the event.Strong K+K−correlations are seen at both short and long range,as expected.For baryon and pion pairs,any long-range correlation will be diluted by the short-range correlation–a high-momentum leading baryon will always be0.20.40.60.800.51.0xpN o r m a l i z e d D i f f e r e n c e D h0.51.01.01.0000.50.51.00.5Figure 6:Normalized differences between hadron and antihadron production in uds jets;the predictions of the three fragmentation models.0500100015002000π+π−π+π+, π−π−0100200300400500K +K −K +K +, K −K−04008001200E n t r i e sπ+K −, π−K +π+K +, π−K−050100150200K +p, K −p K +p, K −p02468| y 1 − y 2 |100200300400π+p, π−p π+p, π−p0246810| y 1 − y 2 |50100150200pp pp, ppSLD Preliminary_______Figure 7:|∆y |distributions for opposite-(histograms)and same-charge (dashed his-tograms)pairs in which both tracks have p >9GeV/c.accompanied by a subleading antibaryon,also with high momentum.We do not observe a long-range correlation for p¯p pairs,however we do observe a significant correlation forπ+π−pairs,providing direct evidence for leading pion production.There are also significant correlations forπK and K p pairs,but not forπp pairs.These cross terms provide new information on leading particle production in jets of differentflavors,which will eventually allow the use of high momentum identified particles to separate u¯u,d¯d and s¯s events from each other.Using the beam polarization to select the quark hemisphere in each event,we have performed a new study[9]of rapidities signed such that y>0(y<0)corresponds to the (anti)quark direction.A pair of identified hadrons can then be ordered,for example by charge to form the ordered rapidity difference∆y+−=y+−y−.A positive value of∆y+−indicates that the positively charged hadron is more in the direction of the primary quark than the negatively charged hadron.The distribution of∆y+−can be studied in terms of the difference between its positive and negative sides.We observe a large difference for K+K−pairs at long range due to leading kaon production in s¯s events.A significant difference at short range for p¯p pairs at all p is direct evidence that the proton in a correlated p¯p pair prefers the quark direction over the antiquark direction.4.Quark Flavor Tagging and Electroweak Physics The identification of theflavor of the quark that initiated a hadronic jet is required for a wide variety of physics.The development of precision vertex detectors has enabled the pure and efficient tagging of b/¯b and c/¯c jets,leading to a number of precise measurements infixed-target and e+e−annihilation experiments and the understanding of top quark production at hadron colliders.For many measurements it is also necessary to distinguish b from¯b or c from¯c jets.The use of charged kaons is envisioned for this purpose in several future B physics experiments, and has recently been pioneered by SLD.We present examples of its use for both b and c physics,which rely on the CRID for high efficiency and purity that is measurable from the data.The identification of lightflavor jets is afield in its infancy.The three lightflavors can be separated from b/¯b and c/¯c jets by the absence of a secondary vertex in the jet;the only known way to distinguish them from each other is by identifying the leading particle in the jet cleanly.Little experimental information on leading particle production in light flavor jets exists(much of which appears in sec.3above),making the measurement of tagging purities and analyzing powers from the data essential.We present a measurement of A s and discuss prospects for light-flavor tagging in general.Proper Time (ps)0.20.30.40.50.60246810M i x e d F r a c t i o nFigure 8:Mixed fraction as a function of proper decay time for tagged B decay vertices.A.B 0-¯B0Mixing To measure the time dependence of B 0-¯B0mixing,one must tag neutral B hadrons and determine their flavor (B or ¯B)at both production and decay time.We first selected a sample of high-mass secondary vertices [10](98%B -purity,∼40%B 0d )and reconstructed the proper decay time τof each.The flavor at production was determined by a combi-nation of the beam polarization and the charges of the tracks,identified K ±,e ±and µ±in the opposite hemisphere,with a correct-sign fraction of 88%.The flavor at decay time was determined from the charge of any identified K ±attached to the secondary vertex,with a correct-sign probability P corr =77%.The fraction of events classified as mixed (different flavors at production and decay)is shown as a function of τin fig.8.A clear increase with time is evident,whichis the signal for B 0d -¯B 0d mixing.A fit to the data yielded a 6%measurement of the mass difference ∆m d .There are several other measurements of ∆m d on the market with similar precision,including three from SLD,however this is the only one using the K ±tag,providing valuable complementarity.There is considerable interest in B 0s -¯B 0s mixing,for which there are currently onlyRel.Corr.Frac.Error on A c Method Fraction b/c Now Now1.0model-dep.0.035–Id’d K±∼0.75/0.900.1380.0500.1stat.ltd.0.0440.070 Rec’d D(∗)∼0.85/1.00–0.072cos θb 020406080100120140160180200T a g g e d E v e n t scos θbFigure 9:Distributions of the b -quark polar angle for events produced with negatively (left)and positively (right)polarized electron beams.a sign to every taggedb ¯b event,but P corr is low,averaging ∼60%,and depends on |Q |.P corr can be measured in the data under some model-dependent assumptions,but the method will reach a systematic limit of a few percent.We have recently demonstrated the use of identified K ±to measure both A b [12]and A c [13].A K ±was identified in ∼40%of the tagged B hadron vertices with P corr =73%,asmaller value than in sec.4.1since B 0-¯B0mixing is now a dilution.This method provides a nice balance between efficiency and purity,yields the cos θb distributions in fig.9,and P corr can be measured unambigusouly in the data.The precision of the P corr measurement depends on the square of the efficiency and is also quite sensitive to background,so that CRID type K ±identification is essential.Currently this measurement is statistics limited,as we have analyzed less than one-sixth of our data sample;we expect to measure P corrto±2%,a valuable result in itself for future B physics experiments,and to achieve one of the best precisions on A b.Furthermore,this is a unique method complementary to those used so far,which give a world average value of A b that differs from the SM prediction by3σ.The situation is even better for charm.A K±was found in∼40%of low mass vertices with zero net charge,and gave P corr>90%.In charged vertices the vertex charge was combined with that of any identified K±to give an average P corr=91%for all charm vertices,and the cosθc distributions shown infig.10.This P corr can be estimated reliably from known charmed hadron branching ratios,and with one-half of our data analyzed, we have the world’s best measurement of A c.A measurement of P corr from the data is feasible and will be required to reach1%precision.C.Light Flavor AsymmetriesIn contrast to the situation with leptons or heavyflavors,there are published measure-ments of Z0couplings to light-flavor quarks(u,d and s)only from DELPHI[14]and OPAL[15],with rather poor precision.The challenge is to separate theseflavors not only from the heavyflavors but also from each other.Leading particles at high momentum can be used to determine the eventflavor,and,if they carry the appropriate quantum number,the direction of the quark.However,the lack of experimental measurements of leading particle effects for theseflavors leads to the choice of relying on a hadronization model to predict sample purities and P corr,or trying to measure these in the data.We have taken the approach of applying hardflavor selection cuts to reduce back-grounds,increase the P corr and therefore reduce the associated systematic errors.A hadronization model was used to predict these,but key quantities were measured in the data,the predictions adjusted accordingly,and the data statistics used to estimate the systematic errors.To measure A s[16],we used the lightflavor sample and tagged s(¯s)hemispheres using identified K−(K+)with p>9GeV/c and reconstructedΛ0→pπ−(¯Λ0→¯pπ+) with p>5GeV/c and the(anti)proton identified in the CRID.Requiring either an s-tag in one hemisphere and an¯s-tag in the other,or an s-or¯s-tag in one hemisphere and a reconstructed K0s→π+π−with p>5GeV/c in the other,yielded an event sample with69%s¯s purity and an average P corr=82%.The distributions of cosθs are shown in fig.11.The heavy-flavor background is substantial but understood,and the associated sys-tematic errors are small.P corr for s¯s events was measured in the data by counting hemi-spheres in which we identified three K±or K0s,since hemispheres with three true kaons are the dominant source of wrong signs.Similarly,the level and asymmetry of the u¯u/d¯d background were measured by counting hemispheres with two identified kaons,and events with an s-tag(or¯s-tag)in both hemispheres.The simulation was used to relate these counts to the relevant quantities,and was checked against our measured KK correlations (sec.3).。

a r X i v :h e p -p h /9703459v 1 31 M a r 1997DPNU-97-18March 1997Possible Signals of D 0-¯D0Mixing and CP Violation ∗Zhi-zhong Xing†Department of Physics,Nagoya University,Chikusa-ku,Nagoya 464-01,JapanAbstractIn view of the discovery potential associated with the future experiments of high-luminosity fixed target facilities,B -meson factories and τ-charm factories,we highlightsome typical signals of D 0-¯D0mixing and CP violation which are likely to show up in neutral D -meson decays to the semileptonic final states,the hadronic CP eigenstates,the hadronic non-CP eigenstates and the CP -forbidden states.Both time-dependent andtime-integrated measurements are discussed,and particular interest is paid to D 0/¯D0→K S,L +π0and D 0/¯D0→K ±π∓transitions.1IntroductionThe study of D 0-¯D0mixing and CP violation in neutral D -meson decays is not only comple-mentary to our knowledge obtained and to be obtained from K 0-¯K0and B 0-¯B 0systems,but also important for exploring underlying new physics that is out of reach of the standard model predictions.A large discovery potential associated with this topic is expected to exist in the future delicate experiments of high-luminosity fixed target facilities,B -meson factories,and τ-charm factories [1].WithoutCPTviolation,the mass eigenstates of D 0and ¯D0mesons can be written as |D L =p |D 0 +q |¯D0 ,|D H =p |D 0 −q |¯D0 ,(1.1)where p and q are complex parameters determined by off-diagonal elements of the D 0-¯D0mixing Hamiltonian.The rate of D 0-¯D0mixing is commonly measured by two well-defined dimensionless quantities,x D ≡∆m2Γ,(1.2)which correspond to the mass and width differences of D H and D L (i.e.,∆m ≡m H −m L and ∆Γ≡ΓL −ΓH ).The latest result from the Fermilab experiment E791has set an upper boundon the rate of D 0-¯D0mixing [2]:r D ≡x 2D +y 2D|p |4+|q |4.(1.4)It is expected that the magnitude of ∆D should be at most of the order 10−3in the standard model.However,a reliable estimation of ∆D suffers from large long-distance uncertainties.(b)CP violation in direct decay .For a decay mode D 0→f and its CP -conjugate process¯D0→¯f ,this implies | ¯f|H eff|¯D 0 |≡nA n e i(δn −φn )=| f |H eff|D 0 |≡nA n e i(δn +φn ),(1.5)where a parametrization of the decay amplitudes with the weak(φn)and strong(δn)phases is also given.We see that n≥2,φm−φn=0orπandδm−δn=0orπare necessary conditions for the above direct CP violation.(c)CP violation from the interplay of decay and mixing.Let us define two rephasing-invariant quantitiesλf≡qf|H eff|D0,¯λ¯f≡p¯f|H eff|¯D0,(1.6)where the hadronic states f and¯f are common to the decay of D0(or¯D0).Even in the assumption of|q/p|=1,indirect CP violation can appear ifImλf−Im¯λ¯f=0.(1.7) Provided f is a CP eigenstate(i.e.,|¯f =±|f )and the decay is dominated by a single weak phase,then we have¯λ¯f=λ∗f.CP violation at the percent level has not been observed in experiments[7].But signals of O(10−3)are expected in some neutral D decays within the standard model,and those of O(10−2)cannot be ruled out in some channels beyond the standard model.Subsequently we shall highlight some typical signals of D0-¯D0mixing and CP violation which are likely to show up in weak decays of neutral D mesons.A systematic and compre-hensive study of this topic can be found in Ref.[6]and references therein.2Typical signals of D0-¯D0mixingFor simplicity and instruction,we assume∆D=0in the discussion of D0-¯D0mixing effects. This assumption should be safe both within and beyond the standard model,and it can be tested by detecting CP violation in the semileptonic decays of D0and¯D0mesons.A.Time-integrated measurementsForfixed target experiments or e+e−collisions at theΥ(4S)resonance,the produced D0 and¯D0mesons are incoherent.Knowledge of D0-¯D0mixing is expected to come from ratios of the wrong-sign to right-sign events of semileptonic D decays:R(D0phys→K+l−¯νl)R(¯D0phys→K+l−¯νl)≈r D(2.1)in the assumption made above.The Fermilab experiment E791gives r D<0.5%at the90% confidence level[2],the best model-independent limit on D0-¯D0mixing today.For aτ-charm factory running on theψ(3.77)resonance,coherent D0¯D0events with odd C-parity can be produced.If e+e−collisions take place at theψ(4.16)resonance,coherent D0¯D0events will be produced throughψ(4.16)→γ(D0¯D0)C−even orψ(4.16)→π0(D0¯D0)C−odd. Three types of joint decay modes are interesting for measuring D0-¯D0mixing:(D0phys¯D0phys)C−→(l±X∓)D(l±X∓)¯D,−→(K±π∓)D(l∓X±)¯D,−→(K±π∓)D(K±π∓)¯D,(2.2) where we have used the notations X+≡K+¯νl and X−≡K−νl.Note that D0→K+π−is a doubly Cabibbo-suppressed decay(DCSD).This effect is usually measured by the following ratio of decay rates:R DCSD≡ K+π−|H eff|D0R DCSD[y D cos(δKπ−φD)−x D sin(δKπ−φD)],T−int=R(l±X∓;l±X∓)CR(K±π∓;l∓X±)CR(K±π∓;K±π∓)CR[D0(t)→K−π+]R[¯D0(t)→K−π+]R[D0(t)→K−π+]=R DCSD+T+int(Γt)+r DR[¯D0(t)→K+π−]=R DCSD+T−int(Γt)+r D¯K0π0|H eff|D02,(2.6)0.60.81.01.21.41.61.8012345ΓtR [¯D0(t )→K L π0]R [D 0(t )→K S π0]Figure 2:Illustrative plot for changes of two D 0-¯D0mixing observables with proper time t ,where (a)x D =y D =0.05,φD =π/4(corresponding to the solid curves)and (b)x D =0.05,y D =0,φD =π/2(corresponding to the dark solid curves)have been taken.analogous to R DCSD defined above.Obviously R ′DCSD and R DCSD are comparable in magnitude.To a good degree of accuracy,the time-dependent decay rates of D 0(t )→K S,L +π0and ¯D 0(t )→K S,L +π0are independent of R ′DCSD [6]:R [¯D0(t )→K S π0]2+2(y D cos φD +x D sin φD )(Γt )+y 2D (Γt )2,R [¯D0(t )→K L π0]2−2(y D cos φD +x D sin φD )(Γt )+y 2D (Γt )2,(2.7)where a tiny CKM phase from the direct transition amplitude has been neglected.One cansee that the deviation of each of the above two observables from unity measures nonvanishing x D sin φD ,while the difference between them measures the magnitude of y D cos φD −x D sin φD .Thus some useful information about x D ,y D and φD should be achievable from the experimental study of those decay modes.We typically take (a)φD =π/4,x D =y D =0.05and (b)φD =π/2,x D =0.05,y D =0,to plot changes of R [¯D0(t )→K S,L +π0]/R [D 0(t )→K S,L +π0]with proper time t in Fig.2for the purpose of illustration.Finally it is worth pointing out that a comparison of the interference terms in (2.7)with T ±int in (2.4)can provide a model-independent constraint on the strong phase shift δKπ.3Typical signals of CP violationIt is expected that CP violation induced by D 0-¯D0mixing (i.e.,∆D )can manifest itself,ap-parently or indirectly,in all neutral D -meson decay modes.But this effect should be negligiblysmall in most cases.A constraint on∆D is possible through measuring the semileptonic decays of either incoherent or coherent D0and¯D0mesons.For example,R(¯D0phys→K−l+νl)−R(D0phys→K+l−¯νl)R(K−l+νl;K−l+νl)C+R(K+l−¯νl;K+l−¯νl)C=∆D(3.2) for both C-odd and C-even cases.In the following we shall pay main attention to the direct and indirect CP asymmetries in some nonleptonic D transitions,where∆D=0will be assumed.A.Time-integrated measurementsFor neutral D mesons decaying to a hadronic CP eigenstate f,the observables of direct CP violation in the decay amplitude and indirect CP violation from the interplay of decay and D0-¯D0mixing are expressed asA dir≡1−|ρf|21+|ρf|2,(3.3)whereρf≡ f|H eff|¯D0 / f|H eff|D0 .In the time-integrated measurements,the following CP asymmetries can be used to probe A dir and A ind:(a)For incoherent decays of D0and¯D0mesons,we haveR(D0phys→f)−R(¯D0phys→f)R(l−X+;f)C+R(l+X−;f)C ≈ A dir(C−odd)A dir+2x D A ind(C−even).(3.5)Clearly it is possible to distinguish between direct and indirect CP-violating signals,if the magnitude of A dir is comparable with that of x D A ind.(c)At theψ(4.16)resonance there may be a type of CP violation arising from the CP-forbidden decay channels.For example,R(f;f)C−oddR(K Sπ0;K Lπ0)≈R(K Lπ0;K Lπ0)If r D were close to its experimental upper bound andφD were enhanced by new physics,this signal could be measured at aτ-charm factory‡.Now we turn our attention to CP violation in neutral D decays to non-CP eigenstates. Again D0/¯D0→K±π∓can be taken as a good example for illustration.It is expected that only indirect CP violation appears in these four decay modes.We denote the signals as follows:A Kπ≡ R DCSD sinφD(y D sinδKπ+x D cosδKπ),(3.8)whereφD andδKπhave been defined before.If|y D|≪|x D|,as anticipated in some non-standard models[4,10],we arrive at A′Kπ≈−A Kπ.For incoherent D-meson decays,A Kπcan be measured from the decay-rate asymmetryR(¯D0phys→K+π−)−R(D0phys→K−π+)R(l+X−;K+π−)C−R(l−X+;K−π+)CR(l−X+;K+π−)CR(l+X−;K+π−)C4A′KπR(K−π+;K+π−)C −R(K−π+;K−π+)C‡In contrast with(3.7),there may be a similar CP-violating signal for B d decays to K S X c and K L X c on theΥ(4S)resonance,where X c=J/ψ,ψ′,ηc,η′c,etc[11].This signal is expected to be of O(10%)due to the large B0d-¯B0d mixing rate(x B≈0.7)and significant CP-violating phase(φB∼19◦−70◦)in the standard model,thus it should be detectable at the forthcoming B-meson factories.-0.8%-0.6%-0.4%-0.2%0.0%0.2%12345ΓtD 0(t )vs ¯D0(t )→K S π0D 0(t )vs ¯D0(t )→K L π0R [D 0(t )→f ]+R [¯D0(t )→f ]≈A dir +x D A ind (Γt ),(3.10)where A dir and A ind have been defined before.Taking D 0/¯D0→K S,L +π0for example,we obtain R [D 0(t )→K S π0]−R [¯D0(t )→K S π0]R [D 0(t )→K L π0]+R [¯D0(t )→K L π0]≈−2Re ǫK −x D sin φD (Γt )(3.11)in the assumption of ∆D =0.Here Re ǫK ≈1.6×10−3,signifying the CP asymmetry inducedby K 0-¯K 0mixing,cannot be neglected [12].Even if the x Dsin φD term is vanishingly small,the effect of Re ǫK is still detectable from the above decay modes.For the purpose of illustration,we take x D =0.01and φD =0.1to plot changes of the CP asymmetries (3.11)with proper time t in Fig.3.Indirect CP violation in neutral D -meson decays to hadronic non-CP eigenstates can beillustrated by taking D 0/¯D0→K ±π∓for example.Assuming ∆D =0,we have R [¯D0(t )→K +π−]−R [D 0(t )→K −π+]-0.10.10.30.50.7012345ΓtD 0(t )→K +π−vs¯D0(t )→K −π+¯D0(t )→K +π−vsD 0(t )→K −π+R [D 0(t )→K +π−]+R [¯D0(t )→K −π+]≈A ′Kπ2(Γt )+r DI would like to thank S.Pakvasa for inviting me to participate in this nice conference.I am grateful to A.I.Sanda for his encouragement and support,which make my participation realizable.This work was supported by the Japan Society for the Promotion of Science.References[1]See,e.g.,Proceedings of the Workshop on the Future of High Sensitivity Charm Experi-ments,Batavia,Illinois,1994,edited by D.M.Kaplan and S.Kwan(Fermilab Report No.94/190,Batavia,1994);Proceedings of the Workshop on the Tau-Charm Factory in the Era of B-Factory and CESR,Stanford,California,1994,edited by L.V.Beers and M.L.Perl(SLAC Report No.451,Stanford,1994);T.Liu,Ph.D.Thesis,Harvard University,Report No.HUHEPL-20(1995).[2]E791Collaboration,E.M.Aitala et al.,Phys.Rev.Lett.77(1996)2384;M.Purohit,in these proceedings.[3]E.Golowich,Report No.hep-ph/9701225(invited talk given at the4th KEK TopicalConference on Flavor Physics,29-31October,1996),to be published in Nucl.Phys.B (Proc.Suppl.).[4]E.Golowich,in these proceedings.[5]I.I.Bigi and A.I.Sanda,Phys.Lett.B171(1986)320;I.I.Bigi,in Proceedings of the Tau-Charm Factory Workshop,Standford,California,1989,edited by L.V.Beers(SLAC Report No.343,Stanford,1989),p.169.[6]Z.Z.Xing,Phys.Rev.D55(1997)196.[7]CLEO Collaboration,J.Bartelt et al.,Phys.Rev.D52(1995)4860;E687Collaboration,P.L.Frabetti et al.,Phys.Rev.D50(1994)R2953.[8]CLEO Collaboration,D.Cinabro et al.,Phys.Rev.Lett.72(1994)406;E791Collaboration,E.M.Aitala et al.,Report No.hep-ph/9608018(1996).[9]Z.Z.Xing,Phys.Lett.B372(1996)317.[10]T.E.Browder and S.Pakvasa,Phys.Lett.B383(1996)475;L.Wolfenstein,Phys.Rev.Lett.75(1995)2460;G.Blaylock,A.Seiden,and Y.Nir,Phys.Lett.B355(1995)555.[11]Z.Z.Xing,Report No.DPNU-97-16(invited talk given at the1997Shizuoka Workshopon Masses and Mixings of Quarks and Leptons,Shizuoka,March19-21,1997),to be published in the workshop proceedings;Z.Z.Xing,Phys.Rev.D53(1996)204.[12]Z.Z.Xing,Phys.Lett.B353(1995)313.。

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a rXiv:h ep-ph/977477v125J ul1997FERMILAB-PUB-97/263-T NUHEP-TH-97-09AMES-HET-97-08July 1997Single top quark production as a probe of R-parity-violating SUSY at pp and p ¯p colliders Robert J.Oakes a ,K.Whisnant b ,Jin Min Yang a,b,1,Bing-Lin Young b ,and X.Zhang c,d a Department of Physics and Astronomy,Northwestern University,Evanston,Illinois 60208,USA b Department of Physics and Astronomy,Iowa State University,Ames,Iowa 50011,USA c Institute of High Energy Physics,Academia Sinica,Beijing 100039,China d Fermi National Accelarator Laboratory,P.O.Box 500,Batavia,IL 60510,USA ABSTRACT We investigate the ability of single top quark production via qq ′→squark→tb and q ¯q ′→slepton →t ¯b at the LHC and Tevatron to probe the strength of R-parity violating couplings in the minimal supersymmetric model.We found that given the existing bounds on R-parity violating couplings,single top quark production may be greatly enhanced over that predicted by the standard model,and that both colliders can either discover R-parity violating SUSY or set strong constraints on the relevant R-parity violating couplings.We further found that the LHC is much more powerful than the Tevatron in probing the squark couplings,but the two colliders have comparable sensitivity for the slepton couplings.PACS:14.65.Ha,14.80.Ly1.IntroductionThe HERA data showed excess events in deep-inelastic positron-proton scattering at high-Q2and high x,which are in apparent conflict with the Standard Model expectation[1].The excess events have been interpreted as evidence of R-parity breaking supersymmetry[2].Hence detailed examination of effects of R-parity breaking supersymmetry in other processes is in order.Some of the phenomenological implications of R-parity violating couplings at e+e−colliders have been investigated in Ref.[3].Constraints on the R-parity violating couplings have also been obtained from perturbative unitarity[4,5],n−¯n oscillation[5,6],νe-Majorana mass [7],neutrino-less doubleβdecay[8],charged current universality[9],e−µ−τuniversality[9],νµ−e scattering[9],atomic parity violation[9],νµdeep-inelastic scattering[9],double nucleondecay[10],K decay[11,12],τdecay[13],D decay[13],B decay[14-16]and Z decay at LEPI [17,18].Another important effect of R-parity violating couplings is that they may enhance the flavor changing top quark decays to the observable level of the upgraded Tevatron and LHC [19].As is shown in Refs.[20-24],single top quark production is very interesting to study at the Tevatron and the LHC since,in contrast to the QCD process of t¯t pair production,it can be used to probe the electroweak theory.Single top production processes have been used to study the new physics effects involving the third-family quarks in a model independent approach[25] and in specific models[26,27].More recently,motivated by the evidence of R-parity breaking supersymmetry[28,29]from the anomalous events at HERA[1],single top quark production q¯q′→t¯b at the Tevatron induced by baryon-number violating(BV)couplingsλ′′(via the exchange of a squark in the t-channel)and by lepton-number violating(LV)couplingsλ′(via the exchange of a slepton in the s-channel)has been studied[30]in minimal supersymmetric model(MSSM).It was found[30]that the upgraded Tevatron can probe the relevant BV couplings efficiently,while the probe for the relevant LV couplings is very limited.In addition to the process q¯q′→t¯b mentioned above,which can be effectively studied at the Tevatron,the R-parity BV coupling can lead to the reaction qq′→tb via an s-channel squark contribution which is suppressed at the Tevatron.This process is suitable for study at the LHCand it probes a different set of BV couplings.In this paper we make a detailed study of the s-channel BV effect.For completeness we study the effect at both the LHC and the upgraded Tevatron.We also study the s-channel slepton contribution to q¯q′→t¯b at the LHC which wecompare to the result obtained for the upgraded Tevatron[30].This paper is organized as follows.In Sec.2we present the Lagrangian for R-parity vi-olating couplings and squared matrix elements for the processes qq′→squark→tb and q¯q′→slepton→t¯b.In Sec.3we evaluate the signal for these processes and the SM back-ground,and give the probing potential of the LHC in comparison to the upgraded Tevatron.2.tb and t¯b production in R-parity violating MSSM2.1Lagrangian of R-parity violating couplingsThe R-parity violating part of the superpotential of the MSSM is given byW R=λijk L i L j E c k+λ′ijk L i Q j D c k+λ′′ijk U c i D c j D c k+µi L i H2.(1) Here L i(Q i)and E i(U i,D i)are the left-handed lepton(quark)doublet and right-handed lepton (quark)singlet chiral superfields,i,j,k are generation indices,and c denotes charge conjugation. H1,2are the chiral superfields representing the two Higgs doublets.Theλandλ′couplings violate lepton-number conservation,while theλ′′couplings violate baryon-number conservation. The coefficientλijk is antisymmetric in thefirst two indices andλ′′ijk is antisymmetric in the last two indices.In terms of the four-component Dirac notation,the Lagrangians for theλ′and λ′′couplings that affect single top production at the Tevatron and the LHC are given by Lλ′=−λ′ijk ˜νi L¯d k R d j L+˜d j L¯d k Rνi L+(˜d k R)∗(¯νi L)c d j L−˜e i L¯d k R u j L−˜u j L¯d k R e i L−(˜d k R)∗(¯e i L)c u j L +h.c.,(2) Lλ′′=−λ′′ijk ˜d k R(¯u i L)c d j L+˜d j R(¯d k L)c u i L+˜u i R(¯d j L)c d k L +h.c..(3) The terms proportional toλare not relevant to our present discussion and will not be con-sidered here.Note that while it is theoretically possible to have both BV and LV terms inthe Lagrangian,the non-observation of proton decay imposes very stringent conditions on their simultaneous presence[31].We,therefore,assume the existence of either LV couplings or BV couplings,and investigate their separate effects in single top quark production.2.2qq′→squark→tbProduction of tb via an s-channel diagram u i d j→˜d k R→tb can be induced by the BV couplingsλ′′.The matrix element squared is given by3kλ′′ijkλ′′33kM t(| p3|,E tˆp3),(5)where h=±1denotes the two helicity states,andˆp3is the unit three-vector in the momentum direction of top quark.Neglecting the contribution of third-family sea quark in the initial states,we obtain3(λ′′112λ′′332)2|Mλ′′(us→tb)|2=32(ˆs−M2˜d )2+(M˜dΓ˜d R)2(p1·p2)[p3·p4−M t(s t·p4)],(7)3(λ′′212λ′′332)2|Mλ′′(cs→tb)|2=32(ˆs−M2˜d )2+(M˜dΓ˜d R)2(p1·p2)[p3·p4−M t(s t·p4)].(9)In the R-parity conserving MSSM,the down-type squark˜d k R can decay into charginos and neutralinos via the processes˜d k R→u k+the relevantλ′′couplings may be quite large,the width of a heavy down-type squark˜d k R canbe large even if we do not consider the decay involving the gluino.We found that within the allowed parameter space(λ′′,chargino and neutralino sector)its widthΓ˜d Rcan be as large asM˜d R/3.2.3q¯q′→slepton→t¯bProduction of t¯b via an s-channel slepton u i¯d j→˜e k L→t¯b can be induced by the LV couplingsλ′.The matrix element squared is given by2λ′1ijλ′133+λ′2ijλ′233+λ′3ijλ′333 2˜χ+j(j=1,2)and˜e L→e+˜χ0j(j=1,2,3,4)[32]. However,in the R-parity violating MSSM,the slepton can also decay into quark pairs via the λ′couplings˜e i L→¯u j L+d k R.Since the allowedλ′couplings are quite small,the dominant decays are the chargino and neutralino modes.The partial widths are given byΓ(˜e L→νe+16πM3˜e |U j1|2M2˜e−M2˜χ+j 2,(11)Γ(˜e L→e+˜χ0j)=g2cW ( 1Due to the large QCD backgrounds at hadron colliders,it is very difficult,if not impossible, to search for the signal from the hadronic decays of the top quark.We therefore look for events with t→W+b→l+νb(l=e,µ).(We take into account of the fact that the top quark is polarized in hadronic production.)Thus,the signature of this process is an energetic charged lepton,missing E T,and double b-quark jets.We assumed silicon vertex tagging of the b-quark jet with50%effeciency and the probability of0.4%for a light quark jet to be mis-identified as a b-jet[33].Although the present events have the unique signal of same sign b-quarks,since the tagging can not distinguish a b-quark jet from¯b-quark jet,there are many potential SM backgrounds [33]:(1)the Drell-Yan like process q¯q′→W∗→t¯b;(2)the quark-gluon process qg→q′t¯b with a W-boson as an intermediate state in eitherthe t-channel or the s-channel of a subdiagram;(3)processes involving a b-quark in the initial state,bq(¯q)→tq′(¯q′)and gb→tW;(4)W b¯b;(5)W jj;(6)t¯t→W−W+b¯b.Background process(2)contains an extra quark jet and can only mimic our signal if the quark misses detection by going into the beam pipe.This can only happen when the light quark jet has the pseudorapidity greater than about3or the transverse momentum less than about10 GeV.In our calculation of the W-gluon fusion process as a background,we imposeη(q′)>3 and p T(q′)<10GeV for the light-quark jet.The bq(¯q)→tq′(¯q′)background is greatly reduced by requiring double b-tagging.The process gb→tW can only imitate our signal if the W decays into two jets,where one jet is missed by the detector and the other is mis-identified as a b quark,which should be negligible.Since we required two b-jets to be present in thefinal state and assumed the probability for a light quark jet to be mis-identified as a b-jet is0.4%,the potentially large background process(5)from W jj is reduced to an insignificant level.Also we required the reconstructed top quark mass M(bW)to lie within the mass range|M(bW)−m t|<30GeV,(13) which can also reduce the backgrounds W b¯b and W jj efficiently.Background process(6)can mimic our signal if both W’s decay leptonically and one charged lepton is not detected,which we assumed to occur ifη(l)>3and p T(l)<10GeV.To make a realistic estimate we also need to consider the detector acceptance.To simulate the detector acceptance,we made a series of cuts on the transverse momentum(p T),the pseudo-rapidity(η),and the separation in the azimuthal angle-pseudo rapidity plane(∆R=E⊕1%,for leptons,(22)√=80%/where⊕indicates that the energy dependent and independent terms are added in quadrature and E is in GeV.We calculated the p¯p(for the Tevatron)and pp(for the LHC)cross sections for the sig-nal with the MRSA′structure functions[34].We have also examined the effect of using the CTEQ3M[35]structure functions and found the difference between the two sets of structure functions to be small.We have explicitly calculated backgrounds(1)and(2),and for the oth-ers used the W jj background analysis of Ref.[36].The effect of the cuts is shown in Table1.√Also,in our numerical calculation,we assumed M t=175GeV,s=14TeV for the LHC.The integrated luminosities for both colliders are assumed to be10fb−1.Assuming Poisson statistics,the number of signal events required for discovery of a signal at the95%confidence level is approximately:S≥3,(24)S+Bwhere S(B)is the number of signal(background)events obtained by multiplying the signal (background)cross section by the luminosity(10fb−1)and the tagging efficiency for two b-jets (0.5×0.5).With all the above assumptions,we now present the results for both processes.3.1The B-violating process of tb productionFor the BV process of tb production,qq′→squark→tb,we neglect ud→˜s→tb and us→˜d→tb sinceλ′′112<10−6[10].For simplicity,we assumeλ′′332andλ′′331do not coexist and hence evaluate cd→˜s→tb and cs→˜d→tb seperately.AssumingΓ˜s=M˜s/5,we obtain Fig.1which shows the value ofλ′′212λ′′332versus strange-squark mass for cd→˜s→tb to be observable at95%confidence level.The region above each curve is the corresponding observable region.The solid curve is for the LHC,the dotted curve is for the upgraded Tevatron and the dashed line is the perturbative unitarity bound[4,5]. Here we see that both the LHC and the upgraded Tevatron can efficiently probe the relevant couplings,and the LHC serves a more powerful probe than the upgraded Tevatron.As was discussed in the above section,the width of a down-type squark depends on manyfree parameters,which can vary in a large range.In order to show the sensitivity of the results to the width of strange-squark,we present in Fig.2the value ofλ′′212λ′′332versus the ratioΓ˜s/M˜s for cd→˜s→tb to be observable at95%confidence level.Here we assume M˜s=300GeV.The region above each curve is the corresponding observable region.The solid curve is for the LHC and the dashed curve is for the upgraded Tevatron.We see from thisfigure that the value of λ′′212λ′′332varies mildly as a function ofΓ˜s/M˜s.Again it is shown in thisfigure that the LHC is more powerful than the upgraded Tevatron in probing the relevant couplings.The value ofλ′′212λ′′331versus down-squark mass for cs→˜d→tb to be observable at95% confidence level is shown in Fig.3.The region above each curve is the corresponding observable region.The solid curve is for the LHC,the dotted curve is for the upgraded Tevatron and the dashed line is the perturbative unitarity bound.The behaviour of thisfigure is similar to Fig.1. But for equal squark mass the value ofλ′′212λ′′331in Fig.3is higher than the value ofλ′′212λ′′332in Fig.1.This shows that the process cs→˜d→tb cannot be probed as efficiently as cd→˜s→tb because of the relative suppression of the strange quark structure function compared to the valence down quark.3.2L-violating process of t¯b productionFor the LV process of t¯b production,q¯q′→slepton→t¯b,we only consider the dominant process u¯d→slepton→t¯b and thus provide the results forλ′111λ′133+λ′211λ′233+λ′311λ′333.The previous study[30]of this process at the upgraded Tevatron has shown that within the allowed range of the relevant coupling constants,this process is observable only when the slepton mass lies in a specific narrow range.Here we will determine if the LHC can do better than the upgraded Tevatron.As discussed in the above section,the allowedλ′couplings which induce a charged slepton to decay into quark pairs are quite small and thus the dominant decays of a charged slepton are the chargino and neutralino modes.So we only consider the chargino and neutralino modes for simplicity.Then the width of the charged slepton only depends on the SUSY parameters M2,M1,µand tanβ.In our calculation we use the GUT relation M1=5M2≈1g2masses are above the present lower limits from LEP II[37].Figure4shows the value ofλ′111λ′133+λ′211λ′233+λ′311λ′333versus the slepton mass for u¯d→slepton→t¯b to be observable at95%confidence level.The region above each curve is the corresponding observable region.The solid curve is for the LHC,the dotted curve is for the upgraded Tevatron and the dashed line is the value obtained by considering the following bounds for squark mass of100GeV[7,11,17]|λ′i11|<0.012,(i=1,2,3),(25)|λ′133|<0.001,(26)|λ′233|<0.16,(27)|λ′333|<0.26.(28) Figure4shows that below the present upper limit for the couplings the LHC cannot do much better than the upgraded Tevatron in further probing the couplings.In summary,we have studied single top quark production via qq′→squark→tb and q¯q′→slepton→t¯b at the Tevatron and the LHC in the MSSM with R-parity violation.Our results show that from the measurement of single top production,the LHC can efficiently probe the relevant R-parity violating couplings.AcknowledgementsWe would like to thank M.Hosch for help in evaluating some of the backgrounds,and A. 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[29]For reviews of R-parity violation,see,for example,G.Bhattacharyya,Nucl.Phys.Proc.Suppl.52A,83(1997).[30]A.Datta,J.M.Yang,B.-L.Young and X.Zhang,hep-ph/9704257,to appear inPhys.Rev.D.[31]C.Carlson,P.Roy and M.Sher,Phys.Lett.B357,99(1995);A.Y.Smirnov andF.Vissani,Phys.Lett.B380,317(1996).[32]H.Baer,A.Bartl,D.Karatas,W.Majerotto and X.Tata,Int.J.Mod.Phys.A4,4111(1989).[33]D.Amidei and C.Brock,“Report of the TeV2000Study Group on Future Elec-troWeak Physics at the Tevatron”,1995.[34]A.D.Martin,R.G.Roberts and W.J.Stirling,Phys.Lett.B354,155(1995).[35]i,J.Botts,J.Huston,J.G.Morfin,J.F.Owens,J.W.Qiu,W.K.Tungand H.Weerts,Phys.Rev.D51,4763(1995).[36]M.Hosch,private communication.The W jj background was evaluated using theVECBOS monte carlo program,(see F.A.Berends,H.Kuijf,B.Tansk and W.T.Giele,Nucl.Phys.B357,32(1991))while the W b¯b and t¯t backgrounds were evaluated using the ONETOP monte carlo(see E.Malkawi and C.-P.Yuan,Phys.Rev.D50,4462(1994);D.O.Carlson and C.-P.Yuan,Phys.Lett.B306,386 (1993).)[37]B.Mele,hep-ph/9705379.Figure CaptionsFig.1The value ofλ′′212λ′′332versus strange-squark mass for cd→˜s→tb to be observable at95%confidence level.The region above each curve is the corresponding observable region. The solid curve is for the LHC,the dotted curve is for the upgraded Tevatron and the dashed line is the perturbative unitarity bound[4,5].Fig.2The value ofλ′′212λ′′332versus the ratioΓ˜s/M˜s for cd→˜s→tb to be observable at 95%confidence level.The region above each curve is the corresponding observable region.The solid curve is for the LHC and the dashed curve is for the upgraded Tevatron.Fig.3The value ofλ′′212λ′′331versus down-squark mass for cs→˜d→tb to be observable at 95%confidence level.The region above each curve is the corresponding observable region.The solid curve is for the LHC,the dotted curve is for the upgraded Tevatron and the dashed line is the perturbative unitarity bound[4,5].Fig.4The value ofλ′111λ′133+λ′211λ′233+λ′311λ′333versus the slepton mass for u¯d→˜l→t¯b to be observable at95%confidence level.The region above each curve is the corresponding observable region.The solid curve is for the LHC,the dotted curve is for the upgraded Tevatron and the dashed line is the present bound,Eqs.(25-28).Table1:Signal and background cross sections in units of fb after various cuts at the Tevatron and the LHC.The qq′→˜q→tb results have been calculated using the unitarity bound for the relevant couplings and assuming M˜q=500GeV andΓ˜q=M˜q/5.The q¯q′→˜l→t¯b results have been calculated using the present upper bound Eqs.(25)-(28)for the relevant couplings and slepton mass of300GeV.The slepton width is calculated by assuming M2=−µ=250GeV and tanβ=2.The charge conjugate channels are included.basic cuts basic+m(bW)+bb-tagcd→˜s→tb1436cs→˜d→tb174u¯d→˜l→t¯b73q¯q′→t¯b75gq→q′t¯b 3.4qb→q′t224W b¯b122W jj45000t¯t7basic cuts basic+m(bW)+bb-tagcd→˜s→tb304800cs→˜d→tb113600u¯d→˜l→t¯b480q¯q′→t¯b547gq→q′t¯b810qb→q′t13440W b¯b338W jj379000t¯t644。

a r X i v :h e p -p h /0007280v 1 25 J u l 2000AMES-HET-00-06July 2000Probing R-violating top quark decays at hadron colliders K.J.Abraham a ,Kerry Whisnant a ,Jin Min Yang b ,Bing-Lin Young a,b a Department of Physics and Astronomy,Iowa State University,Ames,Iowa 50011,USA b Institute of Theoretical Physics,Academia Sinica,Beijing 100080,China ABSTRACT We examine the possibility of observing exotic top quark decays via R-violating SUSY interactions at the Fermilab Tevatron and CERN LHC.We present cross-sections for t ¯t production followed by the subsequent decay of either t or ¯t via the R-violating interaction while the other undergoes the SM decay.With suitable kinematic cuts,we find that the exotic decays can possibly be detected over standard model backgrounds at the future runs of the Tevatron and LHC,but not at Run 1of the Tevatron dueto limited statistics.Discovery limits for R-Violating couplings in the top sector are presented.1IntroductionThe top quark,with a mass of the order of the electroweak symmetry breaking scale,is naturally considered to be related to new physics.Run1of the Fermilab Tevatron has small statistics on top quark events and thus leaves plenty of room for new physics to be discovered at the upgraded Tevatron[1]in the near future.Due to higher statistics, the t¯t events at the upgraded Tevatron are expected to provide sensitive probes for new physics[2].The most popular model for new physics is the Minimal Supersymmetric Model(MSSM)[3].In this model,R-parity[4],defined by R=(−1)2S+3B+L with spin S,baryon-number B and lepton-number L,is often imposed on the Lagrangian to maintain the separate conservation of B and L.As a consequence the sparticle number is conserved.Since instanton effects induce miniscule violations of baryon and lepton number[5],R-parity conservation is not dictated by any known fundamental principle such as gauge invariance or renormalizability.If R-parity is strictly conserved,it is conceivable that the conservation comes from some hitherto unidentified fundamental principle.Hence R-parity violation should be vigorously searched for.The most general superpotential of the MSSM,consistent with the SU(3)×SU(2)×U(1)symmetry,supersymmetry,and renomalizability also contains R-violating interac-tions which are given byW R=12λ′′ijkǫαβγU c iαD c jβD c kγ+µi L i H2,(1) where L i(Q i)and E i(U i,D i)are the left-handed lepton(quark)doublet and right-handed lepton(quark)singlet chiral superfields.The indicies i,j,k are generation indices,α,βandγare the color indices,c denotes charge conjugation,andǫαβγis the total antisym-metric tensor in three-dimension.H1,2are the Higgs-doublets chiral superfields.The coefficientsλandλ′are the coupling strengths of the L-violating interactions andλ′′those of the B-violating interactions.The lower bound of the proton lifetime imposes very strong conditions on the simultaneous presence of both L-violating and B-violating interactions[6]and hence the strength of the couplings.However,the existence of either L-violating or B-violating couplings,but not both at the same time,does not induce nucleon decays and therefore the R-parity violating couplings are less constrained.This separate L and B violation is usually assumed in phenomenological analyses.The study of the phenomenology of R-violating supersymmetry was started many years ago[7].Some constraints on the R-parity violating couplings have been obtained from various analyses,such as perturbative unitarity[8],n−¯n oscillation[9],νe-Majoranamass[10],neutrino-less doubleβdecay[11],charged current universality[12],e−µ−τuniversality[12],νµ−e scattering[12],atomic parity violation[12],νµdeep-inelastic scat-tering[12],µ−e conversion[13],K-decay[16],τ-decay[15],D-decay[15],B-decay[16] and Z-decay at LEP I[17].As reviewed in Ref.[18],although many such couplings have been severely constrained,the bounds on the top quark couplings are generally quite weak.This is the motivation for the phenomenological study of R-violation in processes involving the top quark.The production mechanisms of top pairs and single top in R-violating SUSY at the upgraded Tevatron have been examined in[19]and[20],respectively.In addition,the R-violating couplings can induce exotic decays for top quark at an observable level. For example,the top quark FCNC decays induced by R-violating couplings[21]can be significantly larger than those in the MSSM with R-parity conservation[22].If we allow the co-existence of twoλ′couplings,we have the new decay modes,such as t→ℓ˜d→ℓ+ℓ−u[23].The bilinear termµi L i H2can also induce some new decays for the top quark,as studied in[24].In this work,we focus on the explicit trilinear couplings and assume only one trilinear coupling exists at one time.Then the possible exotic top decay modes aret→˜¯d i¯d j,˜¯d j¯d i→¯d i¯d j˜χ01(2) induced by the B-violatingλ′′3ij,andt→e+i˜d j˜e i d j→e+i d j˜χ01(3) induced by the L-violatingλ′i3j.Here the subscripts i,j are family indices and˜χ01is the lightest neutralino which,in our analysis,is assumed to be the lightest super particle (LSP)as favored in the MSSM where the SUSY breaking is propagated to the matter sector by gravity1.The sfermions involved in these decays can be on-shell or virtual, depending on the masses of the particles involved.Among the exotic decays in(2)and(3),the relatively easy-to-detect modes are those induced byλ′′33j(j=1,2)2andλ′i33(i=1,2,3)because theirfinal states contain a b-quark which can be tagged.One of the L-violating channels,i.e.,t→˜τb(orτ˜b)induced byλ′333has been studied in[25].So in our analysis we focus on the cases ofλ′133and λ′233for L-violating couplings,andλ′′331andλ′′332for B-violating couplings.Since the decay induced byλ′133has the similarfinal states to that induced byλ′233,we take thepresence ofλ′233as an example.For the same reason,we take the presence ofλ′′331as an example in B-violating case.The Feynman diagrams for these two decays induced by λ′′331andλ′233are shown in Figs.1and2,respectively.In our analysis we consider t¯t events where one(t or¯t)decays via R-violating coupling while the other decays by the SM interaction.The SM decay will serve as the tag of the ¯t t event.Furthermore,the penalty of the suppressed R-violation coupling is paid only once.Top spin correlations are taken into account in our calculation.Note that the LSP(˜χ01)is no longer stable when R-parity is violated.In case just one R-violating top quark coupling does not vanish,the lifetime of the LSP will be very long,depending the coupling and the masses of squarks involved in the LSP decay chain(cf.the last paper of[18]).Thus it is generally assumes that the LSP decays outside the detector[26].We will make this assumption in our analysis.This paper is orgnized as follows.In Sec.2,we investigate the potential of observing the B-violating top quark decay at the Tevatron and LHC,and present numerical results.In Sec.3we present similar results for L-violating decay.Finally in Sec.4we present a summary and discussion.2Searching for B-violating decay2.1Signal and backgroundTo probe the decay t→¯b¯d˜χ01in Fig.1,we consider thefinal states given by t¯t production where one(say t)decays via the couplingλ′′331while the other(say¯t has the SM decays to serve as the tag of the¯t t event.Due to the large QCD background at hadron colliders,we do not search for the all-jets channel despite of its higher rate.Instead,we search for the signal given by t¯t events followed by t→¯b¯d˜χ01and¯t→W−¯b→ℓ¯ν¯b(ℓ=e,µ).Then the signature is a lepton,three jets containing two b-jets or two¯b-jets,and missing energy (ℓ+3j/2b+E T).We require that two b-jets are tagged in the signal.The efficiency for double b-tagging is assumed to be42%[1].Note that the present events have the unique signal of the two same sign b-quarks. In our analysis,to be conservative,we assume that the tagging can not distinguish a b-quark jet from¯b-quark jet.Then the SM backgrounds are mainly from(1)t¯t→W−W+b¯b followed by W−→ℓ¯ν(ℓ=e,µ)and W+→τ+νwith theτdecaying into a jet plus a neutrino;(2)t¯t→W−W+b¯b followed by W−→ℓν(ℓ=e,µ)and W+→q¯q′.This processcontains an extra quark jet and can only mimic our signal if the quark misses detection by going into the beam pipe.We assume this can only happen when the light quark jet has the pseudo-rapidity greater than about3or the transverse momentum less than about10GeV.(3)W b¯bj which includes single top quark production via the quark-gluon processqg→q′t¯b as well as non-top processes[27].2.2Numerical calculation and resultsWe calculated the signal and background cross sections with the CTEQ5L structure√functions[28].We assume M t=175GeV and takes=14TeV for the LHC.As shown in Fig.1,there are two contributing graphs.Since among the down-type squarks the sbottom is most likely to be lighter than other squarks(we will elaborate on this later),we assume thefirst graph in Fig.1gives the dominant contribution.(If the ˜d is as light as the sbottom,the second diagram in Fig.1has to be taken into account. Then our results for the signal rate should be quadrupled.To be conservative,we do not consider this case.)For the total width of the sbottom involved in our calculation,we note that since only a light sbottom is meaningful to our analysis(as will be shown in our results), its dominant(or maybe the only)decay mode is˜b→b˜χ01.The charged current decay mode˜b→t˜χ+1is kinematically forbidden for a light sbottom in our analysis.We do not consider the strong decay mode˜b→b˜g since the gluino˜g is likely to be heavy[29]. The signal cross section is proportional to|λ′′331|2.We will present the signal results normalized to|λ′′331|2.The signal cross section is very sensitive to the sbottom mass. We will vary it to see how heavy it can be for the signal to be observable.Other SUSY parameters involved are the lightest neutralino mass and its coupling to sbottom,which are determined by the parameters M,M′,µand tanβ.M is the SU(2)gaugino mass and M′is the hypercharge U(1)gaugino mass.µis the Higgs mixing term(µH1H2) in the superpotential.tanβ=v2/v1is the ratio of the vacuum expectation values of the two Higgs doublets.We work in the framework of the general MSSM.But we assume the grand unification of the gaugino masses,which gives the relation M′= 5choose a representative set of valuesM=100GeV,µ=−200GeV,tanβ=1.(4)They yield the lightest chargino and neutralino masses as m˜χ+1=120GeV,m˜χ01=55GeV.Thus this set of values are allowed by the current experimental bounds on the chargino and neutralino masses,which are about90GeV and45GeV,respectively[30].We simulate detector effects by assuming Gaussian smearing of the energy of the chargedfinal state particles,given by:∆E/E=30%/√E⊕5%,for hadrons,(6)where⊕indicates that the energy dependent and independent terms are added in quadrature and E is in GeV.The basic selection cuts are chosen aspℓT,p jet T,p missT≥20GeV,(7)ηjet,ηℓ≤2.5,(8)∆R jj,∆R jℓ≥0.5.(9) Here p T denotes transverse momentum,ηis the pseudo-rapidity,and∆R is the separa-tion in the azimuthal angle-pseudo rapidity plane(∆R=(| PℓT|+| P miss T|)2−( PℓT+ P miss T)2.(10)As is well-known,if the two components,i.e.,ℓand p missTin our case,are from the decay of a parent particle,the transverse mass is bound by the mass of the parent particle.Sofor W b¯bj background events m T(ℓ,p missT)is always less than M W and peaks just below M W.However,kinematic smearings can push the bound and the peak above M W.In order to substantially suppress the large backgrounds(2)and(3)we apply the following cutm T(ℓ,p missT)>120GeV.(11)We found that the above strong m T(ℓ,p miss)cut suppresses the background process(2)Tand(3)by roughly three orders of magnitude for the smearing in Eqs.(5)and(6),sothat they are much smaller than the other backgrounds we are considering.But since background process(1)contains three neutrinos from different parent particles,it is not supressed by the m T(ℓ,p miss)cut to a negligible level.There is some model dependenceTinvolved the treatment ofτhadronization.To avoid having to consider each of the many hadronic decay modes separately,we assume the invariant mass of the outgoing hadrons to be distributed uniformly from mπto mτ.Furthermore,we assume a uniform angular distribution in the phase allowed by the invariant mass of the outgoing jet.This assumption is probably reasonable in light of the fact that the parentτis heavily boosted in the lab frame.With the above selection cuts,the signal and background cross sections are given in Table1.We see that the signal-to-background ratio can be quite large for light sbottom mass(∼<160GeV),in which the intermediate sbottom can be materialized as a real particle.When the sbottom becomes heavier than the top quark and thus can only appear as a virtual state,the cross section is severely suppressed by the small branching ratio of the decay.From the results for Tevatron(1.8TeV)in Table1we conclude that the luminosity Run1(0.1fb−1)is too low to detect such decays.However,due to the much largerstatistics of Run2(2fb−1)and Run3(30fb−1),it is possible to observe such decays in√these coming runs of the ing the discovery criteria S≥5changing a slepton.As in Sec.2,we assume sbottom can be light and thus concentrate on thefirst graph.In the opposite case that the slepton is light and sbottom is heavy, our following results still hold with the replacement of sbottom mass by slepton mass. If both sbottom and slepton are light and approximately degenerate(which is quite un-likely in the supergravity scenario of supersymmetry breaking,as will be elaborated on later),then our results for the signal rate should be quadrupled.Our examination for this decay is similar to the B-violating decay in the preceding section.We search for the signal given by t¯t events where one(say t)decays via L-violating coupling,t→µ+b˜χ01,while the other(¯t)has the SM decays,¯t→W−¯b.Then there are two possible observing channels for such an event:dilepton+2-jets and single lepton+4-jets,all being associated with missing energies.The dilepton channel has the lower rate and it is difficult tofind a mechanism to enhance the S/B rate so as tofind the ”smoking gun”for the signal.So we search for the single lepton+4-jets channel which has a higher rate.As is shown below,we canfind effective selection cuts to enhance the S/B ratio for this signal.Among the four jets in our signal there are two b-jets(one is b,the other is¯b).We require that at least one b-jet passes b-tagging.The tagging efficiency is53%at Run1 and expected to reach85%at Run2and Run3[1].For the LHC we assume the tagging efficiency to be the same as the Tevatron Run2.So the signature isℓ+4j/b+E T where4j/b represents a4-jets event with at least one of the jets passing the b-tagging criterion.This is the same as one of the typical signatures for t¯t event in the SM,except for the different source of missing energy.To suppress the QCD background,we apply the basic selection cuts in Eqs.(7-9).Under the basic selection cuts the QCD background is reduced to about1/12of the SM t¯t events[1].However,under the basic selection cuts the number of SM t¯t events far surpasses the number of signal events.In order to extract the signal events,we turn to the transverse mass defined in Eq.(10).For the SM t¯t events and W+jets background events the missing energy comes from the neutrino of the W decay,while for the signal events the missing energy comes from the neutralino in the decay t→µ+˜b→µ+b˜χ01. Thus the transverse mass distributions of the SM background and the signal events are different,as shown in Fig.5.In order to enhance the S/B ratio,we apply the following cut,taking into account of the smearing effect,m T(ℓ,p miss)∈50∼100GeV.(12)TOther details in the numerical calculation,such as the smearing of the energy ofthefinal state particles and the choice of SUSY parameters,are the same as in Sec.2. In Table2we present the signal cross section for sbottom mass of150GeV,with the comparison to the SM t¯t background.One sees that the transverse mass cut can enhance the S/B ratio significantly.With the increase of sbottom mass,the signal cross section drops rapidly,as shown in Table3.From Tables2and3one sees that Run1(0.1fb−1)of the Tevatron collider is unable to detect such decays for a sbottom heavier than150GeV andλ′233<1.The possibility of observing such a decay is enhanced at Run2(2fb−1),Run3(30fb−1)and the LHC.√Under the discovery criteria S≥5A few remarks are due regarding our results:(1)The results are sensitive to the sbottom mass;the signal is observable only for alight sbottom.The possibility of a light sbottom is usually motivated as follows: Firstly,the neutral kaon system gives a strong constraint[31]on the masses of thefirst and second generation squarks.The third generation sfermions are much less constrained so far.Secondly,in the supergravity scenario of supersymmetry breaking,mass splitting of the third-generation and the other sfermions results from the renormalization group evolution of the masses between the unification scale and the weak scale,even if the sfermions have equal masses at the unification scale.This splitting is due to the effect of the large Yukawa coupling of the top.The bottom and tau sectors are also affected.Thirdly,there are arguments[32] thatfirst and second generation sfermions can be as heavy as10TeV without conflicting the naturalness problem,while the third generation sfermions have to be rather light.(2)As pointed out in Sec.(1),the two decay processes we considered resemble thefavorable cases in which a b-jet is produced in the decay products.While we can apply our results directly to the cases ofλ′′332andλ′133,we noticed that similar decays induced by other couplings likeλ′′312andλ′232give poor signals since there is no b-quark in their corresponding top decays.(3)We noted that apart from the relevant R-violating couplings and the sbottom mass,our results are also dependent on the mass and coupling of the lightest neutralino.In our calculation we only present some illustrative results byfixing a set of SUSY parameters rather than scanning the entire allowed SUSY parameter space.In some unfavorable cases,such as when the mass of the lightest neutralino(LSP)is close to the sbottom mass so that the b-quark from the sbottom decay(˜b→b˜χ01) is too soft to pass the selection cuts,these exotic decays would be unobservable even at the LHC.(4)As pointed out in Sec.2,the B-violating decay gives the unique signal of samesign b-quarks while the main SM backgrounds give the unlike sign b-quarks.To be conservative,we assumed in our analysis that the b tagging is not of sufficient sensitivity to distinguish between a b-jet and a¯b-jet.If b charge identification can be achieved in future detectors,more stringent discovery limits than those we have presented will be possible.Additional improvements 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The double b-jet tagging with42%efficiency is assumed.The charge conjugate channels have been included.Signal/(λ′′331)211 5.8 2.040.270.010.0050.003(1.8Tev)Signal/(λ′′331)2168.4 3.00.40.020.0070.004 (2Tev)Signal/(λ′′331)2162488537158 1.70.40.3 (14Tev)Table2:Signalℓ+4j/2b+E T and the SM t¯t background cross sections for sbottom mass of 150GeV.The basic cuts are p all T≥20GeV,|ηall|≤2.5and∆R≥0.5,and the transversemass cut is m T(ℓ,p missT)∈50∼100GeV.The signal results were calculated by assuming M=100GeV,µ=−200GeV and tanβ=1.Tagging at least one b-jet is assumed for53% efficiency for the Tevatron(1.8TeV),85%efficiency for the upgraded Tevatron(2TeV)and LHC.The charge conjugate channels have been included.basic cutsm T(ℓ,p missT )cutSignal/(λ′233)2(fb)43 Background(fb)86 Signal/(λ′233)2(fb)96 Background(fb)193 Signal/(λ′233)2(pb)8.2 Background(pb)16Table3:Same as Table2,but for the signal cross section versus sbottom mass under the basic plus transverse mass cut.Tevatron(1.8Tev):150155160165170180190200 Signal/(λ′331)2(fb)Tevatron(2TeV):150155160165170180190200 Signal/(λ′233)2(fb)LHC(14TeV):150155160165170180190200 Signal/(λ′′233)2(pb)Figure1:The Feynman diagram for the B-violating decay induced byλ′′331.Figure2:The Feynman diagram for the L-violating decay induced byλ′233.Figure3:The discovery limits ofλ′′33j versus sbottom mass at Run2(2fb−1),Run3 (30fb−1)and LHC(10fb−1).The region above each curve is the corresponding regionof discovery.Figure4:The exclusion limits ofλ′′33j versus sbottom mass at Run2(2fb−1),Run3 (30fb−1)and LHC(10fb−1).The region above each curve is the corresponding regionof exclusion.Figure5:The transverse mass,m T(ℓ,p missT ),distribution ofℓ+4j/b+E T at theTevatron collider.The solid curve is for the signal event.The dotted curve is for the SM t¯t background.Figure6:The discovery limits ofλ′233versus sbottom mass at Run2(2fb−1),Run3 (30fb−1)and LHC(10fb−1).The region above each curve is the corresponding regionof discovery.Figure7:The exclusion(95%C.L.)limits ofλ′233versus sbottom mass at Run2(2fb−1), Run3(30fb−1)and LHC(10fb−1).The region above each curve is the correspondingregion of exclusion.。

a r X i v :h e p -e x /0308069v 1 28 A u g 20031Presented at QCD 02:High Energy Physics International Conference in Quantum Chromodynamics,Montpellier,France,2-9Jul 2002.Nucl.Phys.B (Proc.Suppl.)121(2003)239-248SLAC-PUB-10138B Decays at B A B A RJ.J.Back a ∗aPhysics Department,Queen Mary,University of London,Mile End Road,London,E14NS,UK (on behalf of the B A B A R Collaboration)We present branching fraction and CP asymmetry results for a variety of B decays based on up to 56.4fb −1collected by the B A B A R experiment running near the Υ(4S )resonance at the PEP-II e +e −B -factory.1.The B A B A R DetectorThe results presented in this paper are based on an integrated luminosity of up to 56.4fb −1collected at the Υ(4S )resonance with the B A B A R detector [1]at the PEP-II asymmetric e +e −col-lider at the Stanford Linear Accelerator Center.Charged particle track parameters are measured by a five-layer double-sided silicon vertex tracker and a 40-layer drift chamber located in a 1.5-T magnetic field.Charged particle identification is achieved with an internally reflecting ring imag-ing Cherenkov detector (DIRC)and from the av-erage d E/d x energy loss measured in the track-ing devices.Photons and π0s are detected with an electromagnetic calorimeter (EMC)consisting of 6580CsI(Tl)crystals.An instrumented flux return (IFR),containing multiple layers of re-sistive plate chambers,provides muon and long-lived hadron identification.2.B Decay ReconstructionThe B meson candidates are identified kine-matically using two independent variables.Thefirst is ∆E =E ∗−E ∗beam ,which is peaked at zero for signal events,since the energy of the B candi-(E ∗2beam −p ∗2B ),where p ∗Bis the momentum of the B meson in the Υ(4S )rest frame,and must be close to the nominal B mass [5].The resolution of m ES is dominated by the beam energy spread and is approximately 2.5MeV /c 2.Several of the B modes presented here havedecays that involve neutral pions (π0)and K 0S particles.Neutral pion candidates are formed by combining pairs of photons in the EMC,with re-quirements made to the energies of the photons and the mass and energy of the π0.Table 1shows these requirements for various decay modes,aswell as the selection requirements for K 0S candi-dates,which are made by combining oppositely charged pions.Significant backgrounds from light quark-antiquark continuum events are suppressed using various event shape variables which exploit the difference in the event topologies in the centre-of-mass frame between background events,which have a di-jet structure,and signal events,which tend to be rather spherical.One example is thecosine of the angle θ∗T between the thrust axis of the signal B candidate and the thrust axis of the2Table1Selection requirements forπ0and K0Scandidates for various B decay modes(h=K/π).Eγis the minimum photon energy and mπ0and Eπ0the mass and energy,respectively,ofπ0candidates.Themass of the K0S is m K0S,the opening angle between the K0Smomentum and its line-of-flight isφK0S,thetransverseflight distance of the K0S from the primary event vertex is d K0Sandτ/σK0Sis the K0Slifetimedivided by its error.B→DK>70[124,144]>200————B→D(∗)D(∗)>30[115,155]>200[473,523]<200>2—B→hπ0>30[111,159]—————B→hK0———[487,509]——>5 B→φK(∗)———[487,510]<100—>3 B→ηh>50[120,150]—————B→ηK0>50[115,155]—[491,507]<40>2—B→η′K(∗)0———[488,508]———B→K∗γ>30[115,150]>200[489,507]———B→K(∗)ℓ+ℓ−———[480,498]—>1—33.B→DKThe decays B−→D0K−and B±→D0±K±,where D0±denotes the CP-even(+)or CP-oddstates(−)(D0±¯D0)/√B(B−→D0π−)=(8.31±0.35±0.13)%,(2)where thefirst error is statistical and the sec-ond error is systematic.This quantity has alsobeen measured by the CLEO and BELLE Col-laborations,where they get R=(5.5±1.4±0.5)%[7]and R=(7.9±0.9±0.6)%[8],re-spectively.Theory predicts,using factorisationand tree-level Feynman diagrams only,a valueR≈tan2θC(f K/fπ)2≈7.4%,whereθC is theCabibbo angle,and f K and fπare the mesondecay constants.For the CP-even mode D0+→K+K−we have measuredB(B−→D0+K−)+B(B+→D0+K+)R CP=B(B−→D0+K−)+B(B+→D0+K+)=0.15±0.24+0.07.(4)44.B→D(∗)D(∗)Time-dependent CP violating asymmetries in the decays B→D(∗)D(∗)can be used to measurethe CKM angleβ[9],in a way complimentary to measurements already made with decays such asB0→J/ψK0S[10].However,the vector-vector decay of B0→D∗+D∗−is not a pure CP eigen-state,which may cause a sizeable dilution to theCP violation that can be observed.In principle,a full time-dependent angular analysis can remove this dilution[11].We reconstruct exclusively the decays B0→D∗+D∗−and B0→D∗±D∓,where D∗±→D0π±or D±π0.Thefinal states we consider for the neutral D mesons are K−π+,K−π+π0, K−π+π−π+and K0Sπ+π−,while we consider theD+final states K−π+π+,K0Sπ+and K−K+π+. B0candidates are reconstructed by performing a mass-constrainedfit to the D and D∗candi-dates.In the case when more than one B candi-date is found for an event,we chose the B candi-date in which the D and D∗mesons have invari-ant masses closest to their nominal values[5]. Signal events are required to satisfy|∆E|< 25MeV and5.273<m ES<5.285GeV/c2. Using a sample of22.7million BΓdΓ4(1−R t)sin2θtr+3B(B+→π+π0),(9)where B(B0→π0π0) CP=15m ES (GeV/c 2)E v e n t s /2 M e V /c2B A B AR5105.2 5.225 5.25 5.2755.3Figure 3.Distribution of m ES for B +→π+π0events in on-resonance data.The solid curve rep-resents the projection of the maximum likelihood fit result,while the dotted curve represents the background contribution.Table 2Two-body charmless B decay branching frac-tions (B )and CP asymmetries (A CP )based on 56.4fb −1.Upper limits are given at the 90%confidence level.π+π04.1+1.1+0.8−1.0−0.7−0.02+0.27−0.26±0.10K +π011.1+1.3−1.2±1.00.00±0.11±0.02π+K 017.5+1.8−1.7±1.8−0.17±0.10±0.02K +6.Three-body Charmless Charged B Decays The decays B +→h +h −h +,where h =πor K ,can be used to measure the angle γ[18].The ba-sic idea is that there can be interference between resonant and non-resonant amplitudes leading to direct CP violation.A Dalitz plot analysis can,in principle,give us information about all of the strong and weak phases in these decays.A first step towards this goal is to measure the branch-ing fractions into the whole Dalitz plot.We can write these asB =1Bi S iBis the total number of B6Figure4.Unbinned Dalitz plots(with no back-ground subtraction or efficiency corrections)for B+→K+π−π+events in on-resonance sideband (top left)and signal(top right)data,and forB+→K+K−K+events in on-resonance side-band(bottom left)and signal(bottom right) data.Open charm contributions are not removed.measure(180±4±11)×10−6for the branch-ing fraction for the B−→D0π−control sample, which agrees with the previously measured value of(203±20)×10−6[5].7.B→φK(∗),φπThese modes are interesting because only pen-guin diagrams contribute to the decay amplitudes (mainly b→s¯s s),and the time-dependent CP asymmetry for the neutral mode B0→φK0S can be used to measure sin2β.Comparison with sin2βresults from charmonium modes will allow Table3Three-body charmless charged B decay branching fractions(×10−6)from B A B A R(51.5fb−1)and BELLE(29.1fb−1).π+π−π+8.5±4.0±3.6(<15)—K+π−π+59.2±4.7±4.955.6±5.8±7.7 K+K−π+2.1±2.9±2.0(<7)<21K+K−K+34.7±2.0±1.835.3±3.7±4.57 Table4Branching fractions(×10−6)for B→φK and B+→φπ+decays from B A B A R(56.3fb−1and20.7fb−1†), BELLE(21.6fb−1)and CLEO(9.1fb−1).φK+9.2±1.0±0.811.2+2.2−2.0±1.45.5+2.1−1.8±0.6φK08.7+1.7−1.5±0.98.9+3.4−2.7±1.0<12.3φK∗+9.7+4.2−3.4±1.7†<36<22.5φK∗08.7+2.5−3.7−1.7−2.1±1.1†13.0+6.4−5.2±2.111.5+4.5+1.8φπ+<0.6—<5Mode B(×10−5)A C PB0→K∗0γ4.23±0.40±0.22−0.05±0.09±0.01B+→K∗+γ3.83±0.62±0.22−0.04±0.13±0.01B(¯B→¯K∗γ)+B(B→K∗γ).(11)Theoretical expectations for the branching frac-tions are in agreement with the measured values.8Table 5Measured branching fractions (×10−6)for B decays with ηand η′mesons from the CLEO,BELLE and B A B A R collaborations.ηπ+1.2+2.8−1.2(<5.7)5.4+2.0−1.7±0.62.2+1.8−1.6±0.1(<5.2)†ηK +2.2+2.8−2.2(<6.9)5.3+1.8−1.5±0.63.8+1.8−1.5±0.2(<6.4)†ηK 00.0+3.2−0.0(<9.3)6.0+3.8−2.9±0.4(<12)†ηK ∗013.8+5.5−4.6±1.616.5+4.6−4.2±1.219.8+6.5−5.6±1.5†ηK ∗+26.4+9.6−8.2±3.326.5+7.8−7.0±3.022.1+11.1−9.2±3.2†η′K +80+10−9±778±6±967±5±5η′K 089+18−16±968±1046±6±4η′K ∗07.8+7.7−5.7(<24)4.0+3.5−2.4±1.0(<13)9) 2c (GeV/ES m)2c (GeV/ES m 2c E n t r i e s /3 M e V /Figure 6.Projections from the likelihood fits of the K (∗)ℓ+ℓ−modes onto m ES for the signal re-gion −0.11<∆E <0.05GeV for electrons and −0.07<∆E <0.05GeV for muons.The dotted lines show the level of background,while the solid lines show the sum of the signal and background contributions.11.ConclusionsWe have shown a selection of results from the B A B A R experiment based on up to 56.4fb −1col-lected at the Υ(4S )resonance.We have made the following observations:•B →DK .We have measured the ratio of the branching fractions for B −→D 0K −and B −→D 0π−,as well as the CP asym-metry for the CP -even mode B −→D 0+K −,which is the first step towards measuring γ.•B →D (∗)D (∗)decays,which can be used to measure β,have been fully reconstructed.We have a first measurement of the CP -oddcontent 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