Search for quark contact interactions and extra spatial dimensions using dijet angular distributions

31 Pages·2014·1.61 MB·English

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP/2014-261
2014/11/10
CMS-EXO-12-050
Search for quark contact interactions and extra spatial
dimensions using dijet angular distributions in
proton-proton collisions at √s = 8TeV
4
1
0
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v The CMS Collaboration
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1

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Abstract
x
e
-
p
A search is presented for quark contact interactions and extra spatial dimensions in
e
h proton-proton collisions at √s = 8TeV using dijet angular distributions. The search
[ isbasedonadatasetcorrespondingtoanintegratedluminosityof19.7fb−1 collected

8 by the CMS detector at the CERN LHC. Dijet angular distributions are found to be
9
in agreement with the perturbative QCD predictions that include electroweak cor-
9
0 rections. Limits on the contact interaction scale from a variety of models at next-to-
1 leading order in QCD corrections are obtained. A benchmark model in which only
1
left-handed quarks participate is excluded up to a scale of 9.0(11.7)TeV for destruc-
1
/ tive(constructive)interferenceat95%confidencelevel. Lowerlimitsbetween6.0and
t
i 8.4TeVonthescaleofvirtualgravitonexchangeareextractedfortheArkani-Hamed–
m
Dimopoulos–Dvalimodelofextraspatialdimensions.
b
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v SubmittedtoPhysicsLettersB
i
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a
c 2014CERNforthebenefitoftheCMSCollaboration. CC-BY-3.0license
(cid:13)
∗SeeAppendixBforthelistofcollaborationmembers

1
1 Introduction
High momentum-transfer proton-proton collisions at the CERN LHC probe the dynamics of
the underlying interaction at distances below 10 19m. Often these collisions produce a pair
−
of jets (dijets) approximately balanced in transverse momentum p . These dijet events pro-
T
vide an ideal testing ground to probe the validity of perturbative quantum chromodynamics
and to search for new phenomena such as quark compositeness or additional, compactified
spatial dimensions. A particularly suitable observable for this purpose is the dijet angular
distribution [1] expressed in terms of χ = exp( (y y ) ), where y and y are the ra-
dijet 1 2 1 2
| − |
pidities of the two jets with the highest transverse momenta. Rapidity is defined as y =
ln[(E+p )/(E p )]/2withEbeingthejetenergyandp theprojectionofthejetmomentum
z z z
−
onto the beam axis. For the scattering of massless partons, χ is related to the polar scatter-
dijet
ingangleθ inthepartoniccenter-of-mass(c.m.) framebyχ = (1+ cosθ )/(1 cosθ ).
∗ dijet ∗ ∗
| | −| |
Thechoiceofthevariableχ ismotivatedbythefactthatforRutherfordscatteringtheangu-
dijet
lar distribution is approximately independent of χ . In perturbative QCD the dijet angular
dijet
distribution at small c.m. scattering angles is approximately independent of the underlying
partonic level process and exhibits behavior similar to Rutherford scattering, characteristic of
spin-1 particle exchange. Signatures of new physics (NP), such as quark contact interactions
(CI) or virtual exchange of Kaluza–Klein [2] excitations of the graviton, that exhibit angular
distributions that are more isotropic than those predicted by QCD, could appear as an excess
ofeventsatlowvaluesofχ .
dijet
Models of quark compositeness [3, 4] postulate interactions between quark constituents at a
Λ Λ
characteristic scale that is much larger than the quark masses. At energies well below ,
theseinteractionscanbeapproximatedbyaCIcharacterizedbyafour-fermioncoupling. The
effectiveLagrangiancanbewrittenas[3,4]:
2π
Lqq = Λ2 (cid:2)ηLL(qLγµqL)(qLγµqL)+ηRR(qRγµqR)(qRγµqR)+2ηRL(qRγµqR)(qLγµqL)(cid:3),
where the subscripts L and R refer to the left and right chiral projections of the quark fields
andη ,η ,andη aretakentobe0,+1,or 1. Thevariouscombinationsof(η , η , η )
LL RR RL LL RR RL
−
correspond to different CI models. The following CI scenarios with color-singlet couplings
betweenquarksareinvestigated:
Λ (η , η , η )
LL RR RL
Λ ( 1, 0, 0)
±LL ±
Λ ( 0, 1, 0)
±RR ±
Λ ( 1, 1, 1)
V±V ± ± ±
Λ ( 1, 1, 1)
±AA ± ± ∓
Λ ( 0, 0, 1)
±(V A) ±
−
Note that the models with positive (negative) η or η lead to destructive (constructive) in-
LL RR
terference with the QCD terms and a lower (higher) cross section in the limit of high partonic
c.m. energies. InallCImodelsdiscussedinthisLetter,next-to-leading-order(NLO)QCDcor-
Λ
rections are employed to calculate the cross sections. In proton-proton collisions the and
±LL
Λ
modelsresultinidenticaltree-levelcrosssectionsandNLOcorrections,andconsequently
±RR
Λ Λ Λ
lead to the same sensitivity. For and , as well as for , the CI predictions are
V±V ±AA ±(V A)
−
identicalattree-level,butexhibitdifferentNLOcorrectionsandyielddifferentsensitivity.
2 2 Eventselection
Measurements of dijet angular distributions at the Fermilab Tevatron have been reported by
the CDF [5] and D0 [6, 7] Collaborations, and at the LHC by the CMS [8–10] and ATLAS [11,
12] Collaborations. The most stringent limits to date on CI models calculated at tree-level
have been obtained by the CMS Collaboration from the inclusive jet p spectrum [13], which
T
excludes Λ+ < 9.9TeV and Λ < 14.3TeV. Constraints on CI models with NLO corrections
LL −LL
havebeenpreviouslyobtainedfromasearchinthedijetangulardistributions[8],excludingin
particularΛ+ < 7.5TeVandΛ < 10.5TeV.
LL −LL
DijetangulardistributionsarealsosensitivetosignaturesfromtheArkani-Hamed–Dimopoulos–
Dvali (ADD) model [14, 15] of compactified extra dimension (ED) that provides a possible
solution to the hierarchy problem of the standard model (SM). In the ADD model, gravity
is assumed to propagate in the entire higher-dimensional space, while SM particles are con-
fined to a (3+1) dimensional subspace. As a result, the fundamental Planck scale M in the
D
ADD model is much smaller than the (3+1) dimensional Planck energy scale M , which may
Pl
lead to phenomenological effects that can be tested with proton-proton collisions at the LHC.
The coupling of the graviton in higher-dimensional space to the SM fields can be described
by a (3+1)-dimensional tower of Kaluza–Klein (KK) graviton excitations, each coupled to the
energy-momentum tensor of the SM field with gravitational strength. The effects of a virtual
graviton exchange can therefore be approximated at leading-order (LO) by an effective (3+1)-
dimensionaltheorythatsumsoverKKexcitationsofavirtualgraviton. Thissumisdivergent,
andthereforehastobetruncatedatacertainenergyscaleoforder M ,wheretheeffectivethe-
D
oryisexpectedtobreakdown. Suchatheorypredictsanon-resonantenhancementofdijetpro-
duction, whose angular distribution differs from the QCD prediction. Two parameterizations
forvirtualgravitonexchangeintheADDmodelareconsidered,namelytheGiudice–Rattazzi–
Wells(GRW)[16]andtheHan–Lykken–Zhang(HLZ)[17]conventions. Thoughnotconsidered
in this paper, another convention by Hewett [18] exists. In the GRW convention the sum over
Λ
theKKstatesisregulatedbyasinglecutoffparameter . TheHLZconventiondescribesthe
T
effectivetheoryintermsoftwoparameters,thecutoffscale M andthenumberofextraspatial
S
dimensions n . The parameters M and n can be directly related to Λ [19]. We consider
ED S ED T
scenarios with 2 to 6 EDs. The case of n = 1 is not considered since it would require an
ED
ED of the size of the order of the solar system, the gravitational potential at these distances
would be noticeably modified and is therefore excluded. The case of n = 2 is special in the
ED
sensethattherelationbetween M andΛ alsodependsontheparton-partonc.m. energy√sˆ.
S T
Signatures from virtual graviton exchange have previously been sought in dilepton [20, 21],
diphoton [22, 23], and dijet [6, 24, 25] final states, where the most stringent limits come from
thedileptonsearchesrangingfrom3.4to4.7TeV.
In this Letter, we extend previous searches for contact interactions to higher CI scales, for a
wide range of models that include the exact NLO QCD corrections to dijet production. In
addition, we explore various models of compactified extra dimensions. Using a data sample
corresponding to an integrated luminosity of 19.7fb−1 at √s = 8TeV, the measured dijet an-
gular distributions, unfolded for detector effects, are compared to QCD predictions at NLO,
includingforthefirsttimeelectroweak(EW)corrections.
2 Event selection
AdetaileddescriptionoftheCMSdetector,togetherwithadefinitionofthecoordinatesystems
usedandtherelevantkinematicvariables,canbefoundinRef.[26]. Thecentralfeatureofthe
CMSapparatusisasuperconductingsolenoidof6minternaldiameter,providinganaxialfield
of 3.8T. Within the solenoid are the silicon pixel and strip trackers, which cover the region of
3
<
pseudorapidity η 2.5. Theleadtungstatecrystalelectromagneticcalorimeterandthebrass
| | <
and scintillator hadron calorimeter surround the tracking volume and cover η 3. Muons
| |
aremeasuredingas-ionizationdetectorsembeddedinthesteelflux-returnyokeofthesolenoid
<
withacoverageof η 2.4.
| |
Events are reconstructed using a particle-flow technique [27, 28] which combines information
fromallCMSsubdetectorstoidentifyandreconstructinanoptimalwaytheindividualparticle
candidates (charged hadrons, neutral hadrons, electrons, muons, and photons) in each event.
Theseparticlecandidatesareclusteredintojetsusingtheanti-k algorithm[29]asimplemented
T
in the FASTJET package [30] with a size parameter R = 0.5. Jet energy scale corrections [31]
derived from data and Monte Carlo (MC) simulation are applied to account for the response
functionofthecalorimetersforhadronicshowers.
TheCMStriggersystemusesatwo-tieredsystemcomprisingalevel-1trigger(L1)andahigh-
leveltrigger(HLT)toselectphysicseventsofinterestforfurtheranalysis. Theselectioncriteria
usedinthisanalysisaretheinclusivesingle-jettriggers,whichrequireoneL1jetandoneHLT
jet with various thresholds on the jet p , as well as trigger paths with thresholds on the dijet
T
massandscalarsumofthejet p . The p ofjetsiscorrectedfortheresponseofthedetectorat
T T
bothL1andtheHLT. Theefficiencyofeachsingle-jettriggerismeasuredasafunctionofdijet
mass M usingeventsselectedbyalower-thresholdtrigger.
jj
Eventswithatleasttworeconstructedjetsareselectedfromaninclusivejetsampleandthetwo
highest-p jetsareusedtomeasurethedijetangulardistributionsfordifferentrangesin M . In
T jj
>
unitsof TeVthe M rangesare(1.9,2.4),(2.4,3.0),(3.0,3.6),(3.6,4.2),and 4.2. Thelowest M
jj jj
range is chosen such that the trigger efficiency exceeds 99%. Events with spurious jets from
noise and noncollision backgrounds are rejected by applying loose quality criteria [32] to jet
properties and requiring a reconstructed primary vertex within 24cm of the detector center
±
alongthebeamlineandwithin2cmofthedetectorcenterintheplanetransversetothebeam.
The main primary vertex is defined as the one with the largest summed p2 of its associated
T
<
tracks. The phase space for this analysis is defined by selecting events with χ 16 and
dijet
y < 1.11, where y = 1 y +y . This choice of values restricts the two jets within
boo<st boost 2| 1 2|
y 2.5. Thehighestvalueof M observedinthisdatasampleis5.2TeV.
jj
| |
3 Cross section unfolding and uncertainties
Themeasured χ distributions,definedas (1/σ )(dσ /dχ ),upto χ = 16ineach
dijet dijet dijet dijet dijet
M range,arecorrectedformigrationeffectsduetothefinitejet p resolutionandpositionres-
jj T
olutionofthedetector. Fluctuationsinthejetresponsecauseeventmigrationsin χ aswell
dijet
asindijetmass. Therefore,atwo-dimensionalunfoldinginthesevariablesisperformedusing
the D’Agostini method [33] as implemented in the ROOUNFOLD package [34]. The unfolding
corrections are determined from a response matrix that maps the true M and χ distribu-
jj dijet
tionsontothemeasuredones. Thismatrixisderivedusingparticle-leveljetsfrom HERWIG++
version 2.5.0 [35, 36] with the tune of version 2.4. The jets are smeared in p with a double-
T
sided Crystal-Ball parameterization [37] of the response, which takes into account the full jet
energyresponseincludingnon-Gaussiantails. Theunfoldingcorrectionfactorsvaryfromless
than3%inthelowest M rangetolessthan20%inthehighest M range.
jj jj
The main experimental systematic uncertainties in this analysis are caused by the jet energy
scale, the jet energy resolution, and the unfolding correction. The overall jet energy scale un-
certaintyvariesbetween1%and2%andhasadependenceonpseudorapidityoflessthan1%
perunitofη [31]. Thejetenergyscaleuncertaintyisdividedinto21uncorrelatedsources[38].
4 4 Theoreticalpredictions
The effect of each source is propagated to the dijet angular distributions and then summed in
quadraturetotakeintoaccountuncorrelated p -and η-dependentsourcesthatcouldcancelif
T
variedsimultaneously. Theresultinguncertaintyintheχ distributionsduetothejetenergy
dijet
scaleuncertaintiesisfoundtobelessthan2.0%(2.6%)atlow(high) M overallχ bins. The
jj dijet
maximumuncertaintyinagiven M binistypicallyfoundtobeinthelowestχ bin.
jj dijet
The largest contributions to the unfolding corrections arise from the use of the Crystal-Ball
parameterization to simulate the jet p resolution of the detector and from the uncertainty in
T
thetailsofthejetresponsefunction. Thesystematicuncertaintyfromusingtheparameterized
model of the jet p and position resolutions to determine the unfolding correction factors is
T
estimatedbycomparingthesmearedχ distributionstotheonesfromadetailedsimulation
dijet
of the CMS detector using GEANT4 [39]. This uncertainty is found to be less than 0.4% (5%)
in the lowest (highest) M range. The systematic uncertainty in the tails of the jet response
jj
functionisevaluatedbydeterminingacorrectionfactorusingaGaussianansatztoparameter-
ize the response and assigning 50% of the difference between this correction and the nominal
correctionastheuncertainty. Thesizeofthisuncertaintyvariesfromlessthan1%inthelowest
M range to less than 13% in the highest M range. Additional systematic uncertainties are
jj jj
evaluatedtoaccountfortheuncertaintyofapproximately10%[31]inthewidthofthecorejet
response function (0.5%(1.5%) in the lowest (highest) M range) and for the modeling of the
jj
dijetspectrawith HERWIG++ (0.1%(1.2%)inthelowest(highest) Mjj range),quantifiedbythe
difference to a response matrix obtained from simulation using PYTHIA 8 version 8.165 with
tune4C[40].
Theuncertaintyfromadditionalinteractionsinthesameprotonbunchcrossingastheinterac-
tion of interest, called pileup, is determined in simulation by varying the minimum bias cross
sectionwithinitsmeasureduncertaintyof6%[41]. Nosignificanteffectisobserved. Thoughin
the statistical analysis of the data the uncertainties are treated separately, for display in tables
andfigures,thetotalexperimentalsystematicuncertaintyintheχ distributionsiscalculated
dijet
asthequadraticsumofthecontributionsduetotheuncertaintiesinthejetenergycalibration,
jet p resolution, and unfolding correction. The total uncertainty including statistical uncer-
T
taintiesislessthan2.4%(49%)forthelowest(highest) M range.
jj
4 Theoretical predictions
The normalized dijet angular distributions are compared to the predictions of perturbative
QCD. TheNLOcalculationisprovidedbyNLOJET++version4.1.3[42,43]withintheFASTNLO
framework version 2 [44, 45]. Electroweak corrections for dijet production have been derived
inRef.[46], theauthorsofwhichprovideduswiththecorrespondingcorrectionsforthe χ
dijet
distributions. These corrections change the predictions of the normalized χ distributions
dijet
by up to 4% (14%) at low (high) M . A figure showing these corrections can be found in the
jj
Appendix. Thefactorization(µ )andrenormalization(µ )scalesaredefinedtobetheaverage
F R
p of the two jets, p . The impact of non-perturbative effects such as hadronization and
T T1,2
h i
multiple parton interactions is estimated using PYTHIA 8 and HERWIG++. These effects are
foundtobenegligible.
The dominant uncertainty in the QCD predictions is associated with the choice of the µ and
R
µ scales and is evaluated following the proposal in Ref. [47] by varying the default choice of
F
scalesinthefollowingsixcombinations: (µ / p ,µ / p ) = (1/2,1/2),(1/2,1),(1,1/2),
F T1,2 R T1,2
h i h i
(2, 2), (2, 1), and (1, 2). These scale variations change the QCD predictions of the normalized
χ distributions by less than 6%(18%) at low (high) M . The uncertainty due to the choice
dijet jj
of parton distribution functions (PDF) is determined from the 22 uncertainty eigenvectors of
5
CT10 [48] using the procedure described in Ref. [48], and is found to be less than 0.6%,(1.0%)
at low (high) M . A summary of the systematic uncertainties in the theoretical predictions is
jj
given in Table 1 together with the experimental ones. In the highest M range, the dominant
jj
experimental contribution is the statistical uncertainty while the dominant theoretical contri-
butionistheQCDscaleuncertainty.
Table 1: Summary of the experimental and theoretical uncertainties in the normalized χ
dijet
distributions. For the lowest and highest M ranges, the relative shift (in %) of the lowest
jj
χ bin from its nominal value is quoted. While in the statistical analysis each systematic
dijet
uncertaintyisrepresentedbyachangeoftheχ distributioncorrelatedamongallχ bins,
dijet dijet
thistablesummarizeseachuncertaintybyarepresentativenumbertodemonstratetherelative
contributions.
< < >
1.9 M 2.4TeV M 4.2TeV
Uncertainty jj jj
(%) (%)
Statistical 0.9 47
Jetenergyscale 2.0 2.6
Jetenergyresolution(tails) 1.0 13
Jetenergyresolution(core) 0.5 1.5
Unfolding,modeling 0.1 1.2
Unfolding,detectorsimulation 0.4 5.0
Pileup 1 1
Totalexperimental 2.4 49
QCDNLOscale(6variationsofµ andµ ) +6.1 +18
R F 2.1 6.3
PDF(CT10eigenvectors) −0.6 −1.0
Electroweakcorrections 0.1 0.1
Non-perturbativeeffects(PYTHIA 8 vs.HERWIG++) 1 1
Totaltheoretical 6.1 18
For calculating the CI terms as well as the interference between the CI terms and QCD terms
atLOandNLOinQCDtheCIJETprogramversion1.0[49]hasbeenemployed. TheCImodels
atLOarecross-checkedwiththeimplementationin PYTHIA 8 andfoundtobeconsistent. The
ADDpredictionsarecalculatedwithPYTHIA 8.
5 Results
InFig.1themeasuredχ distributions,correctedforinstrumentaleffectsandnormalizedby
dijet
their respective event counts, for all M ranges, are compared to theoretical predictions. The
jj
data are well described by NLO calculations that incorporate EW corrections. No significant
deviationfromtheSMpredictionsisobserved. Thedistributionsarealsocomparedtopredic-
tions for SM+CI with Λ+ (NLO) = 10TeV and predictions for SM+ADD with Λ (GRW) =
LL T
7TeV.
The measured χ distributions are used to determine exclusion limits on CI models that in-
dijet
cludefullNLOQCDcorrectionstodijetproductioninducedbycontactinteractionscalculated
withCIJET. LimitsarealsoextractedforCImodelscalculatedatLOwithCIJETandADDmod-
elsimplementedin PYTHIA 8. TotakeintoaccounttheNLOQCDandEWcorrectionsinthese
QCD QCD
LOmodels,thecrosssectiondifferenceσ σ isevaluatedforeach M andχ
NLO+EWcorr− LO jj dijet
bin and added to the PYTHIA 8 +ADD and LO QCD+CI predictions. With this procedure, an
SM+CI (SM+ADD) prediction is obtained where the QCD terms are corrected to NLO with
6 5 Results
19.7 fb-1 (8 TeV)
0.7
et
dij Data CMS
χ N LO QCD+EW prediction
d
/ 0.6 N LO QCD prediction
et
σdij ΛΛ+LL ( G(NRLWO)) == 71 0T eTVeV
d T
0.5
et M > 4.2 TeV (+0.35)
dij jj
σ
/
1 0.4
3.6 < M < 4.2 TeV (+0.2)
jj
0.3
0.2 3.0 < M < 3.6 TeV (+0.1)
jj
2.4 < M < 3.0 TeV (+0.05)
jj
0.1
1.9 < M < 2.4 TeV
jj
0
2 4 6 8 10 12 14 16
χ
dijet
Figure1: Normalized χdijet distributions for 19.7fb−1 of integrated luminosity at √s = 8TeV.
ThecorrecteddatadistributionsarecomparedtoNLOpredictionswithEWcorrections(black
dotted line). For clarity the individual distributions are shifted vertically by offsets indicated
inparentheses. Theoreticaluncertaintiesareindicatedasagrayband. Theerrorbarsrepresent
statisticalandexperimentalsystematicuncertaintiescombinedinquadrature. Theticksonthe
error bars represent experimental systematic uncertainties only. The horizontal bars indicate
thebinwidths. TheNLOQCDpredictionwithoutEWcorrectionsisalsoshown(purpledashed
dotted). The prediction for SM+CI with Λ+ (NLO) = 10TeV is shown (red solid line), and so
LL
isthepredictionforSM+ADDwithΛ (GRW)= 7TeV(bluedashedline).
T
EW corrections while the CI (ADD) terms are calculated at LO. The variations due to theoret-
ical uncertainties associated with scales and PDFs are applied only to the QCD terms of the
prediction,therebytreatingtheeffectivenewphysicstermsasfixedbenchmarkterms.
InFig.2,theχ distributionsforthetwohighest M rangesarecomparedtovariousCIand
dijet jj
ADD models. Only the two highest M ranges are used to determine limits of CI and ADD
jj
modelparameterssincetheaddedsensitivityfromthelower M rangesisnegligible.
jj
WequantifythesignificanceofaNPsignalwithrespecttotheSM-onlyhypothesisbymeansof
the likelihood for the SM-only, L , and the likelihood for the SM with new physics, L .
SM SM+NP
The L and L are defined as products of Poisson likelihood functions for each bin in
SM SM+NP
χ and for the two highest ranges of M . The predictions for each M range are normal-
dijet jj jj
ized to the number of observed events in that range. The p-values for the two hypotheses,
p (q q )andp (q q ),arebasedonthelog-likelihoodratioq = 2ln(L /L ).
SM+NP obs SM obs SM+NP SM
≥ ≤ −
Theyareevaluatedfromensemblesofpseudo-experiments, inwhichsystematicuncertainties
aretakenintoaccountvianuisanceparameterswhichaffecttheχ distribution,variedwithin
dijet
theirGaussianuncertaintieswhengeneratingthedistributionsofq[50].
7
19.7 fb-1 (8 TeV) 19.7 fb-1 (8 TeV)
dijet Data CMS dijet D ata CMS
χd N LO QCD+EW prediction χd N LO QCD+EW prediction
σ/ ddijet 0.2 ΛΛΛ++L−LLL (((NNNLLLOOO))) === 111000 TTTeeeVVV σ/ ddijet 0.2 ΛΛΛ+L−L+LL (((NNNLLLOOO))) === 111000 TTTeeeVVV
σ1/dijet0.15 ΛΛVV−V-VVA ((NNLLOO)) == 1100 TTeeVV σ1/dijet0.15 Λ ΛVV−V-VVA ((NNLLOO)) == 1100 TTeeVV
Λ (GRW) = 7 TeV Λ (GRW) = 7 TeV
T T
3.6 < M < 4.2 TeV M > 4.2 TeV
jj jj
0.1 0.1
0.05 0.05
0 0
2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16
χ χ
dijet dijet
Figure 2: Normalized χ distributions in the two highest M ranges. The corrected data
dijet jj
distributionsarecomparedtoNLOpredictionswithEWcorrections(blackdottedline). Theo-
reticaluncertaintiesareindicatedasgraybands. Theerrorbarsrepresentstatisticalandexper-
imentalsystematicuncertaintiescombinedinquadrature. Theticksontheerrorbarsrepresent
experimental systematic uncertainties only. The horizontal bars indicate the bin widths. The
predictionsforthevariousCIandADDmodelsareoverlaid.
We note that there is an observed difference between the NLO QCD calculations with EW
corrections and the NLO QCD-only hypothesis in the above defined likelihood ratio, which
correspondstoasignificanceof1.1standarddeviation.
The agreement of the data with the SM-only hypothesis is estimated by calculating p (q
SM
≤
q ) for each M bin separately. The largest difference is found in the M range 3.0–3.6TeV
obs jj jj
withasignificanceof1.4standarddeviations, correspondingtoaprobabilityof17%toobtain
a deviation from the SM-only hypothesis larger than the observed. Including the two highest
M binsinthelikelihoodreducesthissignificanceto0.9standarddeviations,correspondingto
jj
aprobabilityof39%.
Λ
Amodified-frequentistapproach[50–52]isusedtosetexclusionlimitsonthescale . Limitson
theSM+NPmodelsaresetbasedonthequantityCL = p (q q )/(1 p (q q )),
s SM+NP obs SM obs
≥ − ≤
which is required to be 0.05 for a 95% confidence level (CL) exclusion. The observed and ex-
pectedexclusionlimitsondifferentCIandADDmodelsobtainedinthisanalysisat95%CLare
listedinTables2and3respectively. NotethattheCIpredictionswithexactNLOQCDcorrec-
tionsshowasmallerenhancementatlowχ relativetoQCDthandothecorrespondingLO
dijet
CIpredictions,asdescribedindetailinRef.[53],andthereforeresultinlessstringentlimits.
These results are also summarized in Fig. 3. The limits on M for the different n (n 2)
S ED ED
directly follow from the limit for Λ . As a cross check, the limits for the CI scale Λ+ ≥are
T LL/RR
alsodeterminedforthecaseinwhichthedataarenotcorrectedfordetectoreffectsandinstead
the simulation predictions are convoluted with the detector resolutions. The extracted limits
arefoundtoagreewiththequotedoneswithin1%. Wealsoquantifytheeffectoftheinclusion
of EW corrections in the QCD prediction on the Λ+ (LO) observed limit, which would be
LL/RR
reducedfrom10.3TeVto9.8TeVifEWcorrectionswereneglected.
8 5 Results
Table 2: Observed and expected exclusion limits at 95% CL for various CI models. The un-
certainties in the expected limits considering statistical and systematic effects for the SM-only
hypothesisisalsogiven.
Model Observed(TeV) Expected(TeV)
Λ+ (LO) 10.3 9.8 1.0
LL/RR ±
Λ
(LO) 12.9 12.4 2.2
−LL/RR ±
Λ+ (NLO) 9.0 8.7 0.8
LL/RR ±
Λ
(NLO) 11.7 11.4 1.8
−LL/RR ±
Λ+ (NLO) 11.3 10.8 1.1
ΛVV ±
(NLO) 15.2 14.6 2.6
ΛV−+V (NLO) 11.4 10.9±1.1
ΛAA ±
(NLO) 15.1 14.5 2.6
Λ−+AA (NLO) 8.8 8.5 ±1.1
(V A) ±
Λ −
(NLO) 8.9 8.6 1.2
−(V A) ±
−
19.7 fb-1 (8 TeV)
18.5
CMS Observed
Contact interaction Expected
Λ+ Expected ±1σ
LL/RR
-
Λ
LL/RR
Λ+
VV
-
Λ
VV
Λ+
AA
-
Λ
AA
Λ+
(V-A)
-
Λ
(V-A)
ADD
Λ (GRW)
T
M (HLZ) n =2
S
ED
M (HLZ) n =3
S
ED
M (HLZ) n =4
S
ED
M (HLZ) n =5
S
ED
M (HLZ) n =6
S
ED
0
6 8 10 12 14 16 18
Lower limit [TeV]
Figure 3: Observed (solid lines) and expected (dashed lines) 95% CL lower limits for the CI
Λ
scales for different compositeness models (NLO), for the ADD model scale with GRW pa-
rameterization Λ and for the ADD model scale with HLZ parameterization M . The gray
T S
bandsindicatethecorrespondinguncertaintiesintheexpectedexclusionlimits.