Missing energy look-alikes with 100 pb-1 at the LHC

48 Pages·2008·0.67 MB·English

FERMILAB-PUB-08-012-T
ANL-HEP-PR-08-30
Missing energy look-alikes with 100 pb−1 at the LHC
Jay Hubisz∗
High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
Joseph Lykken†
Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510, USA
Maurizio Pierini‡ and Maria Spiropulu§
Physics Department, CERN, CH 1211 Geneva 23, Switzerland
(Dated: July 30, 2008)
AmissingenergydiscoveryispossibleattheLHCwiththefirst100pb−1ofunderstooddata. We
presentarealisticstrategytorapidlynarrowthelistofcandidatetheoriesat,orcloseto,themoment
8
ofdiscovery. Thestrategyisbasedonrobustratiosofinclusivecountsofsimplephysicsobjects. We
0
study specific cases showing discrimination of look-alike models in simulated data sets that are at
0
least10to100timessmallerthanusedinpreviousstudies. Wediscriminatesupersymmetrymodels
2
from non-supersymmetric look-alikes with only 100 pb−1 of simulated data, using combinations of

l observables that trace back to differencesin spin.
u
J
PACSnumbers: 11.30.Pb,14.80.Ly,12.60.Jv
0
3

I. INTRODUCTION immediate follow-up of an early LHC discovery.
]
h WhenN islarge,itis notaviablestrategytodiscrim-
p inate between N alternative explanations by performing
A. Twenty questions at the LHC
- N tests. However,as the game “twenty questions” illus-
p
trates, a well-designed series of simple tests can identify
e
Many well-motivated theoretical frameworks make
h the correctalternative in oforder log(N)steps, proceed-
[ dramatic predictions for the experiments at the Large ing alonga decisiontree suchthat, ateachbranching,of
Hadron Collider. These frameworks are generally based order half of the remaining alternatives are eliminated.
2
upon assumptions about new symmetries, as is the
v AddressingtheLHCInverseProblemimpliesdesigning
case for supersymmetry (SUSY) [1, 2] and little Higgs
8 and implementing this series of simple tests in the LHC
(LH)[3, 4], or upon assumptions about new degrees of
9 experiments, so that with high confidence a significant
3 freedom such as extra large [5] or warped [6] spatial di- fraction of the remaining theory space is ruled out at
2 mensions. Within each successful framework, one can eachstep. Theresultsofthefirstfewtestswillshapethe
. construct a large number of qualitatively different mod-
5 requirementsforfuturetests,sotheimmediateneedisto
0 els consistent with all current data. Collectively these developthe strategyfor the early tests. In this paper we
8 models populate the “theory space” of possible physics providethis strategyfor the caseofanLHC discoveryin
0 beyond the Standard Model. The BSM theory space is
the inclusive missing energy signature.
: many dimensional, and the number of distinct models
v
i within it is formally infinite. Since the data will not
X
providea distinctionbetween models thatdiffer by suffi-
B. Missing energy at the LHC
r ciently tiny or experimentally irrelevant details, infinity,
a
in practice, becomes some large finite number N. The
The existence of dark matter provides a powerful mo-
mapping of these N models into their experimental sig-
tivationtoexploremissingenergysignaturesattheLHC,
natures at the LHC, though still incomplete, has been
under the assumption that a significant fraction of dark
explored in great detail.
matter may consist of weakly interacting thermal relics.
AssoonasdiscoveriesaremadeattheLHC,physicists
MissingenergyattheLHCisexperimentallychallenging.
will face the LHC Inverse Problem: given a finite set
Most of the energy of 14 TeV pp collisions is carried off
of measurements with finite resolutions, how does one
byundetectedremnantsoftheunderlyingevent,somiss-
map back [7]-[9] to the underlying theory responsible for
ing energy searches actually look for missing transverse
the new phenomena? So far, not enough progress has
energy(Emiss)ofthepartonicsubprocess. Emisssearches
beenmadeonthisproblem,especiallyasitrelatestothe T T
are plagued by instrumental and spurious backgrounds,
including cosmic rays, scattering off beam halo and jet
mismeasurement. Standard Model processes create an
irreducible Emiss backgroundfrom processes such as the
∗Electronicaddress: [email protected] Z boson decaTy to neutrinos and tt¯production followed
†Electronicaddress: [email protected]
‡Electronicaddress: [email protected] by semileptonic decays of the top.
§Electronicaddress: [email protected] Inmanytheoreticalframeworkswithdarkmattercan-
2
didates, there are heavy strongly interacting particles b tagging in multijet final states will be in development
withthe sameconservedchargeorparitythatmakesthe during the 100 pb−1 era. In many small data samples
dark matter particle stable. These colored particles will peaks and edges in invariantmass distributions may not
be pair-producedatthe LHCwithcrosssectionsroughly be visible, and most observables related to detailed fea-
in the range 0.1 to 100 pb. Their subsequent decays will tures of the events will be rate limited. The observables
produce Standard Model particles along with a pair of that are available to discriminate the look-alikes in the
undetected dark matter particles. Thus the generic ex- very early running will be strongly correlatedby physics
perimental signature is both simple and inclusive: large and systematics making it imprudent to combine them
Emiss accompaniedbymultipleenergeticjets. Adetailed in a multivariate analysis.
T
strategy for early discovery with the inclusive Emiss sig-
T
nature was presented in the CMS Physics Technical De-
sign Report [10]-[12] and studied with full simulation of D. Is it SUSY?
the CMS detector. After a series ofcleanupand analysis
cuts on a simulated Emiss trigger sample targeting the
T Byfocusingonthediscriminationoflook-alikes,weare
reduction of the instrumental and physics backgrounds,
pursuing a strategy of simple binary choices: is Model A
the signal efficiency remained as high as 25%. These re-
a significantly better explanation of the discovery data
sults indicate that, for signal cross sections as low as a
set than Model B? Each answer carries with it a few
few pb, an Emiss discovery could be made with the first
T bitsofimportantfundamentalinformationaboutthenew
100 pb−1 of understood LHC data1. In our study we as-
physicsprocessresponsibleformissingenergy. Obviously
sume as the starting point that a greater than 5σ excess
we will need to make many distinct look-alike compar-
of events will be seen in a 14 TeV LHC data sample of
isonsbeforewecanhopetobuildupaclearpicture from
100 pb−1 with an inclusive missing energy analysis. For
these individual bits.
invariability and comparability we effectively adopt the
Consider how this strategy might play out for answer-
full analysis path and requirements used in [10].
ing the basic question “is it SUSY?” It may not be pos-
sible to answer this question conclusively during the 100
pb−1 era. Our strategy will consist of asking a series of
moremodestquestions,someofthem ofthe form: “does
C. Look-alikes at the moment of discovery
SUSY Model A give a significantly better explanationof
the discovery data set than non-SUSY Model B?” None
At the moment of discovery a large number of theory
ofthese individualbits of informationby itselfis equiva-
models will be immediately ruled out because, within
lenttoanswering“isitSUSY?”Howeverwedemonstrate
conservativeerrors,theygivethewrongexcess. However
that we can build up a picture from the data that con-
a large number of models will remain as missing energy
nects back to features of the underlying theory.
look-alikes, defined as models that predict the same in-
Furthermore,wedemonstrateaconcretemethodtoob-
clusive missing energy excess, within some tolerance, in
tain indirect information about the spin of the new par-
the same analysis in the same detector, for a given in-
ticles. We establish how to discriminate between a non-
tegrated luminosity. The immediate challenge is then to
SUSY model and its SUSY look-alikes. Even though we
begin discriminating the look-alikes.
cannot measure the spins of the exotic particles directly,
The look-alike problem was studied in [9] as it might
spin has significant effects on production cross sections,
apply to a later mature phase of the LHC experiments.
kinematic distributions and signal efficiencies. We are
Evenrestrictedtothesliceoftheoryspacepopulatedbya
thus able to discriminate SUSY from non-SUSY using
partialscanoftheMSSM,ignoringSMbackgroundsand
combinationsofobservablesthattracebacktodifferences
systematic errors, and applying an uncorrelated χ2-like
inspin. Ourstudyshowsthatinfavorablecasesthis can
statistical analysis to 1808 correlated observables, this be accomplished with data sets as small as 100 pb−1.
study found that a large number of look-alikesremained
unresolvedinasimulationequivalentto10fb−1. Amore
recent analysis [13] attempts to resolve these look-alikes
E. Outline
in a simulation of a future linear collider.
At the moment of an early discovery the look-alike
InsectionIIwereviewindetailthemissingenergydis-
problem will be qualitatively different. The data sam-
covery path, including the experimental issues and sys-
ples will be much smaller, with a limited palette of ro-
tematicsthatlimit ourability tofully reconstructevents
bust reconstructed physics objects. For example, τ or
from the discovery data set. We explain how the miss-
ing energy signals are simulated, and the uncertainties
associated with these simulations. In section III we dis-
cuss the problem of populating the parts of the theory
1 Thefirst100pb−1 ofunderstoodLHCdatawillnotbethefirst
space relevant to a particular missing energy discovery.
100pb−1 ofdatawrittentotape. The10TeVdatacollectedin
InsectionIVweintroducetwogroupsoflook-alikemod-
theearlyrunningwillbeusedforcalibrationsandunderstanding
ofbenchmarkStandardModelprocesses. els relative to two different missing energy signals. For
3
models differing only by spins, we discuss how cross sec- and misreconstruction of the primary vertex. Eliminat-
tions,kinematicdistributionsandefficienciescanbeused ing these sources requiresunbiasedfilters basedon clean
to distinguish them, drawing from formulae developed definitions of event quality.
in the Appendix. In section V we define all of the ro- To design a missing energy analysis, we need to have
bust observables that we use to discriminate among the some idea of the source of the Emiss in the signal. The
T
look-alikes, and in section VI we describe the look-alike possibilities include:
analysisitselfandhowwecomputethesignificanceofthe
discriminations. SectionsVIIandVIIIgiveasummaryof • The ETmiss is entirely from neutrinos. This could
ourresults,withdetailsrelegatedtofurther Appendices. arise from the direct decay of new heavy particles
FinallysectionIXdescribesthe stepswe arefollowingto to neutrinos, or decays of new heavy particles to
improve this analysis for use with real data. top, W’s, Z’s or τ’s. One appropriate discovery
strategyforthiscaseistolookforanomaliesinthe
energetic tails of data sets with reconstructed top,
W’s or Z’s.
II. DISCOVERY ANALYSIS FOR MISSING
ENERGY The Emiss originatesfromasingle weaklyinteract-
• T
ing exotic particle in the final state. An example
of this possibility is graviton production in models
Missingenergyhadroncolliderdatahasbeenusedpre-
with large extra dimensions [20]. If strong produc-
viously for successful measurements of Standard Model
processes with energetic neutrinos; these include the Z0 tionoccurs,thesignalwillconsistpredominatelyof
monojets and large Emiss. Successful analyses for
boson invisible decay rates, the top quark cross section, T
this case were carried out at the Tevatron [21, 22].
searchesfortheHiggsboson[14]andapreciseextraction
Other signals that fit this case arise from unpar-
of the W mass from the reconstruction of the W trans-
ticle models [23] and from models with s-channel
verse mass [15]. Pioneering searches for new phenomena
resonances that have invisible decays.
in missing energy data sets at the Tevatron [16]-[19] led
to the developmentand understanding of the basic tech-
The Emiss originates from many weakly interact-
niquesthatwillbeusedinmissingenergysearchesatthe • T
ing exoticparticles. Thiscanbe the caseinhidden
LHC.
valleymodels[24],wheretheweaklyinteractingex-
In an ideal detector, with hermetic 4π solidangle cov-
oticsarelightpionsofthe hiddensector. Thiscase
erage and excellent calorimeter resolution, the measure-
is experimentally challenging.
ment of missing energy is the measurement of the neu-
trino energy and the energy of any other neutral weakly The Emiss originates from two weakly interacting
• T
interacting particles. In a real detector it is also a mea- exotic particles in the final state. This is the case
surement of the energy that escapes detection due to for supersymmetry models with conserved R par-
uninstrumented regions and other detector effects such ity, where the weakly interacting particles are neu-
as imperfect calorimeter response. Muons are sources tralino LSPs. It alsoapplies for moregenericmod-
of missing energy since a muon typically deposits only els with WIMP dark matter candidates.
of order a few GeV of its total energy in the calorime-
ters2. QCD jets produce real Emiss from semileptonic Wefocusonadiscoveryanalysisdevelopedforthelast
T
decays of heavy flavor, and fake Emiss from detector- case. Thus we are interested in signal events with two
T
induced mismeasurements. Thus the Emiss distribution heavy WIMPs in the final state. For early discovery
T
of a pure QCD multijet sample has a long tail related at the LHC, the signal events should have strong pro-
to non-Gaussian tails in the detector response. This duction cross sections; we will assume that each WIMP
gives rise to an important backgroundto missing energy arisesfromthedecayofastronglyinteractingheavypar-
searchesthatisdifficulttoestimatepriortodata. Atthe entparticle. Themostgenericsignatureisthereforelarge
Tevatronit has been shownthat this backgroundcan be ETmissinassociationwithatleasttwohighET jets. There
broughtundercontrolbyexploitingthefactthatthefake will be additional jets if the WIMP is not produced in a
Emissfromjetmismeasurementsishighlycorrelatedwith 2-body decay of the parent particle. Furthermore, there
T
the azimuthal directions of the leading jets [16]. is a significant probability of an extra jet from QCD ra-
There are other important sources of fake Emiss at diation, due to the large phase space. Thus it is only
hadroncolliders,includingbeamhaloinducedEmiTss,cos- slightly less generic to design an inclusive analysis for
T large Emiss in association with three or more energetic
mic ray muons, noise in the data acquisition system, T
jets. We will refer to this as the inclusive missing energy
signature3.
2 Theenergylossofmuonsismostlyduetoionizationuptomuon
energiesof100GeV.Above100GeVbremsstrahlungandnuclear
losses can cause a single “catastrophic” energy loss comparable 3 Therequirementofathirdenergeticjetgreatlyreducesthesize
tothetotal muonenergy. andcomplexityoftheStandardModelbackgrounds. Thuswhile
4
In the basic 2 2 hard scattering, the heavy par- missing transverse energy Emiss 200 GeV and at least
→ T ≥
ent particles of the signal will be produced back-to-back three jets with E 30GeV withinpseudorapidity η <
T
≥ | |
in the partonic subprocess center-of-mass frame; typi- 3. These requirements directly define the missing en-
callythey willhavep roughlycomparabletotheirmass ergy signal signature. In addition the leading jet is re-
T
m . The WIMPs of massm resulting fromthe parent quired to be within the central tracker fiducial volume
p dm
particle decays will fail to deposit energy m in the i.e. η < 1.7. Everywhere in this paper “jets” means
dm
≥ | |
calorimeters; if the WIMPS have fairly large p , a sig- uncorrected (raw) jets with E > 30 GeV and η < 3
T T
nificant fraction of this energy contributes to the Emiss. as measured in the calorimeters; the jet reconst|ru|ction
T
Thus either large m or large m leads to large Emiss. is with a simple iterative cone algorithm with a 0.5 cone
p dm T
Note the azimuthal directions of the WIMPS are anti- sizeintheη φspace. Themissingenergyisuncorrected
−
correlated, a feature inherited from their parents, so the for the presence of muons in the event.
magnitude of the total ETmiss tends to be less than the The rest of the analysis path is designed based on
magnitude of the largest single contribution. elimination of the major backgrounds. The QCD back-
At the LHC, the most important Standard Model ground from mismeasured jets is reduced by rejecting
sources of large real Emiss will be tt¯, single top, W and events where the Emiss is too closely correlatedwith the
T T
Z plus jets associated production, dibosons and heavy azimuthaldirectionsofthejets. Toreducethelargeback-
flavor decays. Most of these processes produce a hard ground from W( ℓν)+jets, Z( ℓℓ)+jets and tt¯pro-
lepton in association with the Emiss from an energetic duction an indire→ct lepton veto (I→LV) scheme is designed
T
neutrino. The exception is Z νν¯. Even with a per- that uses the tracker and the calorimeters. The ILV re-
→
fect detector, Z νν¯ plus jets is an irreducible physics tains a large signal efficiency while achieving a factor of
→
background. two rejection of the remaining W and tt¯backgrounds.
The veto is indirect because we don’t identify leptons–
insteadeventsarerejectediftheelectromagneticfraction
A. Analysis path ofoneofthetwoleadingjetsistoolarge,orifthehighest
p trackoftheeventisisolated. Thesignalsweareinter-
T
ested in are characterized by highly energetic jets while
In the real data this search will be performed start-
leptonsinthesignaloriginatefromcascadedecaysofthe
ing from a primary data set that includes requirements
parents or semileptonic B decays in the jets; thus even
of missing energy, jets and general calorimetric activity
when a signal event has leptons it is relatively unlikely
at the trigger path; the trigger efficiency should be mea-
to be rejected by the ILV. For the models in our study,
sured in other data samples.
approximately85%ofallsignaleventsand70%ofsignal
For the offline analysis, we will adopt the inclusive
events with muons or taus pass the ILV cut.
missing energy benchmark analysis studied with the full
The final selections require that the leading jet has
detector simulation for the CMS Physics Technical De-
E > 180 GeV, and that the second jet has E > 110
sign Report [10, 11]. T T
GeV. We also require H >500 GeV, where
The first phase is a preselection based on the event T
quality. Thepurposeofthisprimarycleanupistodiscard
events with fake Emiss from sources such as beam halo, 4
T H = Ei +Emiss , (1)
data acquisition noise and cosmic ray muons. To elimi- T T T
nate these types of backgrounds the benchmark analysis Xi=2
uses jet variables, averages them over the event to de-
where the E is summed over the second, third and
fine correspondingeventvariables,and uses these to dis- T
fourth (if present) leading jets. These cuts select for
criminaterealEmiss+multijeteventsfromspuriousback-
T highly energeticevents,greatlyfavoringeventswith new
grounds. The event electromagnetic fraction (EEMF) is
heavy particles over the Standard Model backgrounds.
defined to be the E weighted jet electromagnetic frac-
T
TableIsummarizesthebenchmarkanalysispath. The
tion. We define an event charged fraction (ECHF) as
table lists the cumulative efficiencies after each selection
the event average of the jet charged fraction (defined as
for a benchmark signal model and the Standard Model
the ratio of the p of the tracks associatedwith a jet
T
backgrounds. The signal model is the CMS supersym-
overthetotalcalorimetricjetE ). Thepreselectionalso
T
P metry benchmark model LM1, which has a gluino with
has a quality requirement for the reconstructed primary
mass611GeVandsquarkswithmassesaround560GeV.
vertex.
The last line of the table shows the expected number of
Events that are accepted by the preselection require-
eventsthatsurvivetheselectioninadatasetcorrespond-
ments proceed through the analysis path if they have
ing to 1000 pb−1 of integrated luminosity. For the QCD
backgroundandthesingletopbackground,whicharenot
shown in the table, the estimated number of remaining
events is 107 and 3, respectively. Thus the total esti-
mature LHC analyses will explore the fullyinclusive Emiss sig-
T mated Standard Model backgroundafter all selections is
nature,weassumeherethatanearlydiscoverywillbebasedon
amultijet+Emiss datasample. 245 events per 1000 pb−1.
T
5
TABLE I: Cumulative selection efficiency after each requirement in the Emiss+ multijets analysis path for a low mass SUSY
T
signal and the major Standard Model backgrounds (EWK refers to W/Z,WW/ZZ/ZW), see [10, 11]).
Cut/Sample Signal tt¯Z(→νν¯)+ jets EWK + jets
All (%) 100 100 100 100
Trigger 92 40 99 57
Emiss>200 GeV 54 0.57 54 0.9
T
PV 53.8 0.56 53 0.9
N ≥3 39 0.36 4 0.1
j
|ηj1|≥1.7 34 0.30 3 0.07
d
EEMF ≥ 0.175 34 0.30 3 0.07
ECHF ≥ 0.1 33.5 0.29 3 0.06
QCD angular 26 0.17 2.5 0.04
Isoleadtrk =0 23 0.09 2.3 0.02
EMF(j1),
EMF(j2)≥0.9 22 0.086 2.2 0.02
ET,1 > 180 GeV,
ET,2 > 110 GeV 14 0.015 0.5 0.003
H >500 GeV 13 0.01 0.4 0.002
T
eventsremaining per 1000 pb−1
6319 54 48 33
B. Triggers and “boxes” The Muon20 trigger requires an energetic muon
•
that is not necessarily isolated. The trigger is 88%
efficientformuonswithp =20GeV/c,asymptot-
Havingestablishedabenchmarkanalysispath,wealso T
ing to 95% as seen in Figure 4.
need to define benchmark data samples. With the real
LHCdatathesewillcorrespondtodatastreamsanddata
After applying the selection requirements, these four
paths from various triggers. For the inclusive missing
triggers define four potential discovery data sets. In our
energy signature relevant triggers are the Emiss and jet
T simulationtheDiJet,TriJet,andMuon20datasets,after
triggers. A single lepton trigger is also of interest, since
the inclusive missing energy analysispath is applied, are
many models produce energetic leptons in association
all subsets of the MET sample, apart from one or two
with large Emiss. For our study we have chosen simple
T events per 1000 pb−1 5. Thus the MET is the largest,
but reasonable [25, 26] parametrizations of the trigger
most inclusive sample. We perform one complete analy-
efficiencies defining our four benchmark triggers 4 :
sis based on the MET trigger. The other three triggers
arethentreatedasdefiningthreemoreboxes,i.e. experi-
The MET trigger is a pure inclusive Emiss trigger.
• T mentallywell-definedsubsetsofthe METdiscoverydata
It is 50% efficient for Emiss> 80 GeV, as seen in
T set. The simplest physics observables are the counts of
Figure 1.
events in each box.
TheDiJettriggerrequirestwoveryhighE jets. It
T
•
is 50% efficient for uncorrected jet E > 340 GeV,
T C. Backgrounds and systematics
as seen in Figure 2.
IntheCMSstudythetotalnumberofStandardModel
The TriJet trigger requires three high E jets. It
T
• background events remaining after all selections is 245
is 50% efficient for uncorrected jet E > 210 GeV,
T per 1000 pb−1 for an Emiss trigger sample. The error
as seen in Figure 3. T
on this estimate is dominated by i) the uncertainty in
how well the detector simulation software simulates the
4 These are made-up triggers for the purposes of our study. The
guidance on our parametrizations is from the published trigger
andphysicsreportsoftheCMSexperiment. Weexpectthatthe 5 Aperfectlydesignedtriggertablewillgiverisetooverlapsamong
triggertablesoftheLHCexperimentswillincludecorresponding datasets from different trigger paths due to both physics and
triggerpaths,richerandbetter intermsofthephysicscapture. slow/non-sharptriggerefficiencyturn-ons(resolution).
6
y y
nc 1 nc 1
e e
ci ci
effi effi
r r
e 0.8 e 0.8
g g
g g
ri ri
T T
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 50 100 150 200 250 300 100 150 200 250 300 350
Emiss (GeV) E (GeV)
T T
FIG. 1: TheEmiss trigger efficiency. FIG. 3: The TriJet trigger efficiency.
T
y y 1
nc 1 nc
e e
ci ci
r effi r effi 0.8
e 0.8 e
g g
g g
ri ri
T T
0.6
0.6
0.4
0.4
0.2 0.2
0 0
300 310 320 330 340 350 360 370 380 390 400 0 10 20 30 40 50 60
E (GeV) p (GeV/c)
T T
FIG. 2: The DiJet trigger efficiency. FIG. 4: The Muon20 trigger efficiency.
response of the actual CMS detector, and ii) the uncer- overall systematic error. The look-alike analysis will be
tainty on how well the Standard Model event generators degraded,however,intheeventthattheStandardModel
emulate QCD, top production, and W/Z plus jets pro- backgrounds turn out to be much larger than current
duction. Detailed studies of the real LHC data will be estimates.
required in order to produce reliable estimates of these Priortodata,itis alsodifficulttomakeareliableesti-
uncertainties. mateofthemainsystematicuncertaintiesthatwillaffect
Priortodataweassignconservativeerrorbarsonthese the inclusive missing energy analysis. Systematic uncer-
backgroundprojections. We havecheckedthat100pb−1 tainties will decreaseover time, as the detectors are bet-
of data in the MET trigger sample is sufficient for a 5σ ter understood, calibration studies are performed, and
discovery for the eight models in our study, even if we Standard Model physics is analyzed with the LHC data.
triple the backgrounds quoted above and include a 15% For our study we have assumed that, at the moment of
7
discovery,the dominant systematic errorsin the full dis- We performed a preliminary study by comparing PGS
covery data set will come from three sources: results to the full simulation results reported for the
SUSY benchmark model LM1 [10, 11]. We found that
Luminosity uncertainty: it affects the counting of PGS jets are not a good approximation of uncorrected
•
events. This systematic uncertainty is process in-
jets in the full simulation, even for the most basic prop-
dependent.
erties such as the E spectrum. Varying the parameters
T
andaddingsimple improvements,suchastakingintoac-
Detector simulation uncertainty: it mainly affects
• count the 4 Tesla field in the barrel, did not change this
calorimetry-related variables in our study, in par-
conclusion. PGS jets have a behavior, not surprisingly,
ticular jet counting and the missing energy. This
thatis intermediate between generatorleveljets andun-
systematic is partially process dependent.
corrected full simulation jets.
QCD uncertainty: it includes the uncertainties We developed a modified simulation called PGSCMS
•
fromthepartondistributionfunctions,higherorder with the geometry and approximate magnetic field of
matrixelements,andlargelogarithms. Thisuncer- the CMS detector. The PGS Gaussian smearing and
tainty affects event counting, jet counting and the uninstrumentedeffectsinthecalorimetersareturnedoff.
shapes of kinematic distributions. It is partially Electrons,muonsandphotonsareextractedatgenerator
process dependent. level,andPGStaureconstructionisnotused. Trackinfor-
mationisextractedasinthestandardPGS.Thecalorime-
Note that, since we use uncorrected jets, we do not
ter output improveson a generatorlevel analysisin that
have a systematic from the jet energy scale. This is
weinclude approximationsto the effects ofsegmentation
traded for a portion of the detector simulation uncer-
and the 4 Tesla field, as well as an η correction derived
tainty, i.e. how well we can map signal events into un-
fromthezvalueoftheprimaryvertex. Weparameterized
correctedjets as wouldbe measuredin the realdetector.
the detector response in a limited set of look-up tables
as a function of the generator-levelquantities.
At the analysis level we apply parameterized correc-
D. Simulation of the signals
tions and reconstructionefficiencies inspiredby the pub-
lished CMS detector performance [29]. For the jets, we
A realistic study of look-alikes requires full detector
applyanE andηdependentrescalingoftheirE ,tuned
T T
simulation. For the initial phase of this work a genera-
to reproduce the full simulation LM1 results in [10, 11].
torlevelanalysisisattractive,beingcomputationallyless
This rescaling makes the jets softer (i.e. takes into ac-
intensive and providing a clear link between observables
count the detector reconstruction): a 50 GeV generator
and the underlying theory models6.
leveljetbecomesanapproximately30GeVrawjetinour
In a generator level analysis, jets are reconstructed by
analysis.
applying a standard algorithm to particles rather than
The Emiss reconstructed from PGSCMS is essentially
to calorimeter towers. This obviously does not capture T
identical,modulo smallcalorimetersegmentationeffects,
theeffectsofarealisticcalorimeterresponse,calorimeter
to a a generator level analysis, i.e. our Emiss is virtually
segmentation, and energy losses due to material in the T
indistinguishable from the Monte Carlo truth Emiss ob-
tracker as well as magnetic field effects. T
tainedfromminusthevectorsumoftheE ofneutrinos,
Acompromisebetweenthefullsimulationandagener- T
muons and the other weakly interacting particles (such
atorlevelanalysisisaparameterizeddetectorsimulation.
as the LSP). We did not attempt to rescale the Emiss;
For the LHC the publicly availablesoftwarepackagesin- T
this is a complicated task since Emiss is a vector and
clude AcerDET [27], and PGS [28]. In such a simulation, T
in general energy losses, calorimeter response and mis-
electrons, muons and photons can be reconstructed us-
measurements tend to decrease the real large Emiss tails
ing parameterized efficiencies and resolutions based on T
whileincreasingtheEmiss tailsinthedistributionofnon-
abstract but educated rules-of-thumb for modern mul- T
real Emiss events. Instead of attempting to rescale the
tipurpose detectors. Jets are reconstructed in a virtual T
Emiss event by event, we raised the Emiss cut in our
calorimeter,fromparticleenergiesdepositedincellsthat T T
benchmark analysis to 220 GeV7.
roughly mimic the segmentation of a real calorimeter.
Because of the limitations of our fast simulation, we
Calorimeter response is approximated by performing a
Gaussiansmearingontheseenergydeposits. TheEmissis alsosimplifiedpartsofthebenchmarkanalysis. Thefirst
T phase primary cleanup is dropped since it is related to
reconstructed from the smeared energies in these virtual
supressionofspuriousprocessesthatwedonotsimulate,
towers.
anditisnearly100%efficientforthesignal. Wealsodrop
the jet electromagnetic fraction cuts of the ILV, because
6 ThefullGEANT4-basedsimulationistooslowtoadequatelysam-
ple the entire theory space. Having completed the first ex-
ploratory phase of this work, we are repeating the analysis to 7 Inarealisticfullsimulationstudywiththefirstjetdatainhand,
validatetheseresultswiththefullexperimental simulation. ourEmiss analysiswillavoidsuchcompromises.
T
8
they are nearly 100% efficient for the signal. A. SUSY
The resulting performance of our parameterized fast
simulationfortheSUSYbenchmarkmodelLM1isshown In a large class of supersymmetry models with con-
inTableII. Theagreementwiththefullsimulationstudy servedR parity, not necessarily restricted to the MSSM,
is very good. The largest single cut discrepancy is 2%; theLSPiseitherthelightestneutralinooraright-handed
this occurs for the QCD angular cuts, reflecting the ex- sneutrino8.
pected fact that our fast simulation does not accurately
In addition, if the NLSP is a neutralino or sneu-
reproduce jet mismeasurement effects. Since the final trino and the LSP is a gravitino, the Emiss signature
T
efficiencies agree to within 7%, it is plausible that look-
is the same. Models based on gravity-mediated, gauge-
alikes defined in our fast simulation study will remain
mediated or anomaly-mediated SUSY breaking all pro-
look-alikes in our upcoming full simulation study.
vide many candidate models.
It is important to note that this fast simulation does Because this relevant portion of SUSY theory space is
not reproduce the Standard Model background efficien- alreadysovast,thereisatemptationtoreducethescope
cies shown in Table I. In fact the discrepancies in the of the LHC Inverse Problem by making explicit or im-
total efficiencies can approach an order of magnitude. plicit theoretical assumptions. To take an extreme, one
This is to be expected. We are cutting very hard on couldapproachanearlyLHCdiscoveryintheEmisschan-
T
theStandardModelevents,thustheeventsthatpassare nelhavingalreadymadetheassumptionsthat(i)thesig-
very atypical. This is in contrast to the signal events, nalis SUSY, (ii) it has a minimal Higgs sector (MSSM),
where the fraction that pass are still fairly generic, and (iii) it has gravity-mediated SUSY breaking (SUGRA),
their ET and ETmiss spectra near the cuts areless steeply (iv) the breaking is minimal (mSUGRA) and (v) 100%
falling than those of the background. Since SM back- of dark matter is thermal relic LSPs with an abundance
grounds cannot be estimated from a PGS level analysis, given by extrapolating standard cosmology back to the
wetakeourbackgroundsfromthestate-of-the-artanaly- decoupling epoch. We don’t want to make any such as-
sisin[10];thisapproachonlyworksbecausewehavealso sumptions;ratherwewanttotest theoreticalhypotheses
matched the analysis path used in [10]. inthe LHCdiscoverydatasetcombinedwithothermea-
The full software chains we use in our study are sum- surements.
marized in Table III. All of the simulated data sets in- For SUSY we have the benefit of more than one spec-
clude an average of 5 pileup events added to each sig- trum calculator that can handle general models, more
nalevent, correspondingto low luminosity LHC running thanonematrixelementcalculatorandeventgeneration
( 1033 cm−2s−1). scheme, and a standardized interface via the SUSY Les
∼
Houches Accord (SLHA) [32]. There are still a few bugs
in this grand edifice, but the existing functionality com-
bined with the ability to perform multiple cross-checks
III. POPULATING THE THEORY SPACE puts us within sight of where we need to be when the
data arrives.
In Section II we gave a partial classification of BSM
models according to how many new weakly interacting
particles appear in a typical final state. Our benchmark B. Little Higgs
Emiss analysis is optimized for the case of two heavy
T
weaklyinteractingparticlesperevent,asappliestoSUSY
LittleHiggsmodelsareapromisingalternativetoweak
modelswithconservedRparity,little Higgsmodelswith
scalesupersymmetry[33]-[37]. InlittleHiggsmodels,the
conservedT parityandUniversalExtraDimensionsmod-
Higgs is an approximate Goldstone boson, with global
els with conserved KK parity. This study is a first at-
symmetries protecting its mass (which originates from a
tempt atconstructinggroupsoflook-alikemodelsdrawn
quantum level breaking of these symmetries) from large
from this rather large fraction of the BSM theory space,
radiative corrections. Many of these LH models require
and developing strategies to discriminate them shortly
an approximate T parity discrete symmetry to reconcile
after an initial discovery.
LH with electroweak precision data. This symmetry is
One caveat is that models from other corners of the similar to R parity in SUSY models. The new LH par-
theory space may also be look-alikes of the ones consid- ticles that would be produced at the LHC would be odd
eredhere. Forexample,modelswithstrongproductionof under this symmetry, enforcing the stability of the light-
heavyparticlesthatdecaytoboostedtopquarkscanpro- estparticlethatisoddunderT parity. Thisnewparticle
ducehigherET jetsandlargerETmiss fromneutrinosthan isweaklyinteractingandwouldmanifestitselfasmissing
does Standard Model top production. Such look-alike
possibilities also require study, but they are not a major
worrysinceourresultsshowthatwehavesomeabilityto
discriminateheavyWIMPSfromneutrinoseveninsmall 8 Recent analyses [30, 31] have argued for the phenomenological
data sets. viabilityofsneutrinodarkmatter.
9
TABLE II:Comparison of cut-by-cutselection efficiencies for our Emiss analysis applied to theSUSYbenchmark model LM1.
T
“Full” refers to thefull simulation study [10, 11]; “Fast” is what we obtain from ourparameterized fast simulation.
Cut/Software Full Fast
Trigger and
Emiss>200 GeV 53.9% 54.5%
T
N ≥3 72.1% 71.6%
j
|ηj1|≥1.7 88.1% 90.0%
d
QCD angular 75.6% 77.6%
Isoleadtrk =0 85.3% 85.5%
ET,1 > 180 GeV,
ET,2 > 110 GeV 63.0% 63.0%
H >500 GeV 92.8% 93.9%
T
Total efficiency 12.9% 13.8%
TABLE III: Summary of software chains used in this study. The little Higgs spectrum is based on [38]. PGSCMS is a variation
of PGS v4 [28].
Software/Models Group 1 models Group 2 models
Spectrum generator Isajet v7.69 [39] or privatelittle Higgs
or SUSY-HIT v1.1 [40] or SuSpect v2.34 [41]
Matrix element calculator Pythia v6.4 [42] MadGraph v4 [43]
Event generator Pythia v6.4 MadEvent v4 [44]
with BRIDGE [45]
Showering and hadronization Pythia v6.4 Pythia v6.4
Detector simulation PGSCMS v1.2.5 PGSCMS v1.2.5
plusparameterized plus parameterized
corrections corrections
energy at the LHC9. as singlets. The lightest T odd particle in this model we
Just as in SUSY, new colored particles are the dom- labelAH. Itisaheavygaugebosonthatisanadmixture
inant production modes. These particles subsequently of a heavy copy of the hypercharge gauge boson and a
generate high multiplicity final states through decay heavy W3 boson.
chains that end with the lightest T odd particle. In LH Foreventgeneration,we use aprivate implementation
models, the strongly coupled particles are T odd quarks of the littlest Higgs model within MadGraph. There is a
(TOQ’s),analogousto thesquarksofSUSY.The weakly need to generalize this to a wider class of models.
coupledanaloguesofthegauginosareT oddspinonevec-
tor bosons (TOV’s). In the models considered to date,
thereisnoanalogofthegluino: thisisanimportantcon- C. Universal extra dimensions
sideration in constructing supersymmetric look-alikes of
LH models. Universal extra dimensions models are based on orb-
Inthis study,we workwithaminimalimplementation ifolds of one or two TeV−1 size extra spatial dimen-
ofalittleHiggsmodelwithT paritythatisknownasthe sions [49]-[56]. The five-dimensional version of UED is
littlest Higgs model with T parity. This model is based the simplest. At the first level of Kaluza-Klein (KK)
onaSU(5)/SO(5)patternofglobalsymmetrybreaking. excitations, each Standard Model boson has an associ-
EachSM particle except the gluonhas an associatedLH ated partner particle, and each Standard Model fermion
partner odd under T parity. There is also an extra pair has two associated partner particles (i.e. a vector-like
of top partners,one T odd and the other T even, as well pair). These KK partners are odd under a KK parity,
the remnantof the brokentranslationalinvariancealong
the fifth dimension. This parity is assumed to be an ex-
act symmetry. After taking into account mass splittings
9 This symmetry may be inexact, or violated by anomalies [46]. due to Standard Model radiative corrections, one finds
Suchpossibilitiesaremodeldependent [47,48]. thatthelightestKK oddpartnerisnaturallytheweakly
10
interacting partner of the hypercharge gauge boson. A benchmarkmodelLM2;LM2phasaslightlylargervalue
wide variety of spectra for the KK odd partners can be ofm (360versus350GeV)than LM2,whichmakesit
1/2
obtained by introducing additional interactions that are more of a look-alike of the other Group 1 models.
localized at the orbifold fixed points; these choices dis-
tinguish generic UED from the original minimal model
TABLE IV: Input parameters for the mSUGRA models
of [49]. These models resemble SUSY.
LM2p, LM5 and LM8. The notation comforms to [39]. The
A public event generation code based on a modifica-
mass parameters and trilinear A0 parameter have units of
tionofPythiaisavailableforgeneric5-dimensionalUED
GeV.
models [57]. Thereis aneedto generalizethis toa wider
LM2p LM5 LM8
class of models, e.g. 6-dimensional UED. In our study
wehavenotusedanyUEDexamples,butwewillinclude m0 185 230 500
them in the future. m1/2 360 360 300
A0 0 0 -300
tanβ 35 10 10
IV. DESCRIPTION OF THE MODELS sign(µ) + + +
A. Group 1
The five look-alike models of Group 1 are all MSSM
TABLEV:InputparametersfortheMSSMmodelsCS4dand
models. Two of them (LM5 and LM8) are CMS SUSY
CS6. Thenotationconformsto[40,41]. Themassparameters
benchmarkmodels,whileanother(LM2p)isaslightvari-
and trilinear A parameters haveunitsof GeV.
ation of a CMS benchmark. It is a sobering coincidence
CS4d CS6
that these are look-alikesof the Emiss analysis, since the
T
benchmarksweredevelopedbyCMStocoverdifferentex- M1 620 400
perimentalsignatures,notproducelook-alikes. Toround M2 930 600
outGroup1wefoundtwootherMSSMlook-alikeswhose M3 310 200
spectraanddecaychainsareasdifferentfromeachother A ,A ,A ,A ,A ,A -400 -300
τ t b e u d
and from the three CMS benchmarks as we could make
M ,M ,M 340 2000
QL tR bR
them.
M ,M ,M 340 2000
The models are consistent with all currentexperimen- qu uR dR
M ,M ,M ,M 340 340
tal constraints, but do not all give the “correct” relic τL τR eL eR
density of dark matter. Any comparison of relic densi- Mh2u,Mh2d 115600 115600
ties to the so-calledWMAP constraintsassumes at least tanβ 10 10
three facts not yet in evidence: (i) that dark matter is a sign(µ) + +
thermalrelic,(ii)thatthereisonlyonesignificantspecies
of dark matter and (iii) that cosmologicalevolution was
entirely radiation-dominatedfrom the time of dark mat- The Group 1 models CS4d and CS6 are not minimal
ter decoupling until the time of Big Bang nucleosynthe- supergravity; they are more general high scale MSSM
sis. A missing energy discovery at the LHC will help us models based on the compressed supersymmetry idea of
test whether these assumptions have any validity. For Martin [63, 64]. The high scale input parameters are
example, model LM8 produces a relic density an order shown in Table V. We have used m = 175 GeV
top
of magnitude largerthan the WMAP upper bound; thus andthespectrumgeneratorcombinationSuSpect v2.34
discriminating LM8 as a more likely explanation of an with SUSY-HIT v1.1 [40, 41]. Model CS4d is in fact
early missing energy discovery would call into question part of the compressed SUSY model line defined in [63].
[58, 59] assumptions (i) and (iii), or could be a hint that Model CS6 is a modification of compressedSUSY where
the lightest neutralino is not absolutely stable. all of the squarks have been made very heavy, >2 TeV.
LM2p, LM5 and LM8 are minimal supergravity mod- The superpartnermass spectra ofthe Group∼1 models
els [60]-[62]. They are specified by the usual high scale aredisplayedinFigure5. Onenotesimmediatelythatall
mSUGRA input parameters as shown in Table IV; be- of the mSUGRA models are more similar to each other
causetheresultingsuperpartnerspectradependstrongly than they are to either of the more general MSSM mod-
on RGE running from the high scale, a complete specifi- elsCS4dandCS6;thisshowsthelimitationsoftheusual
cation of the models also requires fixing the top quark SUSY analyses that do not go beyond mSUGRA. As
mass and the particular spectrum generator program their name implies, the compressed SUSY models CS4d
used. We have used m = 175 GeV and the ISAJET andCS6haveacompressedgauginospectrumrelativeto
top
v7.69 generator [39], in order to maintain compatibility mSUGRA;thisproduceseitheralightgluino(asinCS6)
with the CMS Physics TDR [10]. Models LM5 and LM8 or a heavy LSP (as in CS4d).
arethenidenticaltothemSUGRAbenchmarkmodelsof The relative frequency of various LHC superpartner
theCMSPhysicsTDR,whileLM2pisalmostidenticalto production processes is summarized in Table VI, for the