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Trilepton Production at the LHC - Standard Model Sources and Beyond

Trilepton Production at the LHC - Standard Model Sources and Beyond
Trilepton Production at the LHC - Standard Model Sources and Beyond

a r X i v :0805.3720v 1 [h e p -p h ] 23 M a y 2008SMU-HEP-08-01,ANL-HEP-PR-08-21,NSF-KITP-08-56

Trilepton Production at the LHC —Standard Model Sources and

Beyond

Zack Sullivan

Southern Methodist University,Dallas,Texas 75275-0175,USA and

High Energy Physics Division,Argonne National Laboratory,Argonne,Illinois 60439,USA Edmond L.Berger High Energy Physics Division,Argonne National Laboratory,Argonne,Illinois 60439,USA (Dated:May 27,2008)Abstract Events with three or more isolated leptons in the ?nal state are known to be signatures of new physics phenomena at high energy collider physics facilities.Standard model sources of isolated trilepton ?nal states include gauge boson pair production such as W Z and W γ?,and t ˉt production.We demonstrate that leptons from heavy ?avor decays,such as b →lX and c →lX ,provide sources of trileptons that can be orders-of-magnitude larger after cuts than other standard model backgrounds to new physics processes.We explain the physical reason heavy ?avor backgrounds survive isolation cuts.We propose new cuts to control the backgrounds in the speci?c case of chargino plus neutralino pair production in supersymmetric models.After these cuts are imposed,we show that it should be possible to ?nd at least a 4σexcess for supersymmetry parameter space point LM9with 30fb ?1of integrated luminosity.PACS numbers:13.85.Qk,13.85.Rm,12.60.Jv

I.INTRODUCTION

Events with three or more isolated leptons in the?nal state have attracted signi?cant attention as possible signatures of new physics phenomena produced at high energy collider physics facilities such as the Fermilab Tevatron and the CERN Large Hadron Collider(LHC). To the extent that new physics at the scale of100GeV or more is related to electroweak symmetry breaking,new states predicted in beyond the standard model(BSM)schemes typically couple to the W±or Z0gauge bosons which,in turn,decay to leptons.

Supersymmetry(SUSY)is a well studied potential realization of physics beyond the standard model[1].Trilepton events have long been mentioned as potential golden discovery modes for SUSY processes in which a chargino χ+i and a neutralino χ0j are jointly produced. Isolated three lepton signatures arise from the decay modes χ+i→W?+ χ01→ˉlν χ01,along with χ0j→Z? χ01→lˉl χ01.In this example,the χ01is the lowest mass SUSY particle assumed to be e?ectively stable and therefore a source of missing energy;W?+and Z?stand for on-shell or virtual gauge bosons.This SUSY example provides a relatively clean source of isolated trilepton events[2,3].Within SUSY,one can also pair-produce heavy sparticles that carry color quantum number,such as gluinos and squarks.The cascade decays of these states,while parameter dependent,will generally result in trilepton?nal states along with hadronic jets[4].

Other BSM constructs,such as Higgsless models,extra-dimensional models,and models with extended gauge groups,predict states at high mass,such as Kaluza-Klein towers and extra gauge bosons,that decay to the more familiar W and Z electroweak gauge bosons.In one example of a Higgsless model,a massive W′is predicted with dominant decays into pairs of gauge bosons,such as W±Z,which is a source of isolated three lepton?nal states[5,6,7]. Our intent here is not to present a survey of BSM sources of multi-lepton events.We cite the cases mentioned as indicative of a range of possibilities.

In this paper we are concerned with obtaining as good an estimate as possible of the production of isolated three lepton?nal states that arise entirely from sources within the standard model(SM)itself.An obvious and important example is the associated production of a pair of gauge bosons,such as W Z,along with its generalizations Wγ?,whereγ?is a virtual photon that decays asγ?→lˉl.We?nd that the Wγ?contribution is much more signi?cant than is widely appreciated.Unlike W Z,the Wγ?contribution cannot be reduced

by an anti-selection of events in which the invariant mass of the lˉl system is in the vicinity of the Z0peak.

In this work,we use MadEvent[8]to compute the full matrix elements for partonic subprocesses that result in a lllν?nal state.For the W Z/γ?process,this method allows us to retain important angular correlations among the?nal leptons.Here Z/γ?stands for the full range of lˉl pairs resulting from a Z,a Drell-Yan virtual photon,and photon-Z interference.Our estimates are larger for this process than those one would obtain from a modeling of W Z alone from within PYTHIA[9],and we describe these di?erences.Inclusion of theγ?contribution accounts for part of these di?erences.Since W Z/γ?is an important standard model background in many searches for new physics,we suggest that events be generated by a matrix element program and be fed into the PYTHIA showering routines, rather than use of the W Z routine built into PYTHIA.

A major new contribution in this paper is the demonstration that isolated leptons from bottom and charm decays are a potent source of standard model backgrounds to new physics signatures in the three lepton?nal state.This study is an extension of our prior investi-gation[10]of SM heavy?avor backgrounds to the isolated two-lepton?nal state that is important in searches for the Higgs boson.In this new paper we compute contributions from a wide range of SM heavy?avor processes including bZ/γ?,cZ/γ?,bˉbZ/γ?,cˉc Z/γ?. We also include contributions from tˉt production,and from processes in which a W is pro-duced in association one of more heavy?avors such as tW,bˉbW,cˉc W.In all these cases, one or more of the?nal observed isolated leptons comes from a heavy?avor decay.The bˉbW and cˉc W contributions have not been examined previously.

To examine signal discrimination(and to compute signal to background ratios),we choose the speci?c case of chargino and neutralino pair production as the signal process.We focus on the SUSY parameter space points LM1,LM7,and LM9considered by the CMS Collaboration[11,12]and on the SU2point studied by the ATLAS Collaboration[13].These points are expected to have favorable SUSY cross sections at the LHC.The dominant nature of some of the SM backgrounds motivates the investigation of new selections(cuts)on the ?nal state kinematic distributions that would be e?ective in reducing the backgrounds.One of these cuts involves selections on the opening angles among the three charged leptons in the?nal state.The cuts are de?ned and their e?ectiveness is discussed in Secs.IV and V.

We begin in Sec.II with an explanation of the source and magnitude of isolated leptons

from heavy?avor production and decay.Issues important in our simulation of?nal states are discussed in Sec.III.We generate events using MadEvent,pass them through a PYTHIA showering Monte Carlo code,and?nally through a heavily modi?ed PGS detector simulation program.Our overall results and comparisons with studies done by the CMS and ATLAS groups are presented in Secs.IV and V.Our conclusions are summarized in Sec.VI.We show that it should be possible to?nd at least a4σexcess in30fb?1for SUSY point LM9.

II.ISOLATED LEPTONS FROM BOTTOM AND CHARM DECAYS

The use of leptons inside jets to tag bottom and charm jets has led to the recognition that strong isolation criteria are required to distinguish leptons from primary interactions from those caused by secondary decays.In Ref.[10]we demonstrate that the rate for secondary leptons to pass isolation cuts is surprisingly large—about1part in200.In this section we explain the reasons these leptons pass the isolation cuts at such a large rate.

The simplest case to understand is the production of muons from b quark decay.The branching fraction of various B hadrons(B d,B s,Λb,etc.)to muons is roughly9–14%. Observation of these leptons requires,however,that their charged tracks generally be above some transverse momentum threshold(see the Appendix for details of isolated lepton re-construction).In the dotted line of Fig.1we show the shape of the probability to produce a muon with p Tμ>10GeV versus the transverse momentum of an initial b quark.This curve is determined predominantly from the V?A matrix element decay of the B hadron into Dlν[9]and kinematics imposed by the muon momentum threshold.1The probability of producing a10GeV muon is small at low b transverse momentum,and it grows toward the branching fraction limit as the transverse energy of the b moves farther above threshold. This curve leads to the false impression that low-p T b quarks are unimportant.

There are two ways in which a muon can pass isolation cuts applied to detector data.The ?rst is if the other decay products of the B hadron are physically separated in pseudorapidity ηand/or radial angleφ.This separation accounts for no more than1/2of the isolated

GeV

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201510FIG.1:Normalized probability for an existing b quark to produce an isolated muon with p T μ>10GeV (solid)vs.the b transverse momentum.This curve is a multiplicative combination of the probability of producing a muon with p T μ>10GeV (dotted)and the probability the muon will be isolated (dashed).The b production spectrum is not included.Muon isolation criteria are described in the Appendix.

rate.One could imagine rejecting secondary muons by increasing the area examined for accompanying radiation,but this technique reduces acceptance of primary muons and is of limited utility.Of more importance is the isolation energy cut.When muons come from low-p T b quarks,they must have taken most of the transverse momentum of the B hadron.This means there is not enough energy left in the other B decay products to fail the energy cuts for isolation.The net isolated muon probability is the multiplication of the probability for production and for passing isolation cuts.This probability is shown as the solid line of Fig.1,and it peaks fairly close to threshold.

There is little freedom to change the picture in Fig.1.An attempt could be made to lower the energy threshold beyond which events are rejected,but this cut is already nearly optimized for the acceptance of real muons.Hence,one might expect to reduce the rate of muons from higher-p T b decays,but there will not be much gain.One other handle might be to look for secondary vertices,but our tests indicate that virtually all muons that pass isolation point back at the primary vertex.A preliminary examination of CDF data [15]appears to con?rm this ?nding.

The physics behind ?nding an isolated electron from b quark decay is similar to that for ?nding a muon.Figure 2demonstrates the same probability for production of an electron.The probability of satisfying the isolation cuts is ?atter with respect to p T b than for the muon,because noise in the electromagnetic calorimeter requires less stringent cuts to maintain electron acceptance.It is possible to achieve some purity with a loss of acceptance,but we ?nd little di?erence in the net rate of leptons from heavy ?avors between the ATLAS reconstruction algorithm that we use [13]and less sophisticated algorithms.

GeV

GeV

(GeV)N o r m a l i z e d P r o b a b i l i t y 55

504540353025201510FIG.2:Normalized probability for an existing b quark to produce an isolated electron with p T e >10GeV (solid)vs.the b transverse momentum.This curve is a multiplicative combination of the probability of producing an electron with p T e >10GeV (dotted)and the probability the electron will be isolated (dashed).The b production spectrum is not included.Electron isolation criteria are described in the Appendix.

While physical limitations of the experimental apparatus control the acceptance of a lepton produced from a b decay,the overall rate of reconstructed leptons includes the e?ect the p T b production spectrum.With the exception of top-quark decay,the p T b spectrum tends to fall steeply.In Fig.3we display the net isolated lepton cross section as a function of p T b for b ˉb production.Despite the larger acceptance for isolated muons around p T b ~25GeV and isolated electrons with p T b ~30–50GeV,the peak production comes from b quarks around 20GeV.The position of this peak has a profound e?ect on the simulation of isolated leptons,because fully 1/2of the reconstructed muon rate comes from b quarks with

p T b <20GeV.A natural tendency is to ignore these lower energy b quarks based on the low probability of lepton production shown in the dotted lines of Figs.1and 2.The complete picture,however,demonstrates that these events are important and most di?cult to reject.

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0FIG.3:Cross section for production of a muon or electron from b ˉb production and decay (solid),an isolated muon (dashed),or an isolated electron (dotted).

An examination of charm decay into isolated muons and electrons leads to essentially identical conclusions as bottom decay with one minor addition.In Fig.4we show the cross section for production of a muon or electron vs.p T c ,and their isolated rates.In practice,because of “fakes”(charged hadrons mistaken for electrons),the reconstructed rate for electrons is larger than expected from the decay of c to e times an isolation acceptance.A large number of charged pions can be produced in decays of D mesons.A reasonable fraction of these pions are reconstructed as electrons,and so the net rate for “isolated electrons”shown as the dot-dashed line is about 50%larger than expected.Electron reconstruction algorithms are constructed in order to balance this contamination of charged pions versus acceptance.The goal across detectors is typically a fake rate for pions from jets of 10?4(compared to the rate of leptons we ?nd of a few times 10?3from b and c decays)[11,13].Depending of the physics study,it may be worth including the decays from heavy quarks as a part of the design of electron isolation algorithms.For the case of trileptons we examine here,the leptons from heavy quarks dominate the backgrounds.

We conclude this section by noting that Figs.3and 4indicate the expected rate of isolated

Tot.“”GeV

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0FIG.4:Cross section for production of a muon or electron from c ˉc production and decay (solid),an isolated muon (dashed),an electron which is then isolated (dotted),or “isolated electron”including fakes (dash-dot).

electrons from processes containing b and c quarks can be signi?cantly larger than the rate for isolated muons.Consequently,new physics processes with muons should have a higher purity than those with electrons.One general strategy would be to look for signals with an excess that is more apparent in muon channels than electron channels.A second observation is that looser cuts cause the typical transverse momentum of surviving isolated electrons to be slightly higher than that for muons.This recognition suggests that electron events will be more suppressed than muon events by cuts on maximum lepton energy,e.g.,the Z -peak cut used below.This lepton ?avor dependence may allow an additional handle on in-situ calibration of background sources.

III.SIMULATION

The backgrounds we discuss tend to arise from the tails or end points of physical pro-cesses and challenge detector capabilities.To achieve a believable and detailed simulation of reconstructed events,we follow the methods developed and validated in Ref.[10],with some modi?cations for e?cient production and analysis of the results.

We generate events with a customized2version of MadEvent3.0[8]and run them through the PYTHIA6.327[9]showering Monte Carlo.Both programs use the CTEQ6L1parton distribution functions[16]evaluated via an e?cient evolution code[17].The showered events are fed through a version of the PGS3.2[18]fast detector simulation,modi?ed to match ATLAS geometries,e?ciencies,and detailed reconstruction procedures[13].We con?rm that our results agree with full ATLAS detector simulations at both the reconstructed object (leptons,jets,/E T)and analysis levels to better than10%(and in some cases better than 1%).

For this paper we use the ATLAS muon and electron reconstruction procedure(described in the Appendix)and detector e?ciencies to produce initial candidate leptons for both CMS and ATLAS studies.We then apply the CMS or ATLAS geometric acceptance,transverse momentum threshold,and analysis cuts in order to compare to their to their respective studies.We reproduce the results of the published CMS analysis to better than1%in most cases.As we expect from Sec.II,and as observed in Ref.[10],we?nd that since the detectors have been optimized for the same lepton acceptance and lepton fake rate from jets,the lepton rate from heavy-?avor decays is insensitive to details of the detector reconstruction.

In Sec.II we explain the physics reasons for simulating low-p T b and c quarks.In Ref.

[10]we determined that at least1000samples of phase space are required to reproduce the interesting angular correlations in phase space for these types of events.As missing energy plays an important role in these signals,we cannot just multiply the spectrum of produced quarks by an average lepton isolation acceptance.Instead,we iterate over each point in phase space between104and5×105times,ensuring we produce at least10events that pass a minimal set of cuts.This number is su?cient if there are two b or c quarks that are needed to produce leptons.

Simulating any cross section that requires3or more heavy quarks to produce leptons (bbbb,cccc,bbcc)would require at least1000times the number of events we simulate.Hence, we can provide only an order-of-magnitude estimate of the e?ect of these four-heavy-?avor processes in Sec.IV.

Several technical hurdles have to be overcome to achieve the statistically signi?cant and systematically controlled results shown in Secs.IV and V.We have already described our

method of iterating multiple times over the same phase space points to give showering an opportunity to generate isolated leptons.Even though the detector simulation is techni-cally a“fast”detector simulation,over10billion events were required to produce su?cient statistics to describe the heavy?avor decays to isolated leptons throughout their available phase space.This computation was carried out with2CPU years of time on the Argonne Laboratory Computing Resource Center JAZZ cluster,a Pentium Xeon Linux cluster with 350compute nodes.The large number of events raises a practical issue regarding the total amount of data generated.Because of the time involved in generation,and our desire to an-alyze both angular correlations and di?erent cuts for CMS and ATLAS,we must store event information.Standard PYTHIA,STDHEP,or compressed data structures for this analysis would require more than100TB of storage,a simply impractical requirement.Therefore, we write only events that produce at least3isolated leptons(see the Appendix for the def-inition of isolation),and store the four-vectors of the leptons,leading jet(for vetoes),and missing transverse energy.This is the minimal necessary information to analyze the data presented below.

https://www.doczj.com/doc/bc3483532.html,PARISON TO CMS

In their technical design report(TDR)[12],the CMS Collaboration de?nes several several sets of minimal supergravity(mSUGRA)parameters that have sensitivity to di?erent aspects of SUSY.The points LM1,LM7,and LM9are the only subset of the9points examined that exhibit a large trilepton signature from χ02 χ±1decay.These points assume A0=0,μ>0, and(m0,m1/2,tanβ)are(60,250,10),(3000,230,10),and(1450,175,50)for LM1,LM7, and LM9,respectively.The reach for discovery of χ02 χ±1decays to trileptons is summarized in the TDR,but we follow the more detailed account from Ref.[19]below.

The basic CMS analysis looks for3isolated leptons,with p Tμ>10GeV,p T e>17GeV, and|ηl|<2.4(see the Appendix for the method of isolation).Events that contain jets with E T j>30GeV are vetoed in order to reduce the contribution from processes such as tˉt production and more complex SUSY processes involving cascade decays of massive SUSY states.Since real Z decays dominate the usual standard model backgrounds,events are removed in which the invariant mass of the opposite-sign same-?avor(OSSF)leptons is more than75GeV.CMS then performs a neural net analysis with7variables to suppress the

backgrounds from SM production of Z+jets and virtual photon+jets(called Drell Yan in their terminology)to achieve a signal to background ratio S/B of1/3.There are not enough details or referenced notes regarding the neural net for us to reproduce the results,but we can con?rm agreement for the backgrounds considered.However,the new backgrounds calculated here far outweigh the ones studied by CMS.As all of our estimated backgrounds are larger than those determined by CMS,we explain in detail where our simulations agree and where and why they di?er.

There are three overriding observations to keep in mind.First,each signi?cant back-ground involving leptons from heavy?avor decays,not estimated by CMS,is more than10 times larger than the largest background considered by CMS.Second,as explained below, our?rst benchmark process,W Z includes additional physics that enhances this background. Third,the ISASUGRA7.69evolution code used by CMS for the supersymmetric spectrum gives mass di?erences and branching fractions incompatible with the more recent version employed in our work.Nevertheless,we?nd good agreement with the CMS results when we consider only their backgrounds and use their assumptions.Therefore,we are con?dent that the simulation improvements discussed below are valid and will be useful for future studies.

A.W Z,tˉt,and W t?nal states

In order to maintain consistency across processes considered,we elect to present results using leading-order cross sections rather than introducing next-to-leading order(NLO)K factors.While NLO calculations exist for most of these processes[21],there is considerable overlap at NLO between?nal states,e.g.,bZ and bˉbZ.Furthermore,the jet veto will reject some of the higher order radiation that enhances the cross sections.Proper matching between orders is beyond the scope of this paper.

Since our goal is to establish a direct connection with the CMS analysis,we?rst con?rm that our detector simulation reproduces the CMS detector simulation for reconstructed leptons.Performing a PYTHIA-based calculation of W Z,minus decays to taus,and using the CMS K-factor of2,we predict171events after cuts in30fb?1vs.173events in Table6 of the CMS analysis[19].Any di?erences in lepton reconstruction enter3times;hence, this comparison shows that our detector simulation agrees exceedingly well with the CMS detector simulation.

The PYTHIA code used by CMS for W Z production omits virtual photon γ?production and interference with the Z .Given that the Z peak will be removed by cuts,we ?nd that the additional contribution from W plus a virtual photon is at least as important.This result agrees with other work [3,20]in which the importance of the virtual photons is emphasized.In all of our simulations we include the virtual photon continuum and photon-Z interference along with the Z .In the case of the SM W Z contribution,we denote the full contribution from W Z ,W γ?,and W +Z,γ?interference by W Z/γ.In Figs.5–7we show the transverse momentum distribution of the p T -ordered leptons from W Z/γcompared with the distributions from W Z alone.The peak at 20GeV in Fig.5is produced by the minimum p T cuts on the individual leptons that make up the virtual photon contribution.Essentially all of the leptons from o?-shell photons combine survive the Z -peak mass cut.When there are 3muons or 3electrons,both OSSF pairings pass the cuts.Hence,about 1/2of the virtual photon events appear twice when counting events.

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0.00FIG.5:Transverse momentum (p T )distribution of the leading-p T lepton in W Z/γcompared with W Z .

Table I compares the LO W Z/γcross section with a virtual photon included to a CMS-like NLO W Z estimate using PYTHIA.Given that a K -factor of 2is used in the CMS estimate,there is a full factor of 6di?erence between W Z built into PYTHIA,and W Z/γgenerated by MadEvent and showered by PYTHIA.Nearly 1/2of the excess is attributable to the virtual photon that is not included in PYTHIA.Some of the excess comes from

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correlations captured by the full matrix element that are sensitive to the cuts.In particular,angular correlations among the ?nal-state leptons are missing from the CMS study.In order to study these correlations,and to quote a more realistic background,we use the full matrix element for W Z/γ→lllνfrom MadEvent showered through PYTHIA in our results below.

TABLE I:Comparison of two backgrounds calculated by CMS and by this study.W Z/γand tˉt are our estimates.W Z PYT is calculated from PYTHIA and normalized to the CMS NLO total cross section.tˉt CMS j uses the CMS acceptance for the jet veto,based on a matched calculation that produces signi?cantly more radiation than a leading order calculation.The second column shows the number of events expected with30fb?1of integrated luminosity after the requirements that there be3leptons and no jets with E T j>30GeV.In the third column an additional requirement is imposed that the invariant mass of any pair of OSSF leptons be no greater than75GeV.

N l=3,

Channel no jets M OSSF

<75GeV

ll

661171

W Z NLO

PYT

tˉt CMS j394208

The remaining increase in the normalization of the cross section is connected with the requirement that there be no jets with E T>30GeV.We compare W Z→lllνevents generated with MadEvent and showered with PYTHIA to W Z events which are generated, decayed,and showered all within PYTHIA.In the process we observe that the initial-state QCD radiation spectrum is harder in the all-PYTHIA events.The jet veto rejects a larger fraction of this pure electroweak process assuming PYTHIA generation,and hence leads to a smaller normalization of the cross section after cuts.This e?ect is consistent across all processes we calculate,and hence leads to an overall uncertainty in the absolute cross section.Our main concern in this paper is to understand the relative importance of the various backgrounds,and their shapes.When data are in hand,we expect the total background to be normalized to data.Because most of the processes we evaluate are not in PYTHIA,we perform and demonstrate the cross sections for MadEvent generated events, and discuss the e?ect of normalization on a discovery signal at the end.

CMS also quotes their estimated background from tˉt production.It is important to compare with their result because this background requires one lepton from a b decay.The CMS analysis uses a matched[22]tˉt cross section which produces more jets in the?nal state than our LO calculation.Hence,CMS has a higher rejection rate based on their jet veto.If

we rescale our result using the e?ciency of their jet veto instead of ours,we?nd208events in 30fb?1vs.239events in the CMS paper.We?nd excellent agreement between our estimate of a background with a lepton from a b and the CMS estimate.A similar rescaling for W t would give us37events vs.45in the CMS paper.Our systematic10%underestimate of the e?ect of isolated leptons from b decay in the tˉt sample suggests our other results involving leptons from heavy?avor decays are conservative.The comparison between our calculation of tˉt and the jet-acceptance reduced version are summarized in Table I.

B.Heavy?avor?nal states

Before addressing the importance of leptons from heavy-?avor decays,we comment on one subtlety in the supersymmetric models studied.The243events we?nd for SUSY point LM9are similar to the238events expected by CMS.However,we predict123events vs. 91for point LM7,and44events vs.70events for LM1.The di?erences are attributable to the use of ISASUGRA7.75in our study vs.ISASUGRA7.69by CMS3.There was a small bug in the evolution codes in ISASUGRA7.69that,when corrected,leads to10GeV shifts in the neutralino mass spectrum.The Z mass peak cut is sensitive to the endpoint of the lepton spectrum,M max

=

ll

3We are unable to use ISASUGRA7.69due to a change in data format.

TABLE II:Leading order signal and background statistics for several?nal states in a CMS-like analysis,and with two additional cuts.The second column shows the number of events expected with30fb?1of integrated luminosity after the requirements that there be3isolated leptons and no jets with E T j>30GeV.In the third column an additional requirement is imposed that the invariant mass of any pair of OSSF leptons be no greater than75GeV.The virtual photon components are large after cuts.

N l=3Angular

Channel no jets M OSSF

<75GeV/E T>30GeV cuts

ll

W Z/γ1880538325302

tˉt1540814696672

tW273146123121

tˉb1.11.00.770.73

bZ/γ140006870270177

cZ/γ345014004535

bˉbZ/γ89902220119103

cˉc Z/γ468018306935

bˉbW9.17.65.65.3

cˉc W0.190.150.120.11 Addressing the contributions of Z/γplus heavy?avors and W plus heavy?avors,we see in Table II that,before the Z peak cut,Z/γplus heavy?avors produces trileptons16 times more often than W Z/γ.After the Z peak cut,the ratio rises to23times W Z/γ.In particular,bˉbZ/γ,which includes a virtual photon,is over30times the CMS estimate of the cross section that does not have a photon.In Figs.8–10,we see the opposite-sign same ?avor(OSSF)dilepton invariant mass for the signals,W Z/γbackground,and(bZ/γ)/5. Cutting out the Z mass peak reduces the backgrounds,but the remaining tail for Z/γplus heavy?avors overwhelms the signal.

The number of handles available to reject the huge background from Z/γ+heavy?avors

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0.20.0FIG.8:Invariant mass of the opposite-sign same-?avor (OSSF)lepton pairs for the SUSY LM1signal (×10,dotted),the W Z/γbackground (dashed),and the bZ/γbackground (divided by 5,solid).Other Z/γ+heavy ?avor backgrounds (not shown)have the same shape as bZ/γ.is limited.In Ref.[10]we recommend raising the minimum lepton p T threshold since the lepton p T spectrum from b and c decays tends to fall rapidly.In typical trilepton studies,however,the leptons are very soft.Hence,any increase in the cut on the lepton p T tends to reject too much of the signal.

Missing transverse energy /E T is a partial discriminator.The SUSY signals contain invis-ible neutralinos which leave a broad range of /E T in the detector.In Fig.11we show the /E T spectrum for the SUSY LM9signal and for the W Z/γand bZ/γbackgrounds.Trilepton

signatures from t ˉt

production generally have two neutrinos which lead to large missing en-ergy.The contribution from Z/γ+heavy ?avor processes peaks at over 400times the size of the LM9signal at low /E T ,but it falls rapidly to below the signal by /E T >50GeV.These di?erences present both opportunities and challenges,especially since the precision of /E T measurements is not as great as one might prefer.

In the fourth column of Table II,we show that the requirement /E T >30GeV removes most of the Z/γ+heavy ?avor backgrounds 4for a modest loss of signal.A cut below 20

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0.4

0.20.0FIG.9:Invariant mass of the opposite-sign same-?avor (OSSF)lepton pairs for the SUSY LM7signal (×2,dotted),the W Z/γbackground (dashed),and the bZ/γbackground (divided by 5,solid).Other Z/γ+heavy ?avor backgrounds (not shown)have the same shape as bZ/γ.

GeV is not as useful and is likely not achievable at the LHC.A cut above 40GeV removes most of the Z/γ+X backgrounds,but it begins to signi?cantly reduce the signal and is of

little additional help with W Z/γand t ˉt backgrounds.The sharply falling /E T spectrum in

Z/γ+X is extremely sensitive to uncertainties in the measurement of /E T .This uncertainty makes it di?cult to predict absolute cross sections after cuts.On the other hand,this sensitivity could provide an excellent opportunity to measure the background in situ and reduce concerns regarding modeling details.The background can be ?t in the data and the /E T cut adjusted to optimize the purity of the sample.

Since the accuracy of /E T measurements is limited,we examine instead the utility of angular cuts without a /E T cut.There are signi?cant angular correlations in the Z/γ+heavy ?avor backgrounds that are di?erent from those in the SUSY trilepton signals or the W Z/γ

and t ˉt

backgrounds.In Figs.12–14we plot the angular distribution between pairs of p T -ordered leptons in the trilepton center-of-momentum (CM)frame without a /E T cut.The Z/γ+heavy ?avor backgrounds have signi?cant peaks at both small and large angles.The

signal and other backgrounds either peak only at large angles (θCM 12,θCM 13),or are fairly

central (θCM 23).

We examine the impact of these angular correlations by themselves by imposing three

()/5SUSY LM9

cut

peak (GeV)(f b /G e V )120

1008060402000.8

0.6

0.4

0.20.0FIG.10:Invariant mass of the opposite-sign same-?avor (OSSF)lepton pairs for the SUSY LM9signal (dotted),the W Z/γbackground (dashed),and the bZ/γbackground (divided by 5,solid).Other Z/γ+heavy ?avor backgrounds (not shown)have the same shape as bZ/γ.

angular cuts in the trilepton center-of-momentum frame:θCM 12>45?,θCM 13>40?,and

θCM 23<160?.These angle cuts reduce the heavy ?avor backgrounds and W Z/γby ~30%,with only a 5%reduction of the signal.These cuts could be further optimized,but in general they are more useful for increasing purity than for increasing signi?cance.

Figures 15–17show the angular distributions between pairs of p T -ordered leptons in the trilepton CM frame after the missing transverse energy cut.The last column of Table II demonstrates the e?ect of adding the three angular cuts after the /E T cut.There is almost no correlation between the e?ects of the angle cuts and the missing transverse energy cut except in bZ/γ,where the cut is slightly more e?ective after the /E T cut (acceptance is 0.32vs.0.37).The real advantage of angular cuts over a /E T cut is that the angles are well measured.Whether or not missing transverse energy can be well-measured,the use of the angular cuts will improve any ?nal analysis.

One class of backgrounds not treated so far is one in which all three leptons come from heavy ?avor production (b ˉbb ˉb ,c ˉc c ˉc ,b ˉbc ˉc ).As mentioned in Sec.III,practical limitations prevent us from simulating this background directly.Instead we provide a rough estimates for the trilepton signature from three sources of b ˉbb ˉb production.First,using W b ˉb production,we obtain an estimate for the probability of ?nding an isolated lepton at the LHC of 7.5×10?3

SUSY LM9

(GeV)(f b /G e V )100

8060402000.8

0.6

0.4

0.2

0.0FIG.11:Missing transverse energy spectrum /E T of the opposite-sign same-?avor (OSSF)lepton

pairs for the SUSY LM9signal (dotted),the W Z/γbackground (dashed),t ˉt

(dot-dashed),and bZ/γ(solid).Other Z +heavy ?avor backgrounds (not shown)have the same shape as bZ/γ.

per b .The cross section for direct production of b ˉbb ˉb from MadEvent multiplied by (7.5×

10?3)3gives about 500trilepton events in 30fb ?1of data.Second,multiple interactions per beam crossing,where more than one b ˉb pair is produced,can lead to a trilepton signature.For a total inelastic cross section of about 80mb [12],the rate for two scatters to give three isolated leptons is about 60events per interaction per 30fb ?1.5At 10interactions per crossing,this method leads to about 600events,though the jet veto will likely reduce this ?gure somewhat.

Multiple scattering in a given interaction (e.g.,double parton scattering),or even show-ering of heavy quarks,is a third source,arising from successive production of b ˉb pairs.The rate may be comparable to direct 4-b production after cuts on transverse momentum [23],and it can double the backgrounds listed so far.These rough estimates are the same order of magnitude as the number of events from Z/γ+heavy ?avor processes,and they are a po-tentially serious problem with the default analysis.A sum over all production processes and decays to both muons and electrons would increase these numbers by an order of magnitude.On the other hand,in Ref.[10]we observe that a missing energy cut serves to signi?cantly

小学三年级英语知识点总结归纳

小学三年级英语:知识点归纳知识归纳是一个不错的学习计划,把知识归纳总结可以帮助自己更方便学习提高效率,减少许多不必要的时间。下面就一起来看看归纳的知识点吧!希望同学们可以学习一下! 一、单词 Unit1学习文具:pen(钢笔)pencil(铅笔)pencil-case(铅笔盒)ruler (尺子)eraser(橡皮)crayon(蜡笔)book(书)bag(书包)sharpener (卷笔刀)school(学校) Unit2身体部位:head(头)face(脸)nose(鼻子)mouth(嘴)eye (眼睛)leg(腿)ear(耳朵)arm(胳膊)finger(手指)leg(腿)foot(脚)body(身体) Unit3颜色:red(红色的)yellow(黄色的)green(绿色的)blue (蓝色的)purple(紫色的)white(白色的)black(黑色的)orange (橙色的)pink(粉色的)brown(棕色的) Unit4动物:cat(猫)dog(狗)monkey(猴子)panda(熊猫)rabbit(兔子)duck(鸭子)pig(猪)bird(鸟)bear(熊)elephant (大象)mouse(老鼠)squirrel(松鼠) Unit5食物:cake(蛋糕)bread(面包)hotdog(热狗)hamburger (汉堡包)chicken(鸡肉)Frenchfries(炸薯条)coke(可乐)juice(果汁)milk(牛奶)water(水)tea(茶)coffee(咖啡)

Unit6数字:one(一)two(二)three(三)four(四)five(五)six(六)seven(七)eight(八)nine(九)ten(十)doll(玩具娃娃)boat(小船)ball(球)kite(风筝)balloon(气球)car (小汽车)plane(飞机) 二。对话、 1、向别人问好应该说——A:Hello!(你好!) B:Hi!(你好!) 2、问别人的名字应该说-——A:What‘syourname?你的名字是什么? B:Myname‘sChenJie.我的名字是陈洁。 3、跟别人分手应该说——A:Bye.\Goodbye!(再见) B:Seeyou.(再见)\Goodbye.(再见) 4、A:Ihaveapencil\bag\ruler我有一只铅笔\书包\尺子。 B:Metoo.我也有。 5、早上相见应该说-——A:Goodmorning.早上好! B:Goodmorning!早上好! 6、下午相见应该说——A:Goodafternoon!下午好! B:Goodafternoon!下午好! 7、跟新朋友第一次见面——A:Nicetomeetyou!见到你很高兴。 B:Nicetomeetyou,too!见到你也很高兴! 8、A:Let‘sgotoschool!让我们一起去上学! B:OK!好的。

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三年级上册英语知识点归纳

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四、我们要知道下面的词的原形及缩写形式: 1)I’m=I am 我是2)name’s=name is 名字是3)what’s=what is 是什么4)let’s=let us让我们 5)that’s=that is 那是6)he’s=he is他是 7)she’s=she is 她是8)who’s=who is是谁 9)don’t=do not不10)isn’t=is not不是 五、单词归类: 1)时间:morning早上,afternoon下午,evening傍晚,night晚上2)家庭成员:mum妈妈,dad爸爸,grandma奶奶, grandpa爷爷,father父亲,mother母亲, sister姐妹,brother兄弟,aunt阿姨,uncle叔叔3)身体部位:face脸,eye眼睛(单数),eyes眼睛(复数), hand手,hands手(复数),hair头发, nose鼻子,ear耳朵,ears耳朵(复数),foot脚, feet脚(复数),head头,mouth嘴巴,leg腿, legs腿(复数),tooth牙齿,teeth牙齿(复数)4)形容词:good好的,fine好的,nice好的,new新的, pretty漂亮的,old老的,cute可爱的,thin瘦的, strong强壮的,young年轻的,tall高的,tidy正确的5)学习用品:ruler尺子,pencil铅笔,bag书包、袋子, pen钢笔,book书,rubber橡皮,box盒子

语文阅读理解题目和答案大全

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Kitty and Alice are good friends. 否定be后加not 4. My eyes are big. My hair is long.

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