Missing energy look-alikes with 100 pb at the CERN LHC

45 Pages·2008·1.33 MB·English

PHYSICAL REVIEW D 78, 075008 (2008)
Missing energy look-alikes with 100 pb(cid:1)1 at the CERN LHC
Jay Hubisz*
High Energy Physics Division, Argonne National Laboratory, Argonne,Illinois 60439,USA
Joseph Lykken+
Fermi National AcceleratorLaboratory, P.O. Box 500,Batavia, Illinois 60510, USA
Maurizio Pierini‡ and Maria Spiropulux
Physics Department, CERN, CH 1211 Geneva 23, Switzerland
(Received 30 May 2008; published 9 October 2008)
A missing energy discovery is possible at the LHC with the first 100 pb(cid:1)1 of understood data. We
present arealisticstrategytorapidlynarrowthelist ofcandidatetheoriesat,orcloseto,themomentof
discovery.Thestrategyisbasedonrobustratiosofinclusivecountsofsimplephysicsobjects.Westudy
specificcasesshowingdiscriminationoflook-alikemodelsinsimulateddatasetsthatareatleast10to100
timessmallerthanusedinpreviousstudies.Wediscriminatesupersymmetrymodelsfromnonsupersym-
metric look-alikes with only 100 pb(cid:1)1 of simulated data, using combinations of observables that trace
back to differences in spin.
DOI: 10.1103/PhysRevD.78.075008 PACS numbers: 11.30.Pb, 14.80.Ly, 12.60.Jv
I. INTRODUCTION When N is large, it is not a viable strategy to discrimi-
nate between N alternative explanations by performing N
A. Twenty questions at the LHC
tests.However,asthegame‘‘twentyquestions’’illustrates,
Manywell-motivatedtheoreticalframeworksmakedra- a well-designed series of simple tests can identify the
maticpredictionsfortheexperimentsattheLargeHadron correct alternative after of order logðNÞ steps, proceeding
Collider. These frameworks are generally based upon as- alongadecisiontreesuchthat,ateachbranching,oforder
sumptionsaboutnewsymmetries,asisthecaseforsuper- half of the remaining alternatives are eliminated.
symmetry (SUSY) [1,2] and little Higgs (LH) [3,4], or AddressingtheLHCinverseproblemimpliesdesigning
upon assumptions about new degrees of freedom such as and implementing this series of simple tests in the LHC
extra large [5] or warped [6] spatial dimensions. Within experiments, so that with high confidence a significant
each successful framework, one can construct a large
fraction of the remaining theory space is ruled out at
number of qualitatively different models consistent with
each step. The results of the first few tests will shape the
all current data. Collectively these models populate the
requirements for future tests, so the immediate need is to
‘‘theory space’’ of possible physics beyond the standard
develop the strategy for the early tests. In this paper we
model (BSM). The BSM theory space is many dimen-
providethisstrategyforthecaseofaLHCdiscoveryinthe
sional, and the number of distinct models within it is
inclusive missingenergy signature.
formallyinfinite.Sincethedatawillnotprovideadistinc-
tion between models that differ by sufficiently tiny or
experimentally irrelevant details, infinity, in practice, be- B. Missing energy at the LHC
comes some large finite number N. The mapping of these
The existence of dark matter provides a powerful moti-
N models into their experimental signatures at the Large
vation to explore missing energy signatures at the LHC,
HadronCollider (LHC),thoughstillincomplete,has been
under the assumption that a significant fraction of dark
explored in great detail.
matter may consist of weakly interacting thermal relics.
Assoon asdiscoveriesare madeattheLHC, physicists
MissingenergyattheLHCisexperimentallychallenging.
will face the LHC inverse problem: given a finite set of
Mostoftheenergyof14TeVppcollisionsiscarriedoffby
measurements with finite resolutions, how does one map
undetected remnants of the underlying event, so missing
back[7–9]totheunderlyingtheoryresponsibleforthenew
energy searches actually look for missing transverse en-
phenomena?Sofar,notenoughprogresshasbeenmadeon
ergy (Emiss) of the partonic subprocess. Emiss searches are
this problem, especially as it relates to the immediate T T
plaguedbyinstrumentalandspuriousbackgrounds,includ-
follow-up of an early LHC discovery.
ingcosmicrays,scatteringoffbeamhalo,andjetmismea-
surement. Standard model processes create an irreducible
*[email protected]
Emiss background from processes such as the Z boson
[email protected] T
‡[email protected] decay to neutrinos and tt(cid:1) production followed by semi-
[email protected] leptonicdecays of the top.
1550-7998=2008=78(7)=075008(45) 075008-1 (cid:1) 2008 The American Physical Society
HUBISZ, LYKKEN, PIERINI, AND SPIROPULU PHYSICAL REVIEW D 78, 075008 (2008)
In many theoretical frameworks with dark matter can- in multijet final states will be in development during the
didates,thereareheavystronglyinteractingparticleswith 100 pb(cid:1)1era.Inmanysmalldatasamplespeaksandedges
the same conserved charge or parity that makes the dark ininvariantmassdistributionsmaynotbevisible,andmost
matterparticlestable.Thesecoloredparticleswillbepair- observables related to detailed features of the events will
produced at the LHC with cross sections roughly in the be rate limited. The observables that are available to
range0.1to100pb.Theirsubsequentdecayswillproduce discriminate the look-alikes in thevery early running will
standard model particles along with a pair of undetected be strongly correlated by physics and systematics making
dark matter particles. Thus the generic experimental sig- it imprudent tocombine them ina multivariate analysis.
nature is both simple and inclusive: large Emiss accompa-
T
niedbymultipleenergeticjets.Adetailedstrategyforearly D.Is it SUSY?
discoverywiththeinclusiveEmiss signaturewaspresented
T Byfocusingonthediscriminationoflook-alikes,weare
intheCMSPhysicsTechnicalDesignReport[10–12]and
pursuingastrategyofsimplebinarychoices:ismodelAa
studied with full simulation of the CMS detector. After a
significantly better explanation of the discovery data set
series of cleanup and analysis cuts on a simulated Emiss
T than model B? Each answer carries with it a few bits of
trigger sample targeting the reduction of the instrumental
importantfundamentalinformationaboutthenewphysics
andphysicsbackgrounds,thesignalefficiencyremainedas
processresponsibleformissingenergy.Obviouslywewill
high as 25%. These results indicate that, for signal cross
needtomakemanydistinctlook-alikecomparisonsbefore
sections as low as a few pb, an Emiss discovery could be
T we can hope to build up a clear picture from these indi-
madewiththefirst100 pb(cid:1)1 ofunderstoodLHCdata.1In vidual bits.
ourstudyweassumeasthestartingpointthatagreaterthan Considerhowthisstrategymightplayoutforanswering
5(cid:1) excess of events will be seen in a 14 TeV LHC data thebasicquestion‘‘isitSUSY?’’Itmaynotbepossibleto
sample of 100 pb(cid:1)1 with an inclusive missing energy answerthisquestionconclusivelyduringthe100 pb(cid:1)1era.
analysis.Forinvariabilityandcomparabilityweeffectively Ourstrategywillconsistofaskingaseriesofmoremodest
adoptthefullanalysispathandrequirementsusedin[10]. questions,someofthemoftheform:‘‘doesSUSYmodelA
giveasignificantlybetterexplanationofthediscoverydata
C. Look-alikes at the moment of discovery set than non-SUSY model B?’’ None of these individual
bitsofinformationbyitselfisequivalenttoanswering‘‘is
At the moment of discovery a large number of theory
itSUSY?’’However,wedemonstratethatwecanbuildup
models will be immediately ruled out because, within
apicturefromthedatathatconnectsbacktofeaturesofthe
conservative errors, they give the wrong excess. However
underlyingtheory.
a large number of models will remain as missing energy
Furthermore, we demonstrate a concrete method to ob-
look-alikes,definedasmodelsthatpredictthesameinclu-
tain indirect information about the spin of the new parti-
sive missing energy excess, within some tolerance, in the
cles. We establish how to discriminate between a non-
same analysis in the same detector, for a given integrated
SUSY model and its SUSY look-alikes. Even though we
luminosity. The immediate challenge is then to begin
cannot measure the spins of the exotic particles directly,
discriminating the look-alikes.
spin has significant effects on production cross sections,
The look-alike problem was studied in [9] as it might
kinematic distributions, and signal efficiencies. We are
apply to a later mature phase of the LHC experiments.
thus able to discriminate SUSY from non-SUSY using
Evenrestrictedtothesliceoftheoryspacepopulatedbya
combinationsofobservablesthattracebacktodifferences
partialscanoftheminimalsupersymmetricstandardmodel
inspin.Ourstudyshowsthatinfavorablecasesthiscanbe
(MSSM),ignoringSMbackgroundsandsystematicerrors, accomplished with data sets as small as 100 pb(cid:1)1.
andapplyinganuncorrelated(cid:2)2-likestatisticalanalysisto
1808 correlated observables, this study found that a large
E. Outline
numberoflook-alikesremainedunresolvedinasimulation
equivalentto10 fb(cid:1)1.Amorerecentanalysis[13]attempts In Sec. II we review in detail the missing energy dis-
to resolve these look-alikes in a simulation of a future coverypath,includingtheexperimentalissuesandsystem-
linear collider. atics that limit our ability to fully reconstruct events from
At the moment of an early discovery the look-alike thediscoverydataset.Weexplainhowthemissingenergy
problem will be qualitatively different. The data samples signalsaresimulated,andtheuncertaintiesassociatedwith
will be much smaller, with a limited palette of robust these simulations. In Sec. III we discuss the problem of
reconstructedphysicsobjects.Forexample,(cid:3)orbtagging populating the parts of the theory space relevant to a
particular missing energy discovery. In Sec. IV we intro-
duce two groups of look-alike models relative to two
1The first 100 pb(cid:1)1 of understood LHC data will not be the
first100 pb(cid:1)1ofdatawrittentotape.The10TeVdatacollected different missing energy signals. For models differing
in the early running will be used for calibrations and under- only by spins, we discuss how cross sections, kinematic
standing of benchmark standard model processes. distributions, and efficiencies can be used to distinguish
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them,drawingfromformulasdevelopedinAppendixC.In (i) TheEmissisentirelyfromneutrinos.Thiscouldarise
T
Sec.Vwedefinealloftherobustobservablesthatweuseto from the direct decay of new heavy particles to
discriminate among the look-alikes, and in Sec. VI we neutrinos, or decays of new heavy particles to top,
describethelook-alikeanalysisitselfandhowwecompute W’s, Z’s, or (cid:3)’s. One appropriate discovery strategy
the significance of the discriminations. Sections VII and forthiscaseistolookforanomaliesintheenergetic
VIIIgiveasummaryofourresults,withdetailsrelegatedto tails of data sets withreconstructed top,W’s or Z’s.
furtherappendices. FinallySec. IX describesthe stepswe (ii) TheEmissoriginatesfromasingleweaklyinteracting
T
are following to improve this analysis for use with real exotic particle in the final state. An example of this
data. possibility is graviton production in models with
large extra dimensions [20]. If strong production
II.DISCOVERYANALYSISFORMISSINGENERGY
occurs, the signal will consist predominately of
Missing energy hadron collider data has been used monojets and large Emiss. Successful analyses for
T
previouslyforsuccessfulmeasurementsofstandardmodel this case were carried out at the Tevatron [21,22].
processes with energetic neutrinos; these include the Z0 Other signals that fit this case arise from unparticle
boson invisible decay rates, the top quark cross section, models [23] and from models with s-channel reso-
searchesfortheHiggsboson[14],andapreciseextraction nances that haveinvisible decays.
oftheW massfromthereconstructionoftheW transverse (iii) The Emiss originates from many weakly interacting
T
mass [15]. Pioneering searches for new phenomena in exoticparticles.Thiscanbethecaseinhiddenvalley
missing energy data sets at the Tevatron [16–19] led to models [24], where the weakly interacting exotics
thedevelopmentandunderstandingofthebasictechniques are light pions of the hidden sector. This case is
that will be used inmissing energy searches at the LHC. experimentally challenging.
Inanidealdetector,withhermetic4(cid:4)solidanglecover- (iv) The Emiss originates from two weakly interacting
T
ageandexcellentcalorimeterresolution,themeasurement exotic particles in the final state. This is the case
of missing energy is the measurement of the neutrino forsupersymmetrymodels withconserved R parity,
energy and the energy of any other neutral weakly inter- wheretheweaklyinteractingparticlesareneutralino
actingparticles.Inarealdetectoritisalsoameasurement lightest superpartners (LSPs) . It also applies for
oftheenergythatescapesdetectionduetouninstrumented more generic models with weakly interacting mas-
regions and other detector effects such as imperfect calo- sive particle (WIMP)dark matter candidates.
rimeter response. Muons are sources of missing energy Wefocusonadiscoveryanalysisdevelopedforthelast
since a muon typically deposits only of order a few GeV case. Thus we are interested in signal events with two
of its total energy in the calorimeters.2 QCD jets produce heavy WIMPs in the final state. For early discovery at
real Emiss from semileptonic decays of heavy flavor, and the LHC, the signal events should have strong production
T
fake Emiss from detector-induced mismeasurements. Thus crosssections;wewillassumethateachWIMParisesfrom
T
theEmiss distributionofapureQCDmultijetsamplehasa the decay of a strongly interacting heavy parent particle.
T
long tail related to non-Gaussian tails in the detector The most generic signature is therefore large Emiss in
T
response. This gives rise to an important background to association with at least two high E jets. There will be
T
missingenergysearchesthatisdifficulttoestimatepriorto additional jets if the WIMP is not produced in a 2-body
data. At the Tevatron it has been shown that this back- decay of the parent particle. Furthermore, there is a sig-
groundcanbebroughtundercontrolbyexploitingthefact nificantprobabilityofanextrajetfromQCDradiation,due
that the fake Emiss from jet mismeasurements is highly tothelargephasespace.Thusitisonlyslightlylessgeneric
T
correlated with the azimuthal directions of the leading todesignaninclusiveanalysisforlargeEmissinassociation
T
jets [16]. withthreeormoreenergeticjets.Wewillrefertothisasthe
ThereareotherimportantsourcesoffakeEmissathadron inclusive missing energy signature.3
T
colliders, including beam halo induced Emiss, cosmic ray In the basic 2!2 hard scattering, the heavy parent
T
muons,noiseinthedataacquisitionsystem,andmisrecon- particles of the signal will be produced back-to-back in
struction of the primary vertex. Eliminating these sources the partonic subprocess center-of-mass frame; typically
requiresunbiasedfiltersbasedoncleandefinitionsofevent they will have p roughly comparable to their mass m .
T p
quality. TheWIMPsofmassm resultingfromtheparentparticle
dm
To design a missing energy analysis, we need to have decays will fail to deposit energy (cid:2)m in the calorim-
dm
some idea of the source of the EmTiss in the signal. The eters; if the WIMPS have fairly large pT, a significant
possibilities include the following:
3The requirement of a third energetic jet greatly reduces the
2The energy loss of muons is mostly due to ionization up to size and complexity of the standard model backgrounds. Thus
muonenergiesof100GeV.Above100GeVbremsstrahlungand whilematureLHCanalyseswillexplorethefullyinclusiveEmiss
T
nuclear losses can cause a single ‘‘catastrophic’’ energy loss signature,weassumeherethatanearlydiscoverywillbebased
comparable to the total muon energy. on a multijetþEmiss data sample.
T
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HUBISZ, LYKKEN, PIERINI, AND SPIROPULU PHYSICAL REVIEW D 78, 075008 (2008)
fractionofthisenergycontributestotheEmiss.Thuseither events where the Emiss is too closely correlated with the
T T
large m or large m leads to large Emiss. Note the azimuthal directions of the jets. To reduce the large back-
p dm T
azimuthal directions of the WIMPS are anticorrelated, a groundfromWð!‘(cid:5)Þþjets,Zð!‘‘Þþjets,andtt(cid:1)pro-
feature inherited from their parents, so the magnitude of duction an indirect lepton veto (ILV) scheme is designed
the total Emiss tends to be less than the magnitude of the thatusesthetrackerandthecalorimeters.TheILVretainsa
T
largest single contribution. largesignal efficiencywhile achievingafactor of2rejec-
AttheLHC,themostimportantstandardmodelsources tion of the remaining W and tt(cid:1)backgrounds. The veto is
of large realEmiss will be tt(cid:1),single top,W and Zplusjets indirectbecausewedonotidentifyleptons-insteadevents
T
associated production, dibosons, and heavy flavor decays. are rejected if the electromagnetic fraction of one of the
Most of these processes produce a hard lepton in associa- twoleadingjetsistoolarge,orifthehighestpTtrackofthe
tionwiththeEmiss fromanenergeticneutrino.Theexcep- event is isolated. The signals we are interested in are
T
tionisZ!(cid:5)(cid:5)(cid:1).Evenwithaperfectdetector,Z!(cid:5)(cid:5)(cid:1) plus characterized by highly energetic jets while leptons in
jets is an irreducible physics background. the signal originate from cascade decays of the parents or
semileptonicBdecaysinthejets;thusevenwhenasignal
event has leptonsit is relatively unlikelytobe rejectedby
A. Analysis path
theILV.Forthemodelsinourstudy,approximately85%of
In the real data this search will be performed starting all signal events and 70% of signal events with muons or
from a primary data set that includes requirements of taus pass the ILV cut.
missing energy, jets, and general calorimetric activity at ThefinalselectionsrequirethattheleadingjethasE >
T
thetriggerpath;thetriggerefficiencyshouldbemeasured 180 GeV, and that the second jet has E >110 GeV. We
T
in other data samples. also require H >500 GeV,where
T
For the offline analysis, we will adopt the inclusive
missing energy benchmark analysis studied with the full X4
detectorsimulationfortheCMSPhysicsTechnicalDesign HT ¼ EiT þEmTiss; (1)
Report [10,11]. i¼2
The first phase is a preselection based on the event
wheretheE issummedoverthesecond,thirdandfourth
quality. The purpose of this primary cleanup is to discard T
(ifpresent) leadingjets.These cuts selectforhighlyener-
eventswithfakeEmissfromsourcessuchasbeamhalo,data
T getic events, greatly favoring events with new heavy par-
acquisition noise, and cosmic ray muons. To eliminate
ticles over the standard model backgrounds.
these types of backgrounds the benchmark analysis uses
Table I summarizes the benchmark analysis path. The
jet variables, averages them over the event to define cor-
table lists the cumulative efficiencies after each selection
responding event variables, and uses theseto discriminate
real Emissþmultijet events from spurious backgrounds.
T
TABLE I. Cumulative selection efficiency after each require-
The event electromagnetic fraction is defined to be the
mentintheEmissþmultijetsanalysispathforalowmassSUSY
E weighted jet electromagnetic fraction. We define an T
T signal and the major standard model backgrounds (EWK refers
event charged fraction as the event averagePof the jet to W=Z,WW=ZZ=ZW), see [10,11]).
charged fraction (defined as the ratio of the p of the
T
tracks associated with a jet over the total calorimetric jet Cut/sample Signal tt(cid:1) Zð!(cid:5)(cid:5)(cid:1)Þþjets EWKþjets
E ).Thepreselectionalsohasaqualityrequirementforthe
T All (%) 100 100 100 100
reconstructed primary vertex.
Trigger 92 40 99 57
Events that are accepted by the preselection require- Emiss>200 GeV 54 0.57 54 0.9
T
ments proceed through the analysis path if they have Primary vertex 53.8 0.56 53 0.9
missing transverse energy EmTiss (cid:2)200 GeV and at least Nj (cid:2)3 39 0.36 4 0.1
threejetswithET (cid:2)30 GeVwithinpseudorapidityj(cid:6)j< j(cid:6)jd1j(cid:2)1:7 34 0.30 3 0.07
3. These requirements directly define the missing energy EEMF(cid:2)0:175 34 0.30 3 0.07
signalsignature.Inadditiontheleadingjetisrequiredtobe ECHF(cid:2)0:1 33.5 0.29 3 0.06
within the central tracker fiducial volume i.e. j(cid:6)j<1:7. QCD angular 26 0.17 2.5 0.04
Everywhere in this paper ‘‘jets’’ mean uncorrected (raw) Isoleadtrk ¼0 23 0.09 2.3 0.02
jets with E >30 GeV and j(cid:6)j<3 as measured in the EMFðj1Þ,
T
calorimeters; the jet reconstruction is with a simple iter- EMFðj2Þ(cid:2)0:9 22 0.086 2.2 0.02
ative cone algorithm with a 0.5 cone size in the (cid:6)(cid:1)(cid:7) ET;1>180 GeV,
E >110 GeV 14 0.015 0.5 0.003
space. Themissingenergyisuncorrectedforthepresence T;2
H >500 GeV 13 0.01 0.4 0.002
of muons inthe event. T
The rest of the analysis path is designed based on events remaining per 1000 pb(cid:1)1
elimination of the major backgrounds. The QCD back-
6319 54 48 33
ground from mismeasured jets is reduced by rejecting
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1 1
0.8 0.8
y y
c c
n n
cie 0.6 cie 0.6
effi effi
r r
e e
g g
rig 0.4 rig 0.4
T T
0.2 0.2
0 0
0 50 100 150 200 250 300 300 310 320 330 340 350 360 370 380 390 400
EmTiss (GeV) ET (GeV)
FIG. 1 (color online). The Emiss trigger efficiency. FIG. 2 (color online). The DiJet trigger efficiency.
T
for a benchmark signal model and the standard model (ii) TheDiJettriggerrequirestwoveryhighET jets.Itis
backgrounds.ThesignalmodelistheCMSsupersymmetry 50%efficient for uncorrected jet ET >340 GeV, as
benchmark model LM1, which has a gluino with mass seen inFig. 2.
611 GeVand squarks with masses around 560 GeV. The (iii) The TriJet trigger requires three high ET jets. It is
lastlineofthetableshowstheexpectednumberofevents 50% efficient foruncorrected jetET >210 GeV, as
that survive the selection in a data set corresponding to seen in Fig.3.
1000 pb(cid:1)1 of integrated luminosity. For the QCD back- (iv) TheMuon20triggerrequiresanenergeticmuonthat
ground and the single top background, which are not is not necessarily isolated. The trigger is 88% effi-
shown in the table, the estimated number of remaining cient for muons with pT ¼20 GeV=c, asymptoting
events is 107 and 3, respectively. Thus the total estimated to95% as seen in Fig.4.
standard model background after all selections is 245 After applying the selection requirements, these four
events per1000 pb(cid:1)1. triggers define four potential discovery data sets. In our
simulation the DiJet, TriJet, and Muon20 data sets, after
the inclusive missing energy analysis path is applied, are
B. Triggers and ‘‘boxes’’
all subsets of the MET sample, apart from one or two
Having established a benchmark analysis path, we also events per 1000 pb(cid:1)1.5 Thus the METis the largest, most
needtodefinebenchmarkdatasamples.WiththerealLHC inclusivesample.Weperformonecompleteanalysisbased
data these will correspond to data streams and data paths on the MET trigger. The other three triggers are then
from various triggers. For the inclusive missing energy treated as defining three more boxes, i.e. experimentally
signature relevant triggers are the EmTiss and jet triggers. well-defined subsets of the MET discovery data set. The
A single lepton trigger is also of interest, since many simplest physics observables are the counts of events in
modelsproduceenergeticleptonsinassociationwithlarge each box.
Emiss.Forourstudywehavechosensimplebutreasonable
T
[25,26]parametrizationsofthetriggerefficienciesdefining
C. Backgrounds and systematics
our four benchmark triggers4:
(i) The missing transverse energy (MET) trigger is a In the CMS study the total number of standard model
pure inclusive Emiss trigger. It is 50% efficient for backgroundeventsremainingafterallselectionsis245per
EmTiss>80 GeV,Tas seen inFig. 1. 1000 pb(cid:1)1 for an EmTiss trigger sample. The error on this
estimateisdominatedby(i)theuncertaintyinhowwellthe
detectorsimulationsoftwaresimulatestheresponseofthe
actual CMS detector, and (ii) the uncertainty on how well
4Thesearemade-uptriggersforthepurposesofourstudy.The the standard model event generators emulate QCD, top
guidance on our parametrizations is from the published trigger
andphysicsreportsoftheCMSexperiment.Weexpectthatthe
trigger tables of the LHC experiments will include correspond- 5A perfectly designed trigger table will give rise to overlaps
ing trigger paths, richer and better in terms of the physics amongdatasetsfromdifferenttriggerpathsduetobothphysics
capture. and slow/nonsharp trigger efficiency turn-ons (resolution).
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HUBISZ, LYKKEN, PIERINI, AND SPIROPULU PHYSICAL REVIEW D 78, 075008 (2008)
1 uncertainties will decrease over time, as the detectors are
better understood, calibration studies are performed, and
standardmodelphysicsisanalyzedwiththeLHCdata.For
0.8 ourstudywehaveassumedthat,atthemomentofdiscov-
ery, the dominant systematic errors in the full discovery
y
c data set will come from three sources:
n
cie 0.6 (i) Luminosity uncertainty: it affects the counting of
effi events. This systematic uncertainty is process
er independent.
g
rig 0.4 (ii) Detector simulation uncertainty: it mainly affects
T
calorimetry-relatedvariablesinourstudy,inparticu-
lar,jetcountingandthemissingenergy.Thissystem-
0.2 atic is partially process dependent.
(iii) QCD uncertainty: it includes the uncertainties from
thepartondistributionfunctions,higherordermatrix
0
elements, and large logarithms. This uncertainty af-
100 150 200 250 300 350
E (GeV) fects event counting, jet counting and the shapes of
T
kinematic distributions. It is partially process
FIG. 3 (color online). The TriJet trigger efficiency. dependent.
Notethat,sinceweuseuncorrectedjets,wedonothave
production,andW=Zplusjetsproduction.Detailedstudies asystematicfromthejetenergyscale.Thisistradedfora
of the real LHC data will be required in order to produce portionofthedetectorsimulationuncertainty,i.e.howwell
reliable estimates of these uncertainties. wecanmapsignaleventsintouncorrectedjetsaswouldbe
Prior to datawe assign conservative error bars on these measured inthe real detector.
background projections. We have checked that 100 pb(cid:1)1
of data in the MET trigger sample is sufficient for a 5(cid:1) D. Simulation of the signals
discovery for the eight models in our study, even if we A realistic study of look-alikes requires full detector
triple the backgrounds quoted above and include a 15% simulation. For the initial phase of this work a generator-
overall systematic error. The look-alike analysis will be level analysis is attractive, being computationally less in-
degraded, however, in the event that the standard model tensiveandprovidingaclearlinkbetweenobservablesand
backgrounds turn out to be much larger than current the underlyingtheory models.6
estimates. In a generator-level analysis, jets are reconstructed by
Prior to data, it is also difficult to make a reliable applying a standard algorithm to particles rather than to
estimate of the main systematic uncertainties that will calorimeter towers. This obviously does not capture the
affect the inclusive missing energy analysis. Systematic effectsofarealisticcalorimeterresponse,calorimeterseg-
mentation,andenergylossesduetomaterialinthetracker
1 as well as magnetic field effects.
A compromise between the full simulation and a
generator-level analysis is a parameterized detector simu-
0.8 lation. For the LHC the publicly available software pack-
ages include AcerDET [27] and PGS [28]. In such a
y simulation, electrons, muons, and photons can be recon-
c
en 0.6 structed using parameterized efficiencies and resolutions
r effici bmausletdipounrpaobssetrdaecttebcutotres.duJectasteadrerurleecso-onfs-ttrhuucmtedbfinoramvoirdteuranl
e
gg 0.4 calorimeter, from particle energies deposited in cells that
Tri roughly mimic the segmentation of a real calorimeter.
Calorimeter response is approximated by performing a
Gaussian smearing on these energy deposits. The Emiss is
0.2 T
0
0 10 20 30 40 50 60 6ThefullGEANT4-basedsimulationistooslowtoadequately
p (GeV/c)
sample the entire theory space. Having completed the first
T
exploratory phase of this work, we are repeating the analysis
FIG. 4 (color online). The Muon20trigger efficiency. tovalidate these results with the full experimentalsimulation.
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reconstructed from the smeared energies in these virtual TABLE II. Comparisonofcut-by-cutselectionefficienciesfor
towers. ourEmTiss analysisappliedtotheSUSYbenchmarkmodelLM1.
We performed a preliminary study by comparing PGS ‘‘Full’’referstothefullsimulationstudy[10,11];‘‘Fast’’iswhat
we obtain from our parameterized fast simulation.
resultstothefullsimulationresultsreportedfortheSUSY
benchmark model LM1 [10,11]. We found that PGS jets Cut/software Full Fast
arenotagoodapproximationofuncorrectedjetsinthefull
Trigger and Emiss>200 GeV 53.9% 54.5%
simulation, even for the most basic properties such as the T
N (cid:2)3 72.1% 71.6%
ET spectrum. Varying the parameters and adding simple j(cid:6)jj1j(cid:2)1:7 88.1% 90.0%
improvements,suchastakingintoaccountthe4Teslafield d
QCD angular 75.6% 77.6%
inthebarrel,didnotchangethisconclusion.PGSjetshave Isoleadtrk ¼0 85.3% 85.5%
a behavior, not surprisingly, that is intermediate between E >180 GeV, E >110 GeV 63.0% 63.0%
T;1 T;2
generator-leveljets and uncorrected full simulation jets. H >500 GeV 92.8% 93.9%
T
We developed a modified simulation called PGSCMS Total efficiency 12.9% 13.8%
with the geometry and approximate magnetic field of the
CMS detector. The PGS Gaussian smearing and uninstru-
mentedeffectsinthecalorimetersareturnedoff.Electrons, electromagnetic fraction cuts of the ILV, because they are
muons, and photons are extracted at generator level, and nearly 100% efficient for the signal.
PGS tau reconstruction is not used. Track information is The resulting performance of our parameterized fast
extracted as in the standard PGS. The calorimeter output simulationfortheSUSYbenchmarkmodelLM1isshown
improves on a generator-level analysis in that we include inTableII.Theagreementwiththefullsimulationstudyis
approximations to the effects of segmentation and the very good. The largest single cut discrepancy is 2%; this
4 Tesla field, as well as an (cid:6) correction derived from the occurs for the QCD angular cuts, reflecting the expected
z value of the primary vertex. We parameterized the de- factthatourfastsimulationdoesnotaccuratelyreproduce
tector response in a limited set of look-up tables as a jet mismeasurement effects. Since the final efficiencies
function of thegenerator-level quantities. agreetowithin7%,it is plausible thatlook-alikes defined
Attheanalysislevelweapplyparameterizedcorrections inourfastsimulationstudywillremainlook-alikesinour
and reconstruction efficiencies inspired by the published upcomingfull simulation study.
CMSdetectorperformance[29].Forthejets,weapplyan It is important to note that this fast simulation does not
E and (cid:6) dependent rescalingof their E ,tunedtorepro- reproduce the standard model background efficiencies
T T
duce the full simulation LM1 results in [10,11]. This shown in Table I. In fact the discrepancies in the total
rescaling makes the jets softer (i.e. takes into account the efficiencies can approach an order of magnitude. This is
detector reconstruction): a 50 GeV generator-level jet be- to be expected. We are cutting very hard on the standard
comes an approximately 30 GeV raw jet inour analysis. model events, thus the events that pass are very atypical.
The Emiss reconstructed from PGSCMS is essentially Thisisincontrasttothesignalevents,wherethefractions
T
identical, modulo small calorimeter segmentation effects, that pass are still fairly generic, and their ET and EmTiss
to a a generator-level analysis, i.e. our Emiss is virtually spectra near the cuts are less steeply falling than those of
T
indistinguishable from the Monte Carlo truth Emiss ob- the background. Since SM backgrounds cannot be esti-
tained from minus the vector sum of the E of neTutrinos, matedfromaPGSlevelanalysis,wetakeourbackgrounds
T
muons,andtheotherweaklyinteractingparticles(suchas from the state-of-the-art analysis in [10]; this approach
theLSP).WedidnotattempttorescaletheEmiss;thisisa only works because we have also matched the analysis
T
complicated task since Emiss is a vector and in general path used in [10].
T
The full software chains we use in our study are
energylosses,calorimeterresponseandmismeasurements
tend to decrease the real large Emiss tails while increasing summarized in Table III. All of the simulated data sets
T
the Emiss tails in the distribution of nonreal Emiss events. includeanaverageof5pileupeventsaddedtoeachsignal
T T event, corresponding to low luminosity LHC running
Instead of attempting to rescale the Emiss event by event,
T ((cid:3)1033 cm(cid:1)2s(cid:1)1).
we raised the Emiss cut in our benchmark analysis to
T
220 GeV.7
III. POPULATING THE THEORY SPACE
Becauseofthelimitationsofourfastsimulation,wealso
simplifiedpartsofthebenchmarkanalysis.Thefirstphase InSec.IIwegaveapartialclassificationofBSMmodels
primary cleanup is dropped since it is related to suppres- according to how many new weakly interacting particles
sionofspuriousprocessesthatwedonotsimulate,anditis appearinatypicalfinalstate.OurbenchmarkEmiss analy-
T
nearly 100% efficient for the signal. We also drop the jet sisisoptimizedforthecaseoftwoheavyweaklyinteract-
ing particles per event, as applies to SUSY models with
7In a realistic full simulation study with the first jet data in conserved R parity, little Higgs models with conserved T
hand, our Emiss analysis will avoid such compromises. parity, and universal extra dimensions models with con-
T
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TABLE III. Summary of software chains used inthis study. The littleHiggs spectrumis basedon [30].PGSCMS is avariation of
PGSv4 [28].
Software/models Group 1 models Group 2 models
Spectrum generator Isajetv7:69 [31] or SUSY(cid:1)HITv1:1 [32] private little Higgs or SuSpectv2:34 [33]
Matrixelement calculator Pythiav6:4 [34] MadGraphv4 [35]
Eventgenerator Pythiav6:4 MadEventv4[36] with BRIDGE [37]
Showering and hadronization Pythiav6:4 Pythiav6:4
Detector simulation PGSCMSv1:2:5 plus parameterized corrections PGSCMSv1:2:5 plusparameterized corrections
served Kaluza-Klein (KK) parity. This study is a first one matrix element calculator and event generation
attemptatconstructinggroupsoflook-alikemodelsdrawn scheme, and a standardized interface via the SUSY Les
fromthisratherlargefractionoftheBSMtheoryspaceand Houches Accord [40]. There are still a few bugs in this
developingstrategiestodiscriminatethemshortlyafteran grandedifice,buttheexistingfunctionalitycombinedwith
initial discovery. theabilitytoperformmultiplecross-checksputsuswithin
One caveat is that models from other corners of the sightof wherewe need to bewhen the data arrives.
theory space may also be look-alikes of the ones consid-
ered here. For example, models with strong production of
B. Little Higgs
heavy particles that decay to boosted top quarks can pro-
duce higher E jets and larger Emiss from neutrinos than LittleHiggsmodelsareapromisingalternativetoweak
T T
scale supersymmetry [41–45]. In little Higgs models, the
does standard model top production.Such look-alike pos-
Higgs is an approximate Goldstone boson, with global
sibilitiesalsorequirestudy,buttheyarenotamajorworry
symmetries protecting its mass (which originates from a
since our results show that we have some ability to dis-
quantum level breaking of these symmetries) from large
criminateheavyWIMPSfromneutrinoseveninsmalldata
radiativecorrections.ManyoftheseLHmodelsrequirean
sets.
approximate T parity discrete symmetry to reconcile LH
A. SUSY withelectroweakprecisiondata.Thissymmetryissimilar
to R parity in SUSY models. The new LH particles that
In a large class of supersymmetry models with con-
would be produced at the LHC would be odd under this
served R parity, not necessarily restricted to the MSSM,
symmetry, enforcing the stability of the lightest particle
the LSP is either the lightest neutralino or a right-handed
sneutrino.8 that is odd under T parity. This new particle is weakly
interacting and would manifest itself as missing energy at
Inaddition,iftheNLSPisaneutralinoorsneutrinoand
the LSP is a gravitino, the Emiss signature is the same. the LHC.9
T
JustasinSUSY,newcoloredparticlesarethedominant
Models based on gravity-mediated, gauge-mediated, or
production modes. These particles subsequently generate
anomaly-mediated SUSY breaking all provide many can-
highmultiplicityfinalstatesthroughdecaychainsthatend
didate models.
Because this relevant portion of SUSY theory space is withthelightestToddparticle.InLHmodels,thestrongly
alreadysovast,thereisatemptationtoreducethescopeof coupled particles are T odd quarks, analogous to the
the LHC inverse problem by making explicit or implicit squarks of SUSY. The weakly coupled analogues of the
theoretical assumptions. To take an extreme, one could gauginosare T odd spin onevector bosons. In the models
approach an early LHC discovery in the Emiss channel consideredtodate,thereisnoanalogofthegluino:thisis
T
having already made the assumptions that (i) the signal is animportantconsiderationinconstructingsupersymmetric
SUSY, (ii) it has a minimal Higgs sector (MSSM), (iii) it look-alikes of LH models.
has gravity-mediated SUSY breaking (SUGRA), (iv) the Inthisstudy,weworkwithaminimalimplementationof
breaking is minimal (mSUGRA), and (v) 100% of dark a little Higgs model with T parity that is known as the
matter is thermal relic LSPs with an abundance given by littlestHiggsmodelwithTparity.Thismodelisbasedona
extrapolating standard cosmology back to the decoupling SUð5Þ=SOð5Þ pattern of global symmetry breaking. Each
epoch. We do not want to make any such assumptions; SMparticleexceptthegluonhasanassociatedLHpartner
rather we want to test theoretical hypotheses in the LHC odd under T parity. There is also an extra pair of top
discoverydata set combined with other measurements. partners, one T odd and the other T even, as well as
For SUSY we have the benefit of more than one spec- singlets.ThelightestT oddparticleinthismodelwelabel
trumcalculatorthatcanhandlegeneralmodels,morethan A . It is a heavy gauge boson that is an admixture of a
H
8Recentanalyses[38,39]havearguedforthephenomenologi- 9Thissymmetrymaybeinexact,orviolatedbyanomalies[46].
cal viability of sneutrino dark matter. Such possibilities are model dependent [47,48].
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heavy copy of the hypercharge gauge boson and a heavy TABLE IV. InputparametersforthemSUGRAmodelsLM2p,
W3 boson. LM5, and LM8. The notation conforms to [31]. The mass
parameters and trilinear A parameter have units of GeV.
Foreventgeneration,weuseaprivateimplementationof 0
thelittlestHiggsmodelwithinMadGraph.Thereisaneed
LM2p LM5 LM8
to generalize this to awider class of models.
m 185 230 500
0
m 360 360 300
1=2
C. Universal extra dimensions A 0 0 (cid:1)300
0
Universal extra dimensions models are based on orbi- tan(cid:8) 35 10 10
folds of one or two TeV(cid:1)1 size extra spatial dimensions signð(cid:9)Þ þ þ þ
[49–56]. The five-dimensional version of universal extra
dimensions(UED)isthesimplest.AtthefirstlevelofKK
energydiscoveryattheLHCwillhelpustestwhetherthese
excitations, each standard model boson has an associated
assumptions have any validity. For example, model LM8
partnerparticle,andeachstandardmodelfermionhastwo
producesarelicdensityanorderofmagnitudelargerthan
associated partner particles (i.e. a vectorlike pair). These
KKpartnersareoddunderaKKparity,theremnantofthe the WMAP upper bound; thus discriminating LM8 as a
broken translational invariance along the fifth dimension. morelikelyexplanationofanearlymissingenergydiscov-
This parity is assumed to be an exact symmetry. After ery would call into question [58,59] assumptions (i) and
taking into account mass splittings due to standard model (iii), or could be a hint that the lightest neutralino is not
radiative corrections, one finds that the lightest KK odd absolutely stable.
partner is naturally the weakly interacting partner of the LM2p,LM5,andLM8areminimalsupergravitymodels
hyperchargegaugeboson.Awidevarietyofspectraforthe [60–62]. They are specified by the usual high scale
KKoddpartnerscanbeobtainedbyintroducingadditional mSUGRAinputparametersasshowninTableIV;because
interactions that are localized at the orbifold fixed points; the resulting superpartner spectra depend strongly on re-
these choices distinguish generic UED from the original normalization group equations (RGE) running from the
minimal model of [49]. These models resemble SUSY. high scale, a complete specification of the models also
Apubliceventgenerationcodebasedonamodification requiresfixingthetopquarkmassandtheparticularspec-
of Pythia is available for generic 5-dimensional UED trum generator program used. We have used m ¼
top
models [57]. There is a need to generalize this to a wider 175 GeV and the ISAJETv7:69 generator [31], in order
classofmodels,e.g.6-dimensionalUED.Inourstudywe tomaintaincompatibilitywiththeCMSPhysicsTDR[10].
havenotusedanyUEDexamples,butwewillincludethem ModelsLM5andLM8arethenidenticaltothemSUGRA
in the future. benchmarkmodelsoftheCMSPhysicsTDR,whileLM2p
isalmostidenticaltobenchmarkmodelLM2;LM2phasa
slightly larger value of m (360 versus 350 GeV) than
IV.DESCRIPTION OF THE MODELS 1=2
LM2, which makes it more of a look-alike of the other
A. Group 1 Group 1models.
The five look-alike models of Group 1 are all MSSM The Group 1 models CS4d and CS6 are not minimal
models. Two of them (LM5 and LM8) are CMS SUSY supergravity; they are more general high scale MSSM
benchmarkmodels,whileanother(LM2p)isaslightvaria- models based on the compressed supersymmetry idea of
tionofaCMSbenchmark.Itisasoberingcoincidencethat Martin[63,64].Thehighscaleinputparametersareshown
thesearelook-alikesoftheEmissanalysis,sincethebench-
T
marks were developed by CMS to cover different experi- TABLE V. Input parameters for the MSSM models CS4dand
mental signatures, not produce look-alikes. To round out CS6.Thenotationconformsto[32,33].Themassparametersand
Group 1 we found two other MSSM look-alikes whose trilinear A parameters haveunits of GeV.
spectra and decay chains are as different from each other
CS4d CS6
and from the three CMS benchmarks as we could make
them. M1 620 400
Themodelsareconsistentwithallcurrentexperimental M2 930 600
M 310 200
constraints, but do not all give the ‘‘correct’’relic density 3
A , A, A , A , A , A (cid:1)400 (cid:1)300
ofdarkmatter.Anycomparisonofrelicdensitiestotheso- (cid:3) t b e u d
M , M , M 340 2000
called WMAP constraints assumes at least three facts not QL tR bR
M , M , M 340 2000
yet in evidence: (i) that dark matter is a thermal relic, qu uR dR
M , M , M , M 340 340
(ii)thatthereisonlyonesignificantspeciesofdarkmatter, (cid:3)L (cid:3)R eL eR
M2 , M2 115600 115600
and (iii) that cosmological evolution was entirely hu hd
tan(cid:8) 10 10
radiation-dominated from the time of dark matter decou-
signð(cid:9)Þ þ þ
plinguntilthetimeofbigbangnucleosynthesis.Amissing
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HUBISZ, LYKKEN, PIERINI, AND SPIROPULU PHYSICAL REVIEW D 78, 075008 (2008)
1000
LM2p LM5 LM8 CS4d CS6 ThesuperpartnermassspectraoftheGroup1modelsare
~d ~u displayed in Fig. 5. One notes immediately that all of the
L L
900 mSUGRAmodelsaremoresimilartoeachotherthanthey
800 ~d~ug~RL ~~udRL ~d~ug~RL ~d~uLR ~u~dg~RL ~d~uRL ~g~ ~u aCthrSea6tt;odtoheiintshosethrogowofsbthteheyeomlniodmreimtagSteiUonGnersRaolAfM.thSAeSsuMsthuemailroSdnUealSmsYeCaSinm4adplylaisenesds,
d R
700 R thecompressedSUSYmodelsCS4dandCS6haveacom-
pressed gaugino spectrum relative to mSUGRA; this pro-
2] s [GeV/c 560000 ~t1 ~t1 ~lR ~∼τt11 χ∼02 g~χ∼±1 dCpurSoTc4dehduse)ce.tiirtoehnleartpiavroelicgefhrstesgqesluueiinsncosyu(amosfminavCrairzSieo6du)soinrLaTHhaCebalvesyuVpLIeS,rPpfoa(rratsntheiner
mas 234000000 ~χ∼χ∼lR01±1 ∼χ∼τ102 ~χ∼χ∼lR01±1 χ∼∼τ102 χ∼χ∼0±1 χ∼02 χ∼χ∼∼τ01±11 ~~lχ∼tR102 ~χ∼lR01 ∼τ1 GTesGstheqvhrlelueuoeenaoiucnrtpttpkhoirso-eoe1gnrpdllemafuuscoicihortuntiadioropopenmrnelaosstnodhfbddrutaahoecnscelttqshtibi.oukoebPnainfenraoskfdeiror-moeasrprmeqiaertuoti;ainmadcntarhusdukticecsoatpshiffiortsfoemntohderrooxeuofrpcmuestetrhuiocsoeredtivnemvelidielvdginliobhCantmetrgSesceisa6anstlf,uaeatsesmcwtteerotihppottfilhhonleieeesr..
100 1
important for model CS4d before the selection cuts, but
after the event selectionvery few of these events remain.
0
Table VII shows the most relevant superpartner decay
FIG. 5(coloronline). ThemassspectraoftheMSSMmodels branching fractions. For models LM2p and LM5, gluino
LM2p, LM5, LM8, CS4d, and CS6. Only the most relevant decay is predominantly to quarkþsquark; for LM8 and
particles are shown: the lighter gauginos (cid:2)~0, (cid:2)~0, and (cid:2)~(cid:4), the CS4d it is dominantly to top and the lightest stop, and
1 2 1
lightest stau (cid:3)~1, the right smuon and selectron denoted collec- gluinosdecayinCS6mostlythroughthethree-bodymode
tivelyas‘~R,thelighteststop~t1,thegluino,andtheleft/rightup qq(cid:2)~0. For models LM2p, LM5, and LM8, left squarks
anddownsquarksu~L,u~R,d~L,andd~R.Theveryheavy’2 TeV casca1de through quarkþchargino or quarkþ
squarks of model CS6 lie outside the displayed range.
second neutralino; right squarks have a two-body decay
in Table V. We have used m ¼175 GeV and the spec- to quarkþLSP; right squarks in model LM8 also have a
top large branching to quarkþgluino. In model CS4d left
trum generator combination SuSpectv2:34 with
squarks decay almost entirely to quarkþgluino, while
SUSY(cid:1)HITv1:1 [32,33]. Model CS4d is in fact part of
right squarks decay almost entirely to quarkþLSP; for
the compressed SUSY model line defined in [63]. Model
CS6 all squarks except the stop decay dominantly to
CS6 is a modification of compressed SUSY where all of
quarkþgluino.
the squarks have been madevery heavy, *2 TeV.
TABLE VI. Summary of LHC superpartner production for the Group 1 MSSM models LM2p, LM5, LM8, CS4d, and CS6. The
relativepercentages are shown for each model, both before and after the event selection. The squark-squark percentages shown are
excludingthecontributionsfrompairproductionofthelighteststops,whichareshownseparately.Notethatsquark-charginoincludes
the production of either chargino, and squark-neutralino includes all of the four neutralinos. The category ‘‘other’’ includes weak
production as well as the associated production of gluinos with charginos or neutralinos. The total NLO cross sections are from
Prospino2 [65].
LM2p LM5 LM8 CS4d CS6
NLO cross section (pb) 8.6 8.1 12.7 14.5 12.6
before cutsafter cutsbefore cutsafter cutsbefore cutsafter cutsbefore cutsafter cutsbefore cutsafter cuts
squark-squark 33% 36% 32% 38% 22% 33% 19% 34% 0.1% 0.1%
squark-gluino 45% 55% 46% 52% 48% 54% 41% 55% 3.7% 7.4%
gluino-gluino 7.2% 6.4% 7.4% 6.4% 14% 8.3% 11% 8% 95% 92%
stop-stop 2.1% 1.1% 2.1% 0.9% 2.6% 1.5% 26% 1.4% (cid:5)(cid:5)(cid:5)- (cid:5)(cid:5)(cid:5)
squark-chargino 2.1% 0.5% 2.1% 0.7% 1.4% 0.7% 0.2% 0.2% (cid:5)(cid:5)(cid:5) (cid:5)(cid:5)(cid:5)
squark-neutralino 1.7% 0.4% 1.8% 0.4% 1.2% 0.6% 0.6% 0.2% (cid:5)(cid:5)(cid:5) (cid:5)(cid:5)(cid:5)
other 9.5% 0.7% 9.3% 0.8% 11% 0.8% 1.9% 0.3% 1.1% 0.1%
075008-10