Vector Boson Production at Hadron Colliders Results from HERWIG and Resummed Calculations
关于科学家的作文100字
关于科学家的作文100字英文回答:Scientists play a crucial role in advancing human knowledge and improving our lives. They are curious individuals who constantly ask questions and seek answers through systematic investigation and experimentation.Scientists use the scientific method to conduct their research. They formulate hypotheses, design experiments, collect and analyze data, and draw conclusions based on evidence. This rigorous approach ensures that their findings are reliable and can be replicated by other scientists.Science covers a wide range of disciplines, including physics, chemistry, biology, and astronomy. Each field of study has its own set of methods and tools. For example, physicists use mathematical equations and complex instruments to understand the fundamental laws of theuniverse, while biologists study living organisms and their interactions with the environment.Scientists also collaborate with colleagues from different countries and backgrounds. This international collaboration allows them to share knowledge, resources, and expertise, leading to breakthrough discoveries and innovations. For instance, the discovery of the Higgs boson particle at the Large Hadron Collider involved scientists from around the world working together.Furthermore, scientists have a responsibility to communicate their findings to the public. They often publish their research in scientific journals and present their work at conferences. By sharing their knowledge, scientists contribute to the collective understanding of the world and inspire future generations to pursuescientific careers.中文回答:科学家在推动人类知识的发展和改善我们的生活方面起着至关重要的作用。
Higgs Boson Production in Weak Boson Fusion at Next-to-Leading Order
a rXiv:h ep-ph/43194v29Oct24ANL-HEP-PR-04-4NSF-KITP-04-13hep-ph/0403194Higgs Boson Production in Weak Boson Fusion at Next-to-Leading Order Edmond L.Berger 1,∗and John Campbell 1,†1High Energy Physics Division,Argonne National Laboratory,Argonne,IL 60439(Dated:March 22,2004)Abstract The weak boson fusion process for neutral Higgs boson production is investigated with particular attention to the accuracy with which the Higgs boson coupling to weak bosons can be determined at CERN Large Hadron Collider (LHC)energies in final states that contain a Higgs boson plus at least two ing fully differential perturbative matrix elements for the weak boson fusion signal process and for the QCD background processes,we generate events in which a Higgs boson is produced along with two jets that carry large transverse momentum.The effectiveness of different prescriptions to enhance the signal to background ratio is studied,and the expected signal purities are calculated in each case.We find that a simple cut on the rapidity of one final-state jet works well.We determine that an accuracy of δg/g ∼10%on the effective coupling g may be possible after ∼200fb −1of integrated luminosity is accumulated at the LHC.PACS numbers:14.80.Bn,12.38.Bx,13.85.-t,12.38.QkI.INTRODUCTIONFollowing the discovery of the neutral Higgs boson H at the CERN Large Hadron Col-lider(LHC),attention will focus on the measurement of its couplings to gauge bosons and fermions.A promising reaction from which to extract some of these couplings,particularly the HW W coupling,is the weak-boson fusion(WBF)process[1]–[14],where the Higgs boson H is produced via fusion of the weak bosons W and Z:W W,ZZ→H,and is accom-panied in thefinal state by two jets that carry large transverse momentum p T.To extract the couplings reliably,a good understanding is required of the production processes and the background processes that lead to the samefinal state.Many strong interactions subpro-cesses also generate Higgs boson-plus-two-jet(H+2jet)final states.These background subprocesses can be computed with the techniques of perturbative quantum chromodynam-ics(QCD).They supply an irreducible background that may be reduced to some extent by judicious selections on thefinal state event topology.In the analysis presented here,we have in mind a situation in which the Higgs boson has been discovered and a sample of events exists containing a Higgs boson and two or more jets.This set of events will contain backgrounds of two types:real H+2jet events produced by QCD mechanisms other than WBF,and events which contain jets and particles that are present in typical Higgs boson decay modes,but without an explicit Higgs boson.Within the full event sample,we discuss the simulation of the real WBF signal and the irreducible QCD H+2jet background.We do not address the second type of contamination,such as events from the QCD Z+2jets process where the Z decay imitates a Higgs boson decay. Our concern is to estimate the expected signal purity,by which we mean the fraction of real Higgs boson events produced by weak boson fusion.The WBF H+2jet signal region is characterized by jets that carry large transverse momentum and large rapidity.Because the jets carry large transverse momentum,it is necessary to use hard QCD matrix elements in order to represent the signal and the H+2jet background reliably.A parton shower approach,for example,would be unlikely to provide a correct estimate of the momentum distribution of the jets in the region of phase space of interest.Next-to-leading order(NLO)QCD corrections to the total WBF production cross section have been known for some time[15],and the corresponding corrections were calculated recently in a fully differential way[16].In this paper,we use an independentcalculation to verify the results of Ref.[16]and to examine in more detail the effects of the WBF selection cuts on the NLO QCD corrections.We also use perturbative QCD expressions for the background H+2jet matrix elements.At present,the fully differential H+2jet background distributions are known only at leading order.In addition to our NLO study of the signal process,we nevertheless provide two estimates of the NLO enhancement of the QCD H+2jet background process,in order to better assess the viability of the WBF channel for measuring the coupling strength of the Higgs boson to vector bosons.Our calculations are fully differential at the partonic level.One limitation of the fact that we omit showering is that forward beam jets,which likely have low p T,are ignored.Since the WBF channel is most interesting for a Higgs boson in the mass range m H= 115−200GeV,we perform calculations with the two extremal values of this range.We compute differential cross sections in rapidity and transverse momentum at a pp collider with √method for defining WBF events with two other popular methods found in the literature: a selection on the difference in rapidities between two tagging jets in thefinal state,and a selection on the invariant mass of a pair of tagging jets.The alternative prescriptions yield some increase in signal purity with respect to our definition,but the gain is sensitive to the cut in transverse momentum used to specify the trigger jets,and it is accompanied by loss of event rate.For values of the jet cut p T>40GeV,our prescription appears to work about as well as the other methods.Relatively high luminosity will be needed for a precise determination of the uncertaintyδg/g.Our simpler definition of the WBF sample in terms of a selection on the rapidity of only one jet offers advantages in a high luminosity environment where a large value of the transverse momentum cut is appropriate and multiple events per crossing may be an issue.We provide two methods for estimating the size of next-to-leading order corrections to the H+2jet background in Sec.V.One of these relies on similarity with the Z+2jet process for which fully differential NLO results are known.The other method is an extrapolation from the known next-to-next-to-leading order(NNLO)results for the fully inclusive Higgs boson production process.The substantially different estimates for the NLO enhancement provided by these two methods show the level of uncertainty of the LO background calculation.A fully differential NLO calculation of the H+2jet background applicable in the region of interest for WBF investigations is needed in order to improve our computations of signal purity and of the expected uncertainty inδg/g.A summary of our conclusions may be found in Sec.VI.II.PRODUCTION CROSS SECTIONSExamples of the WBF diagrams that must be calculated are shown in Fig.1.The basic leading order process is shown in(a),where the exchanged bosons may be either W’s or Z’s, and one or both quark lines may be reversed,yielding qq,q¯q and¯q¯q initial states.The virtual NLO corrections are obtained by adding a gluon loop to either qqV vertex,as illustrated in (b).The remaining real NLO corrections are shown in(c),where either an additional gluon is radiated in thefinal state or a gluon from the proton splits into a q¯q pair.Calculation of the necessary loop diagrams is straightforward,providing a couple of simplifying assumptions are made.First,we ignore contributions of the form q¯q′→V⋆→V H,where V=W,Z.FIG.1:Representative diagrams for the production of a Higgs boson via weak boson fusion:(a)at lowest order;(b),(c)at NLO.Further diagrams can be obtained by crossing incoming and outgoing lines in all cases.All of the virtual corrections are of the vertex correction form,as shown in (b).There are two types of real corrections depicted in(c).Thefirst set corresponds to the emission of a gluon in all possible positions on the quark lines(left-hand diagram)and the second set corresponds to the crossing where a gluon is present in the initial state(right-hand side).Second,we neglect any interference effects from identicalflavor quarks in thefinal state.We checked that both of these approximations have little effect on the calculated cross sections at leading order,particularly in the region of phase space that we consider.The NLO calculation is embedded in the general purpose Monte Carlo program MCFM[17],which uses the dipole subtraction method[19].We use the default set of parameters in this program,in whichα=1/128.89,M W=80.419GeV,M Z=91.188GeV, and sin2θw=0.2285.For the parton distribution functions,we use CTEQ6L1for lowest order and CTEQ6M at NLO[20].In these sets of parton densities,αLO s(M Z)=0.130and (M Z)=0.118.In this paper,we choose the reference valueµ=m H for the renormal-αNLOsization and factorization scales.In Sec.III C we investigate the uncertainty of the signal and of the background associated with variation of the scale over the interval2m H>µ>m H/2.A.Generic cutsThe hallmark of WBF events is a Higgs boson accompanied by two“tagging”jets having large p T and large rapidity.In real events and in computations at NLO,there are generally more than two jets,and the goal is to pick out a clean signal.To simplify our study and to demonstrate the robust character of the WBF process,it is desirable to make as few selections(cuts)as possible on the events.We begin with a basic set of cuts,exactly as in Ref.[16].Jets obtained from the Monte Carlo runs are clustered according to the k T algorithm with p jet T>20GeV,jet pseudo-rapidity|ηjet|<4.5,and jet separation∆R jj=FIG.2:Representative diagrams for the production of a Higgs boson and two jets at lowest order, calculated in the heavy top-quark limit of the Hgg effective coupling.In Sec.V we estimate the NLO corrections to the lowest order result for the H+2jets background process by comparison with the similar Z+2jets process,calculated at NLO in Ref.[17,23],and by extrapolation from NNLO calculations of the fully inclusive process pp→HX[24]–[30],and NLO calculations of pp→H+1jet+X[31].III.RESULTSThe cuts mentioned in the previous section are a generic set of cuts.They do not exploit the kinematic structure of WBF events,where the jets tend to be produced very forward in pseudo-rapidity.In this subsection,we presentfirst the cross sections for the signal and background processes after application of the generic cuts.Without further cuts,the WBF events would be lost in the QCD continuum background.We then apply one additional constraint which defines our WBF sample,and we show results for kinematic distributions, event rates,and signal purities.A.Basic cutsWe examine the effects of the generic cuts in terms of their effects on the WBF signal and the H+2jet background.These cross sections–without any further cuts–are shown in Table I as a function of the minimum jet p T.The WBF signal process is calculated at NLO and,at this point,the H+2jet background at LO.We remark that the effects of the NLO corrections on the WBF process are rather small in this region,corresponding to K-factors between0.95and1.1,depending on the Higgs boson mass and p T cut.The values in the table show that(without consideration yet of NLO effects in the back-ground)the rates for the signal and background are comparable for p min=20GeV,and theTp T cut[GeV]40Signal(m H=115)1081Bkg743118916695896TABLE I:Cross sections in fb for the WBF signal(calculated at NLO)and H+2jet back-ground(LO),as a function of the minimum jet p T.Only the minimal set of cuts of Sec.II is applied.signal-to-background ratio improves as the p T cut is increased.The WBF signal lies above the H+2jet cross section if p minT≥40GeV.B.WBF cutsIn an attempt to exploit the WBF event structure,a popular cut invokes a separation inpseudo-rapidity between the two tagging jets,for instance|ηj1−ηj2|>4.In this paper,we define a slightly different and simpler cut,motivated by our examination of the distributions of the absolute jet pseudo-rapidities shown in Fig.3.In thesefigures,each tagging jet enters with weight one-half and cross sections have been converted to event rates with an integrated luminosity of1fb−1.The area under each curve is equal to the total number of events in that channel.The plots in Fig.3show that the shape of the distribution depends little on either the Higgs boson mass or the jet p T,but–as expected–is very different in the signal process, compared to the H+2jet background.In each case,the WBF events peak at values of |η|≈3,although there is a slight movement to lower values of|η|as the p T cut is increased. The width of the peak also tends to decrease,but the full width at half-maximum is fairly constant at approximately3units of rapidity.In contrast,the rate of background events falls offfairly sharply beyond|η|≈2.Motivated by the comparison of rapidity spectra in Fig.3,and erring on the side of simplicity,we choose a uniform cut that ensures at least one jet lies within the ly,ηpeak−ηwidth/2<|ηj|<ηpeak+ηwidth/2,(1)FIG.3:Dependence of the tagging jet pseudo-rapidities on the minimum jet p T used,for the two cases m H =115GeV (left)and m H =200GeV (right).Each of the two tagging jets in the event is entered in these plots,with weight one-half,and the rates assume an integrated luminosity of 1fb −1.The signal (solid)is calculated at NLO and the background (dashed)at LO.We show results for three different selections of the minimum jet transverse momentum,p T >20,40,and 80GeV.p T cut[GeV]40Signal(m H=115)789Bkg382Purity0.67928121534460.630.72TABLE II:Event rates for the Hjj WBF signal(NLO)and Hjj background(LO),including our WBF requirement that at least one jet carry large|η|,as defined by Eq.(1).We assume1fb−1 of integrated luminosity.Purity is defined as P=S/(S+B),where S stands for the number of signal events and B for the number of background events.for j=j1or j=j2,whereηpeak=3andηwidth=2.8.Equation(1),along with the generic cuts specified above,constitutes our definition of weak boson fusion cuts.The effects of the pseudo-rapidity restriction on the jets are shown in Table II,where we have assumed1fb−1of integrated luminosity.The rates in this table should be contrasted with those in Table I.In Table II,we include values for the signal purity,defined as P=S/(S+B),where S stands for the number of signal events and B for the number of background events.The number of events as a function of the minimum jet p T is also plotted in paring the tables,one can see that the signal rate is diminished only slightly,by about20–30%.On the other hand,the background is shrunk considerably,by about a factor of two.A p T cut of20GeV is barely sufficient to distinguish the WBF signal above the QCD LO Hjj background for m H=115GeV.However,the signal S to background B ratio improves to about2for p cut T≥40GeV.At m H=200GeV,the situation is better,with S/B of about1.7when the p T cut is20GeV,and rising to ∼3for p cut T≥40GeV.A p T cut of40GeV yields a prominent effect across the range of interesting masses,m H=115–200GeV.It is instructive to examine the origin of the different rapidity spectra for the signal and the background.Since H+2jet events are generated in both cases with identical cuts on the transverse momenta of the jets,the different rapidity spectra must originate from dynamics.FIG.4:Numbers of events for the WBF signal and the QCD background as a function of the minimum jet p T,for an integrated luminosity of1fb−1.No branching ratios for the Higgs boson decay have been applied.The pseudo-rapidity restriction on one of the jets has been enforced,as in Table II.The solid line is the NLO signal and the dashed is the LO background.Comparing the LO production diagrams in Figs.1and2,we note that gg and qg initial states contribute to the QCD background but not to the WBF signal.The gluon parton density is notably softer than the quark parton density,suggesting a plausible reason for the differences in the rapidity spectra of thefinal state jets in the two cases.This reasoning is supported by the results shown in Fig.5.The shape of the background rapidity spectrum from the qq, q¯q,and¯q¯q contributions is very similar to that of the signal,albeit with a slight shift of the peak to smaller|η|.The very different rapidity spectra of the signal and the background evident in Fig.3results therefore primarily from the gg and qg initial state contributions. The results shown in Fig.5imply that there is a basic upper limit to the purity one can achieve for the WBF event sample,regardless of which prescription one adopts to define the WBF sample.The qq,q¯q,plus¯q¯q component of the QCD background process generates afinal state event topology essentially identical to the WBF signal process.Values of the purity are listed Table III;there is not much variation with m H or the value of the cut in p T.Our results suggest that purity is bounded from above by at most P<0.95at LHC energies.C.Scale dependence studyTo examine further the effects of NLO corrections,we consider variation of the renormal-ization and factorization scale.A range of values m H/2<µ<2m H is used conventionallyFIG.5:Dependence of the tagging jet pseudo-rapidities for jet p T >40GeV,for the two cases m H =115GeV (left)and m H =200GeV (right).For the background,we show the full result with all contributions included and,for comparison of shapes,the background obtained if only the qq ,q ¯q ,and ¯q ¯q initial state contributions are used.The magnitude of the separate component is multiplied by 20.p T cut [GeV]40Signal (m H =115)789Bkg (qq ,q ¯q ,¯q ¯q )45Purity (qq ,q ¯q ,¯q ¯q )0.959281214780.950.94TABLE III:Event rates for the Hjj WBF signal(NLO)and for the part of the Hjj back-ground(LO)that arises from the qq ,q ¯q ,and ¯q ¯q initial-state terms.to estimate the theoretical uncertainty at a given order in perturbation theory.As a rep-resentative case,we show results for a minimum jet p T of 40GeV and both Higgs boson masses.In Fig.6,we show the tagging jet pseudo-rapidity distributions for the signal and background for a range of values of the common renormalization and factorization scale µ.The signal process shows very little variation with µ,a shift of less than ±2%when |ηj |∼2in the WBF signal region.In contrast,the H +2jet background at LO is enhancedFIG.6:Tagging jet pseudo-rapidity distributions in Hjj events,calculated with a range of values of the renormalization and factorization scale,µ.The signal (solid)is calculated at NLO and the background (dashed)at LO.by approximately 70%when the scale choice µ=m H /2is made,and reduced by 40%for µ=2m H .A fully differential NLO calculation of the H +2jet background process is required to reduce the large uncertainty associated with µvariation apparent in Fig.6.D.Uncertainty on the CouplingsThe signal and background events both include a real Higgs boson along with two jets.We may define a signal “purity”as the ratio S/(S +B ),where S denotes the number of signal events and B the number of background events.The purity as defined here does not improve with greater luminosity nor does it depend on the Higgs boson decay mode considered.Of interest to us is the effect of signal purity on the accuracy of the determination from data of the Higgs boson couplings g W W and g ZZ to the W W and ZZ channels.The WBF crosssection is proportional to a combination of g 2W W and g 2ZZ ,and their relative contributionchanges somewhat with the value of the cut on p T .In this paper,we discuss only an effective coupling strength g .We remark also that in our discussion of the expected accuracy on g ,we limit ourselves to uncertainties at the level of production of the Higgs boson.We set aside uncertainties associated with the fact that the Higgs boson is observed only in specific final states and that all the final states cannot be observed above backgrounds.To derive the uncertainty δg/g on the coupling,we begin with the observed number ofevents N=S+B.We define the ratio r=g2observed/g2predicted.Then,under the assumption that any deviation in the expected total number of events arises from the effective coupling, we obtain r=(N−B)/S.Taking the total derivative,we obtain an expression for the uncertainty in r.δr/r=[(δS/S)2+((δN)2+(δB)2)/(N−B)2].(3)With purity P=S/(S+B),we deriveδg/g=1/2FIG.7:The predicted uncertaintyδg/g in the coupling of the Higgs boson to a pair of W bosons is shown as a function of signal purity P=S/(S+B)for expected statistical accuraciesδN/N of 10%and2%The uncertainties in knowledge of the signal S and background B are assumed to be 5%and30%respectively.choice presupposes that the20%µvariation and5%PDF uncertainty of the fully inclusive NLO cross section for Higgs boson production may also apply to the NLO calculation of H+2jet production in the WBF region of phase-space,once this calculation is done.Based on a study of conventional backgrounds[32],a minimum of roughly10fb−1of integrated luminosity is needed to discover the Higgs boson in the WBF process.This figure would be achieved after one year of LHC operation at a luminosity of1033cm−2s−1. Using the numbers in our Table II,we expect a WBF sample(S+B)of∼12000events for m H=115GeV and p T cut=40GeV,and∼7000events for m H=200GeV and p T cut=40GeV.To translate these event rates into statements about statistical significance, we must specify a Higgs boson decay mode and approximate tagging efficiencies for the decay products.For m H=115GeV,we choose the decay H→τ+τ−,with oneτdecaying leptonically and the other hadronically[8].These choices yield a branching ratio ofBr(H→ττ)×Br(τ→leptons)×Br(τ→hadrons)=0.073×0.7×0.65=0.033.For the efficiency for tagging hadronicτdecays,we take thefigure0.26from Ref.[33]as an optimistic upper bound.1The true value for this efficiency will be known only after analysis of data from LHC experiments.While our choice of tagging efficiency may seem large,it is relatively easy to scale ourfinal results if a different value is preferred.The combination of branching fraction and efficiency results in a reduction in the number events by a factor ǫ=0.033×0.26≈0.01.For m H=200GeV,the decay H→W+W−is prominent,and we select the case in which both W’s decay leptonically[11].2We obtainǫ=Br(H→W W)×Br(W→leptons)2=0.74×0.222=0.036.Using these numbers,we compute expected statistical uncertainties ofδN/N∼10%and ∼6%at m H=115and200GeV,respectively.With statistical accuracyδN/N of10%,δS/S=5%andδB/B=30%,we obtainδg/g≃10%for purity P=0.7when m H= 115GeV,andδg/g≃8%when m H=200GeV.After5years of LHC operation,we can anticipate an integrated luminosity of200fb−1 will have been accumulated.This increase allows us to reduce our estimates ofδN/N to ∼2%and∼1.5%at m H=115and200GeV,respectively,andδg/g∼7%for P=0.7.We remark that the uncertainties in the signal S and background B dominate the uncer-tainty in g.If P=0.7andδN/N=2%,then the uncertaintiesδS/S andδB/B would have to be reduced to3%and6%,respectively,before the statistical uncertainty would control the answer.Even if P=1,δg/g is controlled byδS/S untilδS/S≤δN/N.In Fig.7,we show numerical predictions for the uncertainty as a function of purity,for two choices of the statistical uncertainty.Signal purities of0.65or greater permit determinations ofδg/g of10%or better after200fb−1have been accumulated.As shown in Table II, P>0.65is obtained for p T cut>40GeV at m H=115GeV,and p T cut>20GeV at m H=200GeV.The curves indicate to us that there is not much to gain from purities greater than70%.FIG.8:The predicted uncertaintyδg/g in the coupling of the Higgs boson to a pair of W bosons is shown as a function of signal purity P=S/(S+B)for expected statistical accuraciesδN/N of 10%and2%The uncertainties in knowledge of the signal S and background B are assumed to be 4%and20%respectively.Somewhat smaller values ofδS/S andδB/B are chosen in another recent investigation of anticipated uncertainties in the couplings[18].These values areδS/S=4%andδB/B= 20%.Although the scope of that study is quite different from ours,we may compare our estimates with theirs.In Fig.8,we show the uncertainty as a function of purity for these new estimates ofδS/S andδB/B.For P=0.7,we nowfindδg/g∼9%and∼5%for the low-and high-luminosity data samples.This new lower value ofδg/g is similar to that obtained in Ref.[18]at comparable luminosity3.IV.ALTERNATIVE DEFINITIONS OF THE WBF SAMPLEIn the previous section,we define the WBF sample by a simple selection on the rapidity of one jet in an event in which there is a Higgs boson and two jets each carrying p T greater than a specified minimum value.Other definitions have been used in the literature,and we wish to compare our signal rates and purities with those obtained if we use these alternatives. We examine the traditional cut on rapidity separation between the two trigger jets and a cut on the invariant mass of the pair of trigger jets.A.Rapidity separation cutIn Fig.9,we illustrate the expected event rates as a function of the difference in rapidities between the forward and backward tagging jets.There is a clear separation in the locations of the peaks of the WBF signal and the background,not unlike that seen in our Fig.3. Distributions such as these may motivate the choice of a cut on rapidity separation,|ηj1−ηj2|>4,as in Refs.[1]–[14],and[16].Signal and background rates for WBF events selected in this fashion are shown in Table parison of Tables II and IV shows that the signal rate is diminished somewhat and that the purity is greater when the rapidity separation selection is made.As shown in Figs.7and8,a gain in purity reduces the uncertainty in δg/g.The quantitative shift from P=0.67to P=0.78at M=115GeV and p T>40GeV is an improvement of only3%inδg/g,and this reduction is offset somewhat by the loss in statistical accuracy.At lowest order in perturbation theory,one might expect naively that our simple rapidity selection and the rapidity separation cut are close to identical since there are only two jets in the event,tending to be located in opposite hemispheres.However,thefinite rapidity carried by the Higgs boson introduces differences.Our preference for the simple rapidity cut is based on a few considerations.In data(and at yet-higher orders in perturbation theory),there will be many jets,and the simple specification of events that satisfy Eq.(1) will be easier to implement.Second,in a high luminosity environment with more than one event per beam crossing,a selection on only one jet(in addition to the Higgs boson)reduces the chance that jets from different events are used.Finally,in our study of NLO event topologies with three jets in thefinal state,wefind that a gluon jet,rather than a quark jetFIG.9:The difference between the two tagging jet pseudo-rapidities for a minimum jet p T of 20GeV,for the two cases m H =115GeV (left)and m H =200GeV (right).The rates assume an integrated luminosity of 1fb −1.The signal (solid)is calculated at NLO and the background (dashed)at LO.p T cut [GeV]40Signal (m H =115)718Bkg207Purity0.78911106349200.720.84TABLE IV:Event rates for the Hjj WBF signal(NLO)and Hjj background(LO),without our WBF definition and instead with the rapidity separation cut |ηj 1−ηj 2|>4.We assume 1fb −1of luminosity.The purity and significance are as defined before.is sometimes one of the two jets with largest p T .For example,with a jet cut of 20GeV and m H =115GeV,a gluon is a tagging jet about 25%of the time when we use our definition of WBF events.B.Invariant mass cutAs an alternative to the rapidity separation cut,one might consider a cut on the invariant mass of the two trigger jets.In Fig.10and in Table V,we display the the effects of the mass cut M jj>parison of Figs.10and3shows a decided improvement in the signal to background ratio,an effect that is borne out in the purity numbers shown in Tables V and II.However,the significant gain in purity is true only for the smaller values of the p T cut and is accompanied by a substantial loss of signal rate.Since the smallest value of the p T could be employed only with low-luminosity data samples,it is not evident that the price in loss of signal rate is affordable.The combination of the mass cut and our simple forward jet cut improves purity only slightly and reduces the signal rate further.FIG.10:The tagging jet pseudo-rapidity distribution for a minimum jet p T of20GeV,for the two cases m H=115GeV(left)and m H=200GeV(right)–with a minimum dijet invariant mass, M jj>800GeV.Each of the two tagging jets in the event is entered in these plots,with weight one-half,and the rates assume an integrated luminosity of1fb−1.The signal(solid)is calculated at NLO and the background(dashed)at LO.Using the invariant mass cut to define the WBF sample,we note that the number of events at m H=115GeV with a cut on p T of20GeV is very similar to what we obtain with our WBF prescription but with a cut on p T=40GeV.The purities are also nearly the same.This comparison would seem to favor our simple prescription:a larger value of the cut on p T is more appropriate in a high rate environment and more effective at reducing backgrounds not considered here.We conclude this section with the remark that。
Single production of doubly charged Higgs bosons at hadron colliders
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Single production of doubly charged Higgs bosons at hadron colliders
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Production of bound {$mu^{+}mu^{-}$}-systems in relativistic heavy ion collisions
arXiv:hep-ph/9805375v1 19 May 1998
for Mathematics, 630090 Novosibirsk, Russia f¨ ur Physik komplexer Systeme, Bayreuther Straße 40, 01069 Dresden, Germany‡‡ 3 Institut f¨ ur Theoretische Physik, TU Dresden, 01062 Dresden, Germany 4 D. I. Mendeleev Institute for Metrology, 198005 St. Petersburg, Russia 5 Novosibirsk State University, 630090 Novosibirsk, Russia
The production rate and the lifetime of the dimuonic atoms are both proportional to this value. The lifetimes of low lying states are of the order of τ ∼ 10−12 s and are summarized in Table II. A brief discussion of the evaluation of the lifetime of parastates is given in Appendix A. Main decay channels are the annihilation processes PM → γγ , OM → e+ e− . (4)
2
∼ 0.04 ,
<
(1)
where r 2 is the mean square radius of the charge distribution of the nucleus, and the mass of the dimuonic atom is mµµ ≈ 2 mµ = 211 MeV. Therefore, in all cases under consideration the multiphoton processes set limits on the accuracy on the level of 5 %. 2
Single Top Quark and Light Higgs Boson at Tevatron
a r X i v :h e p -p h /9804328v 2 21 A p r 1998SINGLE TOP QUARK AND LIGHT HIGGS BOSONAT TEV ATRONA.Belyaevs =2TeV and up to about 120GeV at√1.1SignalWe concentrated on the following processes of single top quark production:1.p¯p→tq¯b+X (W-gluon fusion),2.p¯p→t¯b+X,3.p¯p→tq+ X where q is a light quark and X stands for remnants of the proton and antiproton.Feyn-man diagrams for the above processes are shown in Fig.1.We refer to the paper[2]for de-tails.All analytical and almost all numeri-Figure1:Diagrams for single top production cal calculations have been done by means of CompHEP package[3].FORTRAN codes of matrix elements generated by CompHEP have been used in MC generators implemented as external processes of PYTHIA program.For t-quark production we chose Q2scale equal to top mass squared.For a180GeV top quark the total single top plus anti-top cross section is1.76+0.26−0.18pb(√∆φ2jj+∆η2jj).For Wjj background Q2=M2W has been taken.For calculation of jb¯b and jjb¯b processes we choose invariant b¯bmass for Q2scale.Total cross section of W+2jets(Wjj)“glu-onic”background(1000pb)is about2orders of magnitude higher than that of the signal. The specific feature of single top production is highly energetic b quark in thefinal state and one additional b quark for W-gluon fu-sion process.The b quark content of the Wjj processes is small(less then1%)and efficient b-tagging gives us chance to extract the signal from Wjj overwhelming background.We as-sume50%b-tagging efficiency hereafter.For initial cuts mentioned above the total cross section for W+b¯b process(gluon splitting)is 7.2pb.Contribution from Wjj background due to b quark misidentification should also be taken into account.In our study we chose1%misiden-tification probability.Complete set of Feynman diagrams for W±b¯b background is shown in Fig.2.The main con-tions for jb¯b and jjb¯b are204105and66733pb, respectively.process CS(pb)process CS(pb)gg→gb¯b120180gq→qb¯b82290q¯q→gb¯b1635gg→ggb¯b36212q¯q→q¯q b¯b2269q¯q→ggb¯b288gq→gqb¯b26166gg→q¯q b¯b1798 Table1:jb¯b and jjb¯b cross sections.processes1.3Signal and background study Even after b-tagging procedure the signal is more than one order lower than the background. This fact requires special kinematic analysis in order to reduce the background and leave the signal intact as much as possible.The main difference between kinematic dis-tributions for background and signal is that jets from Wjj,jb¯b and jjb¯b processes are much softer and less central than those for the signal with one very hard jet coming from top and another softer jet,accompanying top quark. Among the kinematic variables for separation of the signal and background the most effec-tive are:p⊥of leading jet(Fig.3a)invariantmass of the system√accompanying cuts Top W b¯b W jj j(j)b¯bˆs>180GeV495743375.p T W>30GeV455039376.jj m>25GeV454838377.H T>100GeV44463636 Table2:Signal and background events;ǫb=50%,m top=180GeV,L=1000pb−1of signal and background kinematics the opti-mal set of cuts for the background suppression has been worked out.The effect of consequent application of these cuts is presented in Ta-ble2.As a result the signal-to-background ra-tio becomes equal to1/3and the signal exceeds the background by3standard deviations.pTjetmax[GeV]Numberofevents10002000300040005000600070008000900020406080100120140160180200√s∧ [GeV]Numberofevents2004006008001000120014001600150200250300350400450500550600———background-----200·signala)b)c)d)HT[GeV]Numberofevents20004000600080001000050100150200250300350400di-jet mass [GeV]Numberofevents100020003000400050006000700050100150200250300350400 Figure3:Distributions for signal and back-ground for some most spectacular variables 1.4Wtb coupling and V tbSince the top quark is rather heavy one could expect that new physics might be revealed at the scale of its mass(see refs.65-71in[2]). We examine the effects of a deviation in the Wtb coupling from the standard model struc-ture,and study sensitivity of measurement of the CKM matrix element V tb.Experimental studies of this type are among the main goals of the single top physics.As an example of a deviation from the stan-dard model Wtb coupling,we introduce addi-tional contribution from the nonstandard(V+ A)structure with arbitrary parameter A r by:Γ=eV tb2sinθW[γµ(1−γ5)+A rγµ(1+γ5)] The production rate varies almost quadrati-cally with A r,and is nearly symmetric around A r=0.The cross section rises from2.44pb when A r=0to4.68pb when A r=−1and to 4.73pb when A r=+1.We have calculated the region in the(V tb,A r)plane where future single top measurements are expected to be sensitive. The error of V tb measurement will be half of the error of the single top cross section,since the cross sections for all single top processes are proportional to|V tb|2.This results in an errorfor V tb and A r around12-19%(L=2fb−1)[2].2Higgs bosonLuminosity upgrade of TEVATRON and in-stallation of the efficient b-tagging system opens also opportunities for the Higgs boson search. This task is crucial since the Higgs boson is the last particle(in the frame of SM)which has not been discovered yet.The most promising will be the Higgs bo-son search in association with the electroweak W and Z bosons[4,5]:Here we concentrated on detailed study of Higgs p¯p→W±H+Xp¯p→ZH+Xs=2TeV the Higgs production cross section is about0.03-0.3pb depending on the Higgs mass and therefore one can expect30-300signal events for integrated luminosity L= 1000pb−1.However the total reaction rates are about two orders of magnitude larger that the Higgs signal.That is why one has to make a detailed analysis of different4-fermionfinal state distributions tofind out whether it is pos-sible tofind a set of cuts to suppress the huge background strongly enough.For the cross sec-tion calculation and event simulation the same procedure has been done as for the single top quark study,including the effect of initial andfinal state radiation.2.2Background studyFrom the complete set of diagrams for back-ground the dominant contribution comes from several subprocesses:1)QCD2→3type mainbackground subprocesses:q¯q′→W±b¯b,q¯q→Zb¯b,gg→Zb¯b;2)2→2electroweak subpro-cesses:q¯q′→W±Z,q¯q→(Z/γ∗)(Z/γ∗);3) single top quark production q¯q′→t¯b or¯t b. Single top background has not been taken into account in the previous studies.This contri-bution becomes more important with growth of the invariant b¯b-pair mass.Signal and background kinematical distri-butions differ mainly due to concentration of events of QCD backgrounds mostly in the re-gion of small p⊥.We study b quark and charged lepton distributions over transverse momentum p⊥(b)and p⊥(ℓ)as well as b¯b distributions over transverse momentum p⊥(b¯b)and miss-ing energy/E⊥.It turned out that pair charac-teristic p⊥(b¯b)related to high transverse mo-menta of Higgs boson is very important for background suppression.After detailed com-parison of the signal and the background distri-butions appropriate set of cuts has been found:1)p⊥(b),p⊥(b¯b)>20GeV;p⊥(ℓ)>15GeV;2)typical cuts for TEVATRON detectors:/E⊥>20GeV;|ηb|<1.5;|ηℓ|<2;|∆R¯b|>0.7; |∆R bℓ|>0.7;3)−2∆M¯b+M¯b<M¯b<2∆M¯b+ M¯b.This set of cuts reduces the total back-ground more than40times.The number of events corresponding to signal and background after the cuts application is presented in Ta-ble3.Requiring3-standard deviation criteria one canfind Higgs up to the mass≃100GeV at√s=4TeV.These numbers are obtained under assumption of50%efficiency of double b-tagging.One can see that with the decreasing Higgs boson mass the contribution of the single top processes to the total background becomes more significant.√M HW ±HZHW b ¯b +W Z +b ¯t Zb ¯b +ZZs =4TeVTable 3:Number of events for Higgs bosonsignal and background after cuts N u m b e r o f e v e n t s√s = 2 TeV pp → (l ν– + l l – +ν ν– ) + bb – + X M H = 80 GeVall cuts absentall cuts appliedInvariant bb –mass distribution[ GeV ]N u m b e r o f e v e n t s250500750100012501500175020002040608010012014010203040506020406080100120140Figure 4:Invariant b ¯b mass distribution be-fore and after cutsIt should be noted also that Wbb background increases approximately two times with the in-creasing of√s =2TeV without any cuts andwith cuts applied revealing clear peak from Higgs boson.ConclusionsStudy of single top quark and Higgs boson pro-duction at the upgraded Tevatron is not only important but also convenient since they have very similar signatures.It was shown that the signal from the sin-gle top quark can be extracted and therefore Wtb vertex and V tb CKM parameter at theupgraded TEVATRON can be measured.Themain backgrounds have been studied:W ±b ¯b,Wjj,jb ¯b +jjb ¯b and the set of kinematical cuts on p ⊥(jet),√s =2TeV and up to about 120GeVat√。
t tbar Production via Vector Boson Fusion at High Energy e^+ e^- Colliders
calculations have also been performed for vector boson fusion tt¯ production the picture is far from complete. To the full calculations of these processes exist in the literature. The total cross section for e+e− → ℓℓ¯tt¯, using
which → tt¯)
corresponds to t√he LET. in the 2MW,Z / s = 0
We give approxi-
mation and show how this approximation effects the results.
I. INTRODUCTION
Understanding the mechanism responsible for electroweak symmetry breaking is one of the most pressing problems in particle physics. Quite generally, there are two scenarios. In the first, the Higgs boson is light and at high energies the weak sector remains weakly coupled. In this scenario the Higgs boson should be observed at one of the high energy colliders under consideration. In the second scenario the Higgs boson is heavy and at high energies the weak sector becomes strongly interacting. If this were the case a new spectroscopy is likely to manifest itself at energies beyond a TeV. In our view this is a very intriguing possibility. Unfortunately, it will be very difficult to detect and even more difficult to understand. Considerable work has been devoted to understanding this problem using vector boson scattering at high energy colliders with questionable success. However, it has been shown that tt¯production via vector boson fusion at high energy colliders also provides a potentially powerful tool for understanding a strongly interacting weak sector [2] and this subject has attracted growing interest [3, 4]. This is simply a manifestation of the equivalence theorem where longitudinal bosons take on the couplings of the scalars from which they acquire mass and a consequence of the fact that the Higgs boson couples most strongly to the most massive particle available.
On transverse energy production in hadron collisions
ar X i v :h e p -p h /0005010v 1 1 M a y 2000FIAN/TD-04/2000BNL-NT-00/12ON TRANSVERSE ENERGY PRODUCTION IN HADRON COLLISIONS Andrei Leonidov (a ),(b )(a )Physics Department,Brookhaven National Laboratory Upton,NY 11973,USA (b )Theoretical Physics Department,P.N.Lebedev Physics Institute 117924Leninsky pr.53,Moscow,Russia 1Abstract The transverse energy spectrum in the unit rapidity window in p ¯p collisions at √1Permanent address1In this note we calculate to the next-to-leading(NLO)order accuracy the transverse energy spectrum in the central rapidity window within perturbative QCD and compare it to experimental data obtained by UA2collaboration[2].The NLO calculation of a generic jet cross section requires using a so-called jet defining algorithm specifying the resolution for the jet to be observed,for example,the angular size of the jet-defining cone,see e.g.[5],The cross section in question is calculated by integrating the differential one over the phase space,with the integration domain restricted by the jet characteristicsfixed by the jet-defining alogorithm.Schematically the NLO distribution of the transverse energy produced into a given rapidity interval y a<y<y b is given,to the O(α3s)order,by dσδ(E⊥−2 i=1|p⊥i|θ(y min<y i<y max))d4p1d4p2+ D3P S dσs= 540GeV measured by UA2Collaboration[2].We see that the perturbative LO+NLO calculations start merging with the experimental data only around quite a large scale E⊥∼60GeV.It is interesting to note,that it is precisely around this energy,that the spaceacurrently available3.In practical terms this means that additional model assumptions are needed to achieve agreement with experimental data strongly indicating that higher order corrections and higher twist effects have to be taken into account(in a necessarily model-dependent way) in order to describe them.In the popular Monte-Carlo generators such as PYTHIA[3] and HIJING[4]such effects as multiple binary parton-parton collisions,initial andfinal state radiation and transverse energy production during hadronization are included.In Fig.2we compare the same experimental data by UA(2)[2]with the spectrum calcuated with HIJING event generator.To show the relative importance of different dynamical mechanims,in Fig.2we plot the contributions from the hard parton scattering without initial andfinal state radiation,full partonic contribution and,finally,the transverse energy spectrum offinal hadrons.We see,that taking into account additional partonic sources such as,e.g.,initial andfinal state radiation,allows to reproduce the(exponential) form of the spectrum,but still not the magnitude.The remaining gap isfilled in by soft contributions due to transverse energy production from decaying stretched hadronic strings.The results confirm those earlier communicated to the author by M.Gyulassy [10].Let us note,that the spectrum calculated in HIJING is somewhat steeper than the experimental one.Additionalfine-tuning can be achieved by probing different structure functions.The above results clearly demonstrate that in order to reproduce the experimentally observed transverse energy spectrum,one has to account for complicated mechanisms of parton production,such as initial andfinal state radiation accompanying hard parton-parton scattering,production of gluonic kinks by strings,as well as for nonperturbative transverse energy production at hadronization stage.This statement is a calorimetric analog of of the well-known importance of the minijet component in describing the tails of the multiplicity distributions,[11]and[4](see,however,the alternative explanation based on accounting for multipomeron contributions described in[12]).Let us note that the result has straightforward implications for describing the early stages of heavy ion collisions.In most of the existing dynamical models of nucleus-nucleus collisions they are described as an incoherent superposition of nucleon-nucleon ones.As we have seen,to correctly describe the partonic configuration underlying the observed transverse energyflow in nucleon-nucleon collisions,mechanisms beyond conventional collinear factorization are necessary.In particular this indicates that the results obtained within minijet approach based on colinearly factorized QCD,see e.g.the recent review [13]and references therein,must be taken with care.(((G s G (^ P E *H 9(^ *H9Figure 2:Transverse energy spectrum in p ¯p collisions calculated in HIJING vs the exper-imental data by UA2collaboration [2]AcknowledgementsI am grateful to Yu.Dokshitzer,M.Gyulassy,Yu.Kovchegov,L.McLerran and D.Soper for useful discussions.I am also grateful to Theoretical Physics Institute,University of Minnesota,where this work was started,and Brookhaven National Laboratory,where it was completed,for kind hospitality.This manuscript has been authored under Contract No.DE-AC02-98CH10886with the U.S.Department of Energy.This work was partially supported by RFBR Grant 00-02-161015References[1]A.Leonidov and D.Ostrovsky,Eur.Phys.Journ.C11(1999),495[2]UA2Collaboration,M.Banner et.al.,Phys.Lett.B118(1982),203[3]T.Sjostrand,mun.82(1994),74;[4]X.-N.Wang and M.Guylassy,Phys.Rev.D44(1991),3501;D45(1992),844;mun.83(1994),307[5]D.Soper,”Jet observables in theory and reality”[hep-ph/9706320][6]S.D.Ellis,Z.Kunszt and D.E.Soper,Phys.Rev.Lett.64(1990),2121;Phys.Rev.D40(1992),2188[7]Z.Kunszt and D.E.Soper,Phys.Rev.D46(1992),192[8]K.J.Eskola and K.Tuominen,”Production of Transverse Energy from Minijets inNext-to-Leading Order Perturbative QCD”,[hep-ph/000208][9]G.Pancheri and Y.Srivastava,Phys.Lett.B128(1983),433;”Jets in Minimum Bias Physics”,in Proc.5th Topical Workshop on Proton-Antiproton Collider Physics,Saint Vincent,Italy,1985,ed.M.Greco,World Sci-entific,1985;C.T.H.Davies and B.R.Webber,Zeit.Phys.C24(1984),133M.Greco,Phys.Lett.B121(1983),360;Nucl.Phys.B2501985,450[10]M.Gyulassy,private communication.[11]T.Sjostrand and M.van der Zijl,Phys.Rev.D36(1987),2019[12]S.G.Matinyan and W.D.Walker,Phys.Rev.D59(1999),034022[13]K.J.Eskola,”High-Energy Nuclear Collisions”,[hep-ph/9911350]6。
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a rXiv:h ep-ph/7295v126J ul2UR-1610ER/40685/949Vector Boson Production at Hadron Colliders:Results from HER WIG and Resummed Calculations 1G.Corcella Department of Physics and Astronomy,University of Rochester,Rochester,NY 14627,U.S.A.Abstract.We discuss vector boson production at hadron colliders and the treatment of the initial-state radiation according to Monte Carlo parton shower simulations and resummed calculations.In particular,we investigate the effect of matrix-element cor-rections to the HERWIG event generator on W/Z transverse momentum distributions.INTRODUCTION The production of vector bosons W ,Z and γ[1]is one of the most interesting processes in the phenomenology of hadron collisions and provides an environment to test both Quantum Chromodynamics and the Standard Model of electroweak interactions (see [2,3]for a review).The lowest-order processes q ¯q ′→V are not sufficient to make reliable predictions,but the initial-state radiation should be taken into account.Monte Carlo event generators and resummed analytical calculations are available tools to describe the multiple radiation accompanying the incominghadrons.Standard Monte Carlo algorithms [4,5]describe the initial-state parton showers in the soft/collinear approximation,but can have ‘dead zones’,where no radiation is permitted.The radiation in these regions can be generated by the use of the exact first-order matrix element.Referring to the HERWIG event generator,matrix-element corrections to Drell–Yan processes have been implemented in [6],following the general method of [7],and included in the new version HERWIG 6.1[8].Another possible approach consists of performing an analytical resummation of the large logarithmic coefficients which multiply the strong coupling constant.Con-sidering the transverse momentum q T distribution,logarithms of the ratio m V /q T ,m V being the vector boson mass,arise in calculating higher-order corrections to the Born process.The resummation of these logarithms,which are large at small q T,was initially proposed by Dokshitzer,Dyakonov and Troyan(DDT)[9],then accomplished by Collins,Sterman and Soper(CSS)[10].CSS performed the resum-mation in the space of the impact parameter b,which is the Fourier conjugate of q T.Their results have been implemented numerically in[11,12],while more recent analyses can be found in[13–15],where the resummation is performed in both q T-and b-space.In this paper,we review some results for the W/Z transverse momentum distri-bution according to the HERWIG event generator and resummed calculations.2 THE HER WIG PARTON SHOWER ALGORITHM HERWIG simulates the initial-state radiation in hadron collisions according to a‘backward evolution’[17],in which the scale is reduced away from the hard ver-tex and traces the hard-scattering partons back into the incoming hadrons.The branching algorithm relies on the universal structure of the elementary probabil-ity in the leading infrared approximation.The probability of the emission of an additional soft/collinear parton from a parton i is given by the general result:dP=dq2i ziq i ∆S,a(q2i,q2c)x i/z i f a(x i,q2i).(1)The ordering variable is q2i=E2ξi,where E is the energy of the parton that splits andξi=p·p i2π q22q21dk22)See also[16]for a similar comparison for Higgs production at hadron colliders.factor sums up all-order virtual and unresolved contributions.In(1),q i max is the maximum value of q,fixed by the hard process,and q c is the value at which thebackward evolution is terminated,corresponding,in the case of HERWIG,to acutoffon the transverse momentum of the showering partons.However,since q cis smaller than the minimum scale at which the parton distribution functions are evaluated,an additional cutoffon the evolution variable q2i has to be set.If the backward evolution has not resulted in a valence quark,an additional non-perturbative parton emission is generated to evolve back to a valence quark.Such avalence quark has a Gaussian distribution with respect to the non-perturbative in-trinsic transverse momentum in the hadron,with a width q T int that is an adjustable parameter and whose default value is zero.We needfinally to specify the showering frame,the variables q2i and z i beingframe-dependent.One can show that,as a result of the q2-ordering,the maximumq-values of two colour connected partons i and j are related via q i max q j max=p i·p j, which is Lorentz-invariant.For vector boson production,symmetric limits are setin HERWIG:q i max=q j max=√p i·p j.It follows that ordering according to q2impliesξ<z2.The regionξ>z2is therefore a‘dead zone’for the shower evolution.In sucha zone the physical radiation is not logarithmically enhanced,but not completely absent as happens in the standard algorithm.We therefore need to improve the HERWIG parton showers by the use of matrix-element corrections.MATRIX-ELEMENT CORRECTIONSAccording to[7],we populate the‘dead zone’of the phase space using the ex-act O(αS)matrix element(hard correction).We also correct the emission in the already-populated region using thefirst-order result any time an emission is capa-ble of being the‘hardest so far’(soft correction),where the hardness of an emission is measured in terms of the transverse momentum of the emitted parton relative to the splitting one.We consider the process q(p1)¯q′(p2)→V(q)g(p3),define the Mandelstam vari-ablesˆs=(p1+p2)2,ˆt=(p1−p3)2andˆu=(p2−p3)2and obtain the total phase-space limitsm2V<ˆs<s,(3)m2V−ˆs<ˆt<0,(4) s being the total centre-of-mass energy.We observe that the soft singularity corre-sponds to s=m2V and the linesˆt=0andˆt=m2V−ˆs to collinear gluon emission. After relating the parton shower variables z andξtoˆs andˆt,as done in[6],andsettingξ<z2,one can get the HERWIG phase-space limits in terms ofˆs andˆt.√In Fig.1we plot the total and the HERWIG phase space forFIGURE1.Total(solid line)and HERWIG(dashed)phase space limits for√f q/1(η1)f¯q′/2(η2)C FαSˆs2ˆtˆu (m2V−ˆu)2+(m2V−ˆt)2 ,(5)where f q/1(χ1)and f¯q′/2(χ2)are the parton distribution functions of the scattering partons inside the incoming hadrons1and2for energy fractionsχ1andχ2in the process q¯q′→V g,while f q/1(η1)and f¯q′/2(η2)refer to the Born process.A similar treatment holds for the Compton process q(p1)g(p3)→q′(p2)V(q),as discussed in[6].The distribution(5)or the equivalent one for the Compton process is imple-mented to generate events in the missing phase space and in the populated region every time an emission is the hardest so far.TRANSVERSE MOMENTUM DISTRIBUTIONS:HER WIG RESULTSAn interesting observable to study is the vector boson transverse momentum, which is constrained to be q T<m V in the soft/collinear approximation.After matrix-element corrections,a fraction of events at higher q T is to be expected.In Figs.2and3we plot the W q T distribution at the Tevatron and at the LHC,FIGURE2.W transverse momentum distributions at the Tevatron,according to HERWIG6.1 (solid line)and HERWIG5.9(dotted).according to HERWIG5.9and HERWIG6.1,the new version including matrix-element corrections,for q T int=0.We see a big effect at large q T:after some q T the 5.9version does not generate events anymore,while we still have a non-zero cross section after matrix-element corrections.Moreover,a slight suppression can be seen at small q T.It is related to the fact that,although we are providing the shower with the tree-level O(αS)corrections, virtual contributions are missing and we still get the leading-order cross section. The enhancement at large q T is therefore compensated by a suppression in the low-q T range.It is now interesting to compare the HERWIG results with some Tevatron data. In Fig.4we compare the HERWIG6.1distribution with some DØdata[19]and find reasonable agreement over the whole q T range.As shown in[6],smearing the HERWIG curve to account for detector effects must be included to achieve this agreement.Also,we do not see any relevant impact of setting q T int=1GeV after detector corrections.In Fig.5we compare the HERWIG5.9and6.1results,for different values of q T int,with some CDF data[20],already corrected for detector effects.Wefind good agreement after matrix-element corrections,while the5.9 version is not able tofit in with the data for q T>50GeV.At low q T,the best agreement to the data is obtained for q T int=2GeV,as shown in Fig.6.While the Z distribution strongly depends on q T int at small q T,in[21]and Fig.7it is shown that the ratio R of the W and Z spectra is approximately independent of it.3.Such a ratio is one of the main inputs for the W mass measurement in hadronFIGURE3.As in Fig.2,but at the LHC.parison of the DØdata to the HERWIG6.1result,for an intrinsic q T of0 (solid line)and1GeV(dashed).FIGURE parison of the CDF data on the Z transverse momentum to HERWIG 5.9(dotted line)and 6.1for an intrinsic q T of 0(solid line),1GeV (dashed)and 2GeV (dot-dashed).collisions and it is good news that it does not depend on unknown non-perturbative parameters.RESUMMED CALCULATIONSAnother possible approach to study the vector boson transverse momentum dis-tribution consists of resumming the logarithmic terms l =log(m 2V /q 2T )in the low-q T range.It is interesting to compare the HERWIG phenomenological results with those of some resummed calculations,in particular [13]and [14].According to [9],the resummed differential cross section for W production can be written as:d 2σdq 2T q,q ′|V q ¯q ′|2 10dx 1dx 2δ(x 1x 2−τ)× f q/1(x 1,q T )f ¯q ′/2(x 2,q T )exp[S (m V ,q T )]+(q ↔¯q ′) ,(6)where V q ¯q ′is the relevant Cabibbo–Kobayashi–Maskawa matrix element and τ=m 2V /s .In (6),exp[S (m V ,q T )]is a Sudakov-like form factor which resums the large logarithms associated to the initial-state radiation.It reads:S (m V ,q T )=− m 2V q 2T dµ2µ2+B (αS (µ2)) ,(7)where A (αS )and B (αS )can be expanded as:FIGURE6.As in Fig.5,but in the low-q T range.FIGURE7.The ratio of the W to the Z spectrum at small q T for an intrinsic transverse momentum of zero(solid),1(dashed)and2GeV(dotted).A(αS)=A1αS+A2α2S+...;B(αS)=B1αS+B2α2S+ (8)As far as the logarithms which contribute to the resummation are concerned,twoconflicting nomenclatures exist.One consists of looking at Sudakov exponent, where the leading logarithms(LL)are∼αn S l n+1and the next-to-leading ones(NLL)∼αn S l n.It is straightforward to show that the LL contributions are obtained by keeping only the A1term in the expansions(8)while NLL accuracy is achieved byconsidering A2and B1as well.In this sense,the approach[14]is NLL.Another classification relies on the expansion of the exponentS(m V,q T)= n c n,n+1αn S l n+1+ n c n,nαn S l n,(9)where the leading term is∼αS l2,so that the leading contributions to exp[S(m V,q T)]are∼αn S l2n,terms∼αn S l2n−1being next-to-leading.This is equiv-alent to saying that in the differential cross section the LL and NLL contributions are∼(1/q2T)αn S l2n−1and∼(1/q2T)αn S l2n−2respectively.According to this nomen-clature,the calculations[13]and[15]are NNLL and NNNLL respectively.In the b-space formalism,following[14],the differential cross section reads:d2σ4π q,q′|V q¯q′|2 10dx1dx2δ(x1x2−τ) d2b e i q T· b× f q/1(x1,c1/b)f¯q′/2(x2,c1/b)exp[S(m V,b)]+(q↔¯q′) ,(10) where c1and c2are integration constants of order1and S(m V,b)is the Sudakov exponent in b-space.For high b values,i.e.small q T,non-perturbative effects are taken into account via a Gaussian function F NP=exp(−gb2),as suggested in[11].In both[13]and [14]the value g=3GeV2is chosen.Also,in order to allow resummed calculations to be reliable even at large q T,we wish to match the calculations of[13]and[14]to the exact O(αS)result.We add thefirst-order cross section to the resummed result and,in order to avoid double counting,we subtract offthe term which they have in common,which is the q T→0 limit of the exact O(αS)result.According to our prescription,the matching works fine if at the point q T=m V we have a continuous distribution.COMPARISON OF HER WIG AND RESUMMEDCALCULATIONSA detailed and general discussion on the comparison of angular-ordered parton shower algorithms with resummed calculations for Drell–Yan processes was already performed in[22],where the authors showed that,forτ→1,HERWIG always accounts for the term A1,corresponding to the leading logarithms in the exponent, and B1as well.Furthermore,one is able to account for the NLL term A2bysimply modifying the Altarelli–Parisi splitting function introducing a second-order contributionP′qq(αS,z)=αS1−z+C Fπ 2K18−π29N f,(12)N f being the number offlavours,C F=4/3and C A=1/2.This is equivalent to redefining the QCD parameterΛto the‘Monte Carlo’ΛMC:ΛMC=Λexp(K/4πβ0),(13) withβ0=(11C A−2N f)/(12π).Even after these replacements,the HERWIG algorithm cannot be considered completely accurate at the next-to-leading level, since it is still missing higher-order contributions in the strong coupling constant or the parton distribution functions(see,for instance,the discussion in[3]).In Fig.8we show the W transverse momentum distribution at the Tevatron in the low-q T range according to HERWIG6.1and the calculations of[13]in q T-space and of[14]in q T-and b-space.The HERWIG curve lies within the range of the resummed calculations,which is a reasonable result,considering that we are actually comparing different approaches.In Fig.9we consider the whole q T range, with the resummations matched to the exactfirst-order amplitude.Wefind that the matching worksfine only for the approach[14]in q T-space,the others showing a step at q T=m W,due to uncompensated contributions of orderα2S or higher. The well-matched distribution agrees with the HERWIG6.1prediction at large q T.CONCLUSIONSWe studied the initial-state radiation in vector boson production according to the HERWIG event generator and some resummed calculations.In particular,we in-vestigated the effect of the recently-implemented matrix-element corrections to the HERWIG algorithm.We found a big effect of such corrections on W/Z transverse momentum distributions at the Tevatron and at the LHC,and good agreement with the DØand CDF data,with a crucial role played by such corrections in order to be able tofit in with the data at large q T.We also found that,even though the spectra at small q T do depend on the intrinsic non-perturbative transverse momentum,the ratio of the W to the Z spectrum is roughly independent of it. We then considered some resummed calculations,which we matched to the exact O(αS)matrix element,which makes them reliable at large q T as well.We found reasonable agreement of such approaches with HERWIG andfine matching onlyFIGURE8.The W q T distribution at the Tevatron,according to HERWIG with matrix-element corrections,with zero intrinsic q T(solid histogram)and an q T int of1GeV(dashed histogram), compared with the resummed results of[14]in q T-space(solid line)and in b-space(dotted line) and of[13](dashed line)in q T-space.FIGURE9.As in Fig.8,but with the resummed results matched with the exact O(αS)matrix element.for the calculation which keeps all the next-to-leading logarithms in the Sudakov exponent in q T-space.Finally,we have to say that the discussed method of improving the initial-state radiation in parton-shower Monte Carlo simulations can be extended to a wide range of interesting processes for the phenomenology of hadron colliders.The implementation of hard and soft corrections to top and Higgs production is in progress.ACKNOWLEDGEMENTSThe presented results have been obtained in collaboration with Mike Seymour. 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