Quark Excitations Through the Prism of Direct Photon Plus Jet at the LHC

0.54 MB·English

by  Satyaki Bhattacharya

Quark Excitations Through the Prism of Direct Photon Plus Jet at the LHC
Satyaki Bhattacharya∗, Sushil Singh Chauhan†, Brajesh Chandra Choudhary‡ and Debajyoti Choudhury§
Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
Thequesttoknowthestructureofmatterhasresultedinvarioustheoreticalspeculationswherein
additional colored fermions are postulated. Arising either as Kaluza-Klein excitations of ordinary
quarks, or as excited states in scenarios wherein the quarks themselves are composites, or even
in theories with extended gauge symmetry, the presence of such fermions (q∗) can potentially be
manifested in γ+jet final states at theLHC. Using unitarized amplitudes and the CMS setup,we
9
0 demonstratethatintheinitialphaseofLHCoperation(withanintegratedluminosityof200pb−1)
0 one can discover such states for a mass upto 2.0 TeV. The discovery of a q∗ with a mass as large
2 as 5 TeV can be acheived for an integrated luminosity of 140fb−1. We also comment on the
∼ ∼
feasibility of mass determination.
n
a
PACSnumbers: 12.60.Rc,13.40.-f,13.85.Qk
J

5
2 I. INTRODUCTION with quarks and/or leptons. In many such models[3, 4],

though not all, quarks and leptons share at least some
]
h common constituents.
Thereplicationoffermionfamilies,whilebeingofpro-
p Accepting this hypothesis would naturally lead to the
found significance in our understanding of fundamental
- existence of excited states of fermions at a mass scale
p issues such as CP-violation and baryogenesis, nonethe-
e lessispuzzlinginitsownright. Despiteitsenormoussuc- comparable to the dynamics of the new binding force.
h In the simplest phenomenologicalmodels [5], the excited
cess in explaining all observed phenomena in the regime
[ fermions are assumed to have both spin and isospin 1/2
of particle physics, the Standard Model (SM) has been
andtohaveboththeirleft-andright-handedcomponents
1 entirelyunabletoprofferanyinsightintothisaspect. In-
v deed, though the observed mass hierarchies and fermion in weak isodoublets (i.e. they are vector-like). Similar is
7 mixingscaneasilybeaccommodated,theSMframework, the case for, say higher-dimensional models wherein the
2 known universe is constrained to be on a 4-dimensional
byitsverystructure,isunabletoevenasksuchquestions
9 subspace (a 3-brane) while the SM fields—in particular,
ofitself. Thishasledtovariousspeculativeideasseeking
3
the fermions—live in all the dimensions. The analogues
. to explain these ill-understood issues. Prominentamong
1 of the excited fermions would be the Kaluza-Klein ex-
these are (i) models with extended (family) symmetry,
0 citations with the mass scale being identified with the
(ii) constructions based on higher dimensional theory
9 inverse of the compactification scale.
(withorwithoutastringtheorymotivation)and(iii)the
0
Giventhatthe“excitedstates”dosuffertheSMgauge
: possibility of quark-lepton compositeness, namely that
v interactions, these may be produced at high-energy col-
the SM fermions are not elementary at all.
i lidersand,subsequently,woulddecay,radiatively,intoan
X Many of the ideas discussed in this article would be
ordinary fermion and a gauge boson (photon, W, Z or
r equally applicable—possibly with minor variations—to
a gluon). At an e+e− collider, charged excited fermions
theories belonging to any of these three classes. How-
could be pair-produced via s-channel (γ and Z) ex-
ever, for the sake of concreteness, we shall consider the-
changes in collisions, while for excited neutrinos only Z
ories of compositeness as the basic template for our dis-
exchange contributes. Although t-channel diagrams are
cussions. Part of the motivation lies in the fact of these
also possible (W for ν∗ and γ/Z for e∗), such contri-
theories having a more straightforward ultraviolet com- e
butions to the overall pair production cross-section are
pletion and, furthermore, suffering from a fewer number
generally much smaller on account of the smallness of
of extra channels,thereby reducing possible ambiguities.
the cross-couplings [5] between the excited state, its SM
Insuchtheories,the fundamental constituents ofmat-
counterpart and a gauge boson. This very same cou-
ter,veryoftentermedpreons[1],arepostulatedtoexperi-
pling, on the other hand, may be used to singly produce
ence anhitherto unknownforceonaccountofanasymp-
such states (through both s- and t-channel diagrams).
totically free but confining gauge interaction[2], which
ThefourLEPcollaborationshaveusedthese(andother)
becomes very strong at a characteristic scale Λ, thereby
modestoessentiallyruleoutsuchexcitationsalmostupto
leading to bound states (composites) to be identified the kinematically allowed range [6]. At the hera, on
the other hand, both excited leptons and quarks may be
produced singly through t-channel diagrams and these
processes have been looked at without any positive re-
∗EmailAddress: [email protected]
sults [7].
†EmailAddress: [email protected]
‡EmailAddress: [email protected] If quarksand leptons are composite particles made up
§EmailAddress: [email protected] ofsmaller constituents, phenomenologicaleffects may be
2
observableatthe LHC andmightevenshow up atTeva- process gleaned from previous experiments and studies.
tron once sufficiently large luminosities are accumulated The rest of the paper has been organized as follows.
and analysed. If the compositeness/excitation scale (Λ) In section II we have discussed the effective Lagrangian
is not too high, then excited quarks can be produced on for the theory andnew physics contribution. In Sections
shell,whileatenergiessufficientlybelowΛsuchaneven- III and IV, we respectively discuss the backgrounds and
tuality would manifest itself as an effective four fermion event generation. Section V describes the photon and
contact interaction invariant under SM guage transfor- jet algorithms used for the analysis. In section VI we
mations [8, 9]. Based on phenomenological studies of discuss the smearings due to detector resolution effects.
flavour independent contact interactions for two photon SectionVIIgivesthedetailsofkinematicalvariablesused
production, the lower bound has been estimated to be to separate the signalfromthe backgroundwhereas Sec-
Λ >2.88(3.24)TeVat95%CL foranintegratedlumi- tion VIII deals with isolation study. The significance of
±
nosity of 100 (200) fb−1 [10] at the LHC. signalanddiscoveryarediscussedinsectionIXandXre-
Both the experiments at the Tevatron, the CDF and spectively. In section XI we have presented the result of
DØ, have searchedfor excited quarks. The latter are as- the analysis. Systematics isdiscussedindetailin section
sumed to couple to the SM particles primarily through XII followed by our conclusions and outlook.
gauge couplings. Their most visible signature could be
either pair production or single excited state production
viaquark-gluonfusion,providedtheq∗qg couplingissuf- II. NEW PHYSICS CONTRIBUTION TO γ+Jet
ficiently large. Enhanced dijet production rate with an PRODUCTION
invariant mass peak above the SM continuum is one of
the prominent signals, extensively searched for at the With our interest lying not in the pair-production of
Tevatron and the DØ collaboration has excluded the such excited states, but rather on their contribution to
mass range of 200-720 GeV[11]. Similarly, the CDF col- the photon plus single jet rates at a hadronic collider,
laboration has excluded a mass range of 80-570 GeV we confine ourselves to examining only the relevant part
[12, 13] based on searches with various final states. In of the Lagrangian, namely the (chromo-)magnetic tran-
a similar vein, the CDF collaboration has put a lower sition between ordinary and excited states. In general,
bound of Λ 2.81 GeV at 95% CL using the qq¯ eν these may be parametrized by
≥ →
prcoess[14] whereas the DØ collaboration rules out Λ
≤
2.0 TeV at 95% CL from diject mass peak searches[15]. 1
= q¯∗ σµν g b Ta Ga q +h.c., (1)
AttheLHC,boththeATLASandtheCMScollabora- Lint 2Λ R " i i i iµν# L
i
tions have predicted the sensitivity in the dijet produc- X
tion mode. The ATLAS collaboration has xlaimed that where the index i runs over the three SM gauge groups,
the use nof dijet angular distributions would allow con- viz. SU(3), SU(2) and U(1) and g , Ga and Ta are
i iµν i
tact interactions to be probed upto Λ =10 TeV with a the corresponding gauge couplings, field strength ten-
integrated luminosity of 700 pb−1. The CMS collabora- sors and generatorsrespectively. The dimensionless con-
tion, onthe other hand, hasestimated thatΛ= 6.2TeV stants b are, a priori, unknown and presumably of or-
i
canbeexcludedat95%CLwithaluminosityof100pb−1 der unity. With these determining both the production
and that 5σ sensitivity could be reached for Λ =8 TeV rates and the branching into various modes, clearly, the
with just 1fb−1 of data[16]. Recently, the possibility of phenomenologywoulddependconsiderablyontheir(rel-
top quark compositeness has been explored through the ative)sizes. Inthisarticle,weshallmakethesimplifying
pp tt¯tt¯production process and it has been estimated assumption that the excited states do not couple at all
→
thata5σexcesscanbeobservedforanewstateof2TeV tothe weakgaugebosons,butdo sowiththe gluonsand
[17]. the photon. At first glance, this might seem incompat-
As an effective tool for the measurement of gluon ible with a SU(2) U(1) invariant structure. However,
⊗
density inside the colliding hadrons and for precision complicatedembeddingscouldbetheanswer. Morethan
test of pQCD predictions, the isolated γ+jet final state this, since the assumption would not change the results
has been studied with great detail at the Tevatron qualitatively, it, at least, has the merit of reducing the
collider[18, 19, 20] and fixed target experiments[21]. number of possible couplings and hence simplifying the
Since γ + jet final state will be one of the key back- analysis.
grounds for the H γγ search at the LHC, extensive A further point needs to be noted here. With the La-
→
isolation studies addressing all known issues have been grangian of eq.(1) being a higher dimensional operator,
performed with this process both theoretically and with the cross sections would typically grow with the center
detailed detector simulations. It is also an important of mass energy, consequently violating unitarity. This
backgroundformanynewphysicsscenarioe.g. LargeEx- is not unexpected in an effective theory as the term in
tra Dimensions[22, 23], Randall Sundrum Gravitons[24] eq.(1) is only the first term and the loss of unitarity, to
etc. It will, thus, be very interesting to look at γ+jet as a given order, is presumably cured once suitable higher
a probe of excited quarks in view of the unprecedented dimensional operators are included. An equivalent way
energy scale at LHC and the in-depth knowledge of this to achieve the same goal is to consider the b to be form
i
3
γ
factorsratherthanconstants. Tothisend,weshalldefine q γ q
the q∗qγ and q∗qg vertices to be given by
q
q*
ee f Q2 −n1
q∗qγ (p): q 1 1+ σ pν
µ Λ Λ2 µν g q g q
g f (cid:18) Q2 −(cid:19)n3 (2) (a) (b)
q∗qg (p): s 3 1+ σ pν T
µ Λ Λ2 µν α q γ q γ
(cid:18) (cid:19)
where Q denotes the relevant momentum transfer and
fi 1aredimensionlessconstantsrelatedtobiofeqn.(1). q* q
It ∼can be checked that, for Q2 = s, unitarity is restored
as long as the constants n 1. From now on, eqn.(2)
i
definesourtheory[1]. Forthe≥restofouranalysis,weshall g q g q
confine ourselves to a discussion of n = 1. While this (c) (d)
i
might seem to be an optimistic choice, it is not quite so.
Infact,thecollidersearchlimitsintheliteratureactually FIG. 1: Production of γ +Jet final state through excited
correspondton =0and,thus,ourlimitswouldbemore quark mediation (a & c) as well as SM processes (b & d).
i
conservative.
WiththeaforementionedLagrangian,thewidthofthe
q is given by contribution as portrayed in Fig.1(a). Adding this con-
∗
tribution to the pure QCD one, the ensuing differential
Γ(q ) = Γq+g+Γq+γ cross section reads
∗
Γq+g = 2αsf32 Γ0 dσ = −πααse2q C +2f1f3C + f12f32C
3 dtˆ 3sˆ2 sm Λ2 I Λ4 Q
Γ = e2qαf12 Γ (3) (cid:12)(cid:12)(cid:12)qg→qγ uˆ sˆ (cid:20) (cid:21)
q+γ 2 0 (cid:12) Csm +
≡ sˆ uˆ
2
Γ0 ≡ MΛq23∗ 1− 4Mmq2∗2q! 1− Mmq22q∗! CI ≡ (sˆ−sˆ2M(sˆq2−∗)M2+q2∗Γ)2FMsq2∗ + uˆuˆ−2FMuq2∗
and can be very large for a heavy q∗ (see Table I). As a CQ ≡ sˆuˆ+Mq2∗t
fat resonance is often difficult to observe, this will turn
(cid:0) sˆ2(cid:1) 2 uˆ2 2
out to have profound consequences. Fs + Fu
"(sˆ−Mq2∗)2+Γ2Mq2∗ (uˆ−Mq2∗)2 #
TplAinBgLsEtreI:ngΓth(qs.∗)Baosthaαfusnacntidonαeomf Marqe∗(e=vaΛlu)afoterddaiffteMrenq∗t.cou- + 2Mq2∗uˆ−sˆtˆMuˆq2∗ (sˆ(−sˆ−MMq2∗)q22∗)+FΓs2FMuq2∗
Mq∗ Γ (GeV) s 1+sˆ/Λ2 −(n1+n3)
F ≡
(TeV) f1 =f3 =1.0 f1 =f3 =0.5 (cid:0)1 tˆ/Λ2(cid:1)−(n1+n3)
t
0.5 34.4 8.61 F ≡ −
1.0 63.6 15.9 (cid:0)1 uˆ/Λ2(cid:1)−(n1+n3)
2.0 118 29.6 Fu ≡ −
3.0 170 42.6 (4)
(cid:0) (cid:1)
4.0 221 55.2 with the SM result being recoveredin the limit Λ .
→∞
5.0 271 67.6 Thenewphysicscontributiontothedifferentialcrosssec-
6.0 319 79.8 tion thus depends on four parameters, namely f ,f ,Λ
1 3
7.0 367 91.8 andthemassoftheexcitedstateMq∗. Forsimplicity,we
assumethesetobeflavour-independent(withinagenera-
tion, it obviouslyhas to be so). For eq.(1) to make sense
With the introduction of these (flavour-diagonal) ver-
as an effective Lagrangian, the masses have to be less
tex as in eq.(2), the subprocess qg qγ acquires a new
→ than Λ (Ref.[25] requires that Mq∗ < Λ/√2). Note that
aslongasΛ sˆ,oneoff canalwaysbeabsorbedinΛ.
1,3
≫
In our analyses, we would be considering only moderate
values for these parameters.
[1]While a Lagrangian formulation leading to such vertices would
For qq¯ gγ,the Feynmandiagramsare as in Fig.1(c-
necessitate a seemingly non-local Lagrangian, this is not unex-
→
pectedinaneffective theory. d); the differential cross-sections are related to those in
4
eqn.(4) by crossing symmetry and are given by g γ
dσ = 8πααse2q B 2f1f3B + f12f32B
dtˆ 9sˆ2 sm− Λ2 I Λ4 Q
(cid:12)qq¯→gγ (cid:20) (cid:21)
(cid:12) g g
(cid:12) uˆ tˆ
(cid:12) B +
sm ≡ tˆ uˆ
tˆ2 uˆ2 FIG. 2: Type-I Background: Additional contribution from
B Ft + Fu gluon fusion. Lowest order background emanates from (b)
I ≡ tˆ−Mq2∗ uˆ−Mq2∗ and (d) in Fig.1.
tˆ2 2 uˆ2 2
B tˆuˆ Ft + Fu
Q ≡ "(tˆ−Mq2∗)2 (uˆ−Mq2∗)2# q g
2 q q
tˆ uˆ
+ Mq2∗sˆ"tˆ−FMtq2∗ + uˆ−FMuq2∗# q g
(5)
q
q
g q
III. BACKGROUNDS q q g g
Theγ+jetfinalstatecanbemimickedbymanyknown
processesoftheSM.Weconsideralltheleadingcontribu- g g
tions(boththephysicsbackgroundsaswellasthe detec-
tor ones) and broadly categorize these into three classes
viz., q q g g
Type-I:where a photonand a hard jet is produced FIG. 3: Type-II Background: QCD jet production where a
• in the hard scattering. jet fakes a photon giving a γ+Jet final state.
Type-II:QCDdijet,whereoneofthejetsfragments
• into a high ET π0 which then decays into a pair of ina2 2hardscatteringprocess),the totalproduction
overlapping photons and, hence, is registered as a crosss→ectionis 104 times largerthanthe Type-I back-
singlephoton. Moreover,insomecasesthe electro- ground. Howeve∼r,the factofthe probabilityofa jet fak-
magnetic fraction of a jet can mimic a photon in ingaphotoninthedetectorbeing 10−3 10−4reduces
the detector. theType-IIbackgroundtothesam∼eorder−asthe Type-I.
Moreover, for high transverse momenta the QCD dijet
Type-III: Photon + dijet production, where one of
• falls very rapidly ( P−4), thereby suggesting a simple
the jets is either lost or mismeasured. This could ∼ T
mechanism of suppressing this background
proceed either from hard processes such as qq¯
→ Although the total Type-III background is very small
qq¯γ,ggγ (with all possible interchanges of initial
comparedtotheothers,fortheP rangeunderconsider-
and final state partons) or result from W/Z + γ T
ationinthisanalysis,itturnsouttobeofthesameorder
production with the heavy bosons decaying into a
as gg γg. And while nonresonant subprocesses (such
pair of jets. →
as the (α2α) contributions to qq¯ qq¯γ or gg qq¯γ)
O s → →
While the leading contributions to the Type-I back- can,inprinciple,besubstantial,notethatthese,insome
ground emanates from the SM amplitudes of Fig. 1, a sense are related to the much larger Type-I and Type-II
further contribution is displayed in Fig.2. In Figs.3 & 4, backgrounds. Consequently,theformeraretypicallysup-
we show the major contributing Feynman diagrams for pressed when appropriate phase space cuts are imposed
the Types II & III backgrounds respectively.
At the LHC, the Type-I background is dominated by q γ q γ
the Compton process (qg γq), while the other two
→
subprocesses,namelyanihilation(qq¯ γg)andgluonfu-
→
sion (gg γg) contribute only a small fraction in the q q
→
low transverse momentum (P ) ranges. For higher P ,
T T
the annihilation subprocess can contribute upto about
23% of the total Type-I background. q Z0 q’ W
∼
TheType-IIbackgroundaccruesmainlyfromqg qg,
qq¯ qq¯andgg gg. ForPˆ 200GeV(herePˆ →isthe FIG.4: Type-IIIBackground: HereW/Z0 decaystotwojets
T T
P →oftheoutgoi→ngpartonsinc≥enterofmomentumframe and only oneof thejets passes the trigger threshold.
T
5
TABLEII: Production cross section in different PˆT binsfor various Standard Model backgroundswith γ+Jet final state.
Subprocess 50-100 GeV 100-200 GeV 200-400 GeV 400-600 GeV 600-1000 GeV 1000-1500 GeV 1500 GeV and above
(pb) (pb) (pb) (pb) (pb) (pb) (pb)
qg γq 7.22 103 569 36.3 1.53 2.22 10−1 1.19 10−2 7.6 10−4
qq¯→γg 65×2 65.3 5.56 3.18 10−1 5.67×10−2 3.76×10−3 2.8×10−4
gg→γg 1.79 8.6 10−2 3.1 10−3 7.04×10−5 6.32×10−6 1.75×10−7 5.8×10−9
→ × × × × × ×
QCD Jet 1.71 107 9.70 105 4.44 104 1.39 103 171 8.19 5.34 10−1
× × × × ×
aZ(jj)+γ 5.08 8.49 10−1 9.50 10−2 6.23 10−3 1.16 10−3 8.48 10−5 6.46 10−6
aW(jj)+γ 4.80 6.93×10−1 6.19×10−2 4.16×10−3 7.39×10−4 4.67×10−5 2.99×10−6
× × × × × ×
aHerethebranchingfractionistakenintoaccount.
to reduce the latter. here that in the final selection of γ, we have used the
In Table-II we show the production cross section for fiducial volume of the electromagneticcalorimeter of the
all backgrounds in different Pˆ ranges. CMS detector i.e. η 2.5 with 1.444 η 1.566 ex-
T
| |≤ ≤| |≤
cluded on account of the insensitive region between the
barrel and the endcaps[28]. The jets were selected up to
IV. EVENT GENERATION & CUTS η 3.0 only, because of poor resolution in the forward
| |≤
calorimeter.
The event generation for signal and different back-
groundprocesseswasdonewithpythia-v6.325[26]. For
Fig. 5 shows the deviation in the total cross-sectionof
saingdna(l5)evwenertegiemnperleamtioenntetdheinmsiadteritxheelepmytenhtisaoffraEmqw.o(r4k). tqigon→isγw+eljl-eatpapsrfouxnimctaiotnedobfyMaq∗Λ(−=2Λco)n.tCrilbeuartliyo,ntshuepvearrimia--
We used the following common parameters and pythia posed upon a constant (the SM value). This is reflective
switches:
of the fact that, for large Λ, the new physics contribu-
tion is dominated by the interference term in Eqs.(4,5)
• Parton Distribution Function(PDFs): CTEQ ratherthanthe pureΛ−4 term. Only ifwe hadimposed
5L [27];
harder cuts on the photons, would the latter term have
Q2 = sˆ; dominated (albeit at the cost of reducing event numbers
• and hence the sensitivity).
MultiParton Interaction(MPI): “ON”;
•
Initial State Radiation(ISR) and Final State Radi-
•
ation (FSR): “ON”.
LHC s =14TeV
104
To get enough statistics for both the signal and the qg→ γ+jet
backgrounds, we divided the whole analysis into three qq→ γ+jet
phase space regions determined by the value of the P 103
T
of the final state γ and the jet. For this purpose, the
followingPˆT (ckin(3)parameterofpythia)criteriawere (fb)M102
used for different mass points of signal: S
σ
Pˆ 180GeV: 1.0–3.0 TeV, σ - 10
T
• ≥
PˆT 450GeV: 3.5–4.5 TeV, 1
• ≥
Pˆ 950GeV: 5.0–6.0 TeV.
T
• ≥ 10-1
1 2 3 4 5 6
A total of 16 mass points, 11 for coupling strength M = Λ (TeV)
q*
f = f = 1.0 (with a step size of 0.5 TeV) and 5 for
1 3
f =f =0.5weregenerated. Thedifferentbackgrounds
w1ere a3lso generated in various PˆT range. No pseudora- FatIG√.s5=: D14evTiaeVtio.n of cross section from SM with Mq∗(= Λ)
pidityrestrictionwasappliedwhilegeneratingtheevents
as the large Pˆ cut requirement naturally restricts the
T
events to well within η < 5.0. We must also mention
| |
6
V. PHOTON AND JET CANDIDATES AT THE scheme( Pi). The computed direction is then used to
GENERATOR LEVEL seed a new proto-jet. The procedure is repeated until
P
both the energy and the direction of the putative jet is
Although a mass peak in the signal will appear as an stable between iterations. We quantify this by requiring
excessofevents overthe continuumSMbackground,the that the energy should change by less than 1% and the
significance for such an observation will depend on the direction by less than ∆R=0.01. When a stable proto-
size of this continnum. Hence, to enhance the signal jetisfound,allobjectsintheproto-jetareremovedfrom
peak,itisnecceassarytoreducethebackgroundasmuch the listofinputobjectsandthe stable proto-jetisadded
as possible. For the signal under investigation, QCD di- to the list of jets. The whole procedure is repeated until
jet is the largest background, as it mimics γ+jet final the list is bereft of objects with an ET above the seed
state when one of the jet fakes a photon. To estimate threshold. The cone size and the seed threshold are the
this backgroundreasonablyat the generatorlevel, it is a parameters of the algorithm.
must to have a proper understanding of the reconstruc-
tionalgorithmforaspecificdesignofthe detectorrather
VI. SMEARING EFFECTS
than limit ourselves to only partonic level photon and
jets from the final state in an event.
Taking this into consideration, we have used a clus- While a detailed and full-scale detector simulation is
teringalgorithmtoaccountforfakephotonsarisingfrom beyond the scope of this work, realistic detector effects
jets[29]. Theelectromganeticcalorimeter(ECAL)ofthe can easily be approximated. To this end, we smear the
CMS detector is made up of PbWO crystals and each generatorlevelinformation with ECAL and HCAL reso-
4
crystal covers 0.0175 0.0175 (equivalently, 1◦) in the lutions of the CMS detector.
∆η ∆φspace(φbein×gtheazimuthalangle). Forphoton For the ECAL resolution function, we use the form
−
reconstruction, we have used the “hybrid” algorithm[30]
δE a a
where we consider only those final state electromagnetic = n C (6)
particles (i.e., γ,e+ ande−) in the η φ space suchthat E √E ⊕ E ⊕
−
neither ofthe distances∆η and∆φ fromthe seedobject
whereadenotesthestochasticterm,a isthewhitenoise
n
exceeds 0.09. This extension is equivalent to a 10 10
× termandC istheconstantterm,withthethreecontribu-
crystalsizeintheCMSdetector. Theseedforsuchaclus-
tionsbeingaddedinquadrature. Foreachoftheseterms,
teringmusthaveaminimumP of1GeV.Aphotoncan-
T we use values identical to those for the electromagnetic
didate is either a direct photon or other electromagnetic
calorimeter of the CMS [30], namely
obejcts such as π0 γγ,ρ0 γγ etc. The main con-
tribution of fake ph→otons com→es from π0 γγ( 81%), C = 0.55%
→ ∼
η γγ( 12%) while other sources give only a small 2.1 10−3GeV η <1.5
→ ∼
contribution. A detailed discussion of this reconstruc- a = × | |
tion algorithm at the generator level can be found in a n ( 2.45 10−3GeV 1.5 η 2.5
× ≤| |≤
previous work [31]. 2.7 10−2GeV1/2 η <1.5
a = × | |
For jet reconstruction, various algorithms have been
( 5.7 10−2GeV1/2 1.5 η 2.5 .
usedbydifferentcolliderexperiments. Theseinclude the × ≤| |≤
MidpointCone[32],IterativeCone[33,34],andtheK al-
t Theresolutionsfor∆ηand∆φweretakentobe0.02and
gorithms [35, 36, 37]. The K and MidPoint algorithms
t 0.001 respectively for both the barrel and endcap.
are used mostly for offline analysis. Since we have used
Forthehadroniccalorimeter,theresolutionswereonce
the CMS setup in our analysis,we use the IterativeCone
again assumed to be the same as those for the CMS
algorithm to reconstruct jets at the generator level. Be-
HCAL [39, 40], namely,
ingmuchfaster,thisiscommonlyusedforsoftwarebased
triggers. While the first algorithms for the jets at the Barrel:
•
hadroncollidersstartedwithsimpleconesinthe∆η ∆φ
− δE 65%
space [38], clustering techniques have greatly improved = 5%,∆η =0.04,∆φ=0.02
in sophistication over the last two decades [32, 35]. E E/GeV ⊕
Forarealdetector,thefirststepinthereconstruction,
p
before invoking the jet algorithm, is to apply noise and Endcaps:
•
pile-up suppression with a set of cuts on E . To make
T
δE 83%
“perfect detector jets”, we used a seed P cut on the
T = 5%,∆η =0.03,∆φ=0.02
P -ordered final state particles and selected only those E E/GeV ⊕
T
which had a transverse momentum above the required
p
minimum[2] of P 1.0 GeV. Once the seed is se-
Tseed
≥
lected, we search around for all the particles in a cone
of ∆R 0.5. The objects inside the cone are used to
[2]Theseedthresholdcanvaryfrom0.5to 2.0GeVdependingon
≤
calculate a proto-jet direction and energy using the E- theenergyofreconstructedjet.
7
Forwardregion:
• TABLE III: Preselection-efficiency and geometrical accep-
δE 100% tencefor various SMbackgrounds and few signal points.
= 5%,∆η =0.04,∆φ=0.04 .
E E/GeV ⊕ Selection Cut Signal γ+Jet QCD Z+γ W +γ
% % % % %
p Pγ,jet 200GeV 48.7 44.2 0.90 38.4 37.1
The four momenta of the photon and jet were recal- T ≥
[1 TeV]
culated after applying these resolution effects using an
appropriate Gaussian smeared function. In Fig. 6, we
Pγ,jet 500GeV 40.2 39.8 0.42 50.4 50.6
show the effect of resolutionon the mass peak for a Mq∗ T ≥ [4 TeV]
of 1 TeV.
It should be noted that the ATLAS detector at the Pγ,jet 1TeV 47.4 46.0 0.51 58.8 59.9
LHChasabetterjetenergyresolutionwiththeconstant T ≥ [5 TeV]
term being 2 % [41] compare to 5 % in the CMS
∼ ∼
detector. Onthe other hand, the CMS ECAL has a bet- ηγ 2.5, ηjet 3.0, 42.4 38.2 0.81 32.8 33.2
ter resolution than the ATLAS one owing to a smaller |ηγ|≤ [1.44|42,1|.≤5666] [1 TeV]
| |6∈
constant term. However,with the resolving power being
dominated by the jet energy resolution, ATLAS should 38.2 37.8 0.40 47.4 48.4
do somewhat better. In other words, our results corre- [4 TeV]
spond to a conservative choice.
46.4 45.0 0.50 56.3 58.7
[5 TeV]
6000
Smeared
Unsmeared
5000
bands. It may be noted that the QCD dijet background
is more than 10 times as large as the signal, but falls
s4000
nt very rapidly with Pγ/jet (the mistagging probability has
e T
Ev already been included). Fig. 7(f) shows the distribution
3000
in the subprocess center of mass scattering angle, with
cosθ∗ = tanh[(ηγ ηjet)/2.0]. Note that major differ-
−
2000 ences between the signal and background profile occur
onlyforp andinvariantmassdistributions,whereasthe
T
otherphasespacevariablesarenotverysensitivediscrim-
1000
inants.
800 850 900 950 1000 1050 1100 1150
M (GeV)
γ-jet Fig. 8 shows similar distributions as in Fig. 7 but for
the Mq∗ = 5 TeV point instead. For these distributions
FIG. 6: Effect of smearing on the mass peak for an excited we have used a Pγ,jet cut of 1 TeV at the pre-selection
T
quark of 1 TeV.
level. With the P spectrum for the photon from QCD
T
background falling very rapidly, the signal dominates
overthe backgroundabove 2 TeV even without isolation
cuts. As for the corresponding invariant mass (M )
γ−jet
VII. KINEMATICAL VARIABLES distribution—see Fig. 8(e)— a combination of the large
natural width and smearing effects results in a broad
InFig.7,weshowthekinematicaldistributionsforthe bump rather than a sharp one. Once again, the other
leading photon and the leading jet for Pγ,jet 200 GeV distributions do not discriminate between the signaland
T ≥
dataset for the background and the signal for Mq∗ =1 backgroundin any forceful manner. While the the slight
TeV. For purpose of visual clarity, the distributions for dip in the central ηγ region for the W +γ process might
Z +γ and W +γ backgrounds have been scaled up by seem intriguing (especially in the absence of any such
a factor of 10. The bump in the transverse momentum dipin theZ+γ distribution), itis but astraightforward
distributionsareprimarilydrivenbytheon-shellproduc- reflection of the well-known Radiation-Amplitude-Zero
tion of the q∗ and, therefore, are centred slightly below (RAZ) present in the former [42, 43]. That the RAZ in
Mq∗/2. As is evident from Fig. 7(e), an excess in the in- the angular distributuion is apparent only for the high
variantmassspectrumwouldbequiteprominentforeven Pγ,jet cutoff case can be understood by realising that
T
L.dt =1pb−1. The t-channel contribution has been in- the rapidityofthe photonas measuredinthe laboratory
cluded and manifests itself in the elongation of the side can be related to the rapidity (scattering angle) in the
R
8

-1No of Events / 10.00 GeV / 1 pb11111000100----0432121 QSZγW i+C( gj( DjjnJ)j )ae + d+lt iγ jγe ( tx(x 1 100)) -1No of Events / 10.00 GeV / 1 pb111100010----014321 QSWγZ iC+( g(j DjjnJ)j) ae + d+lt iγ jγe ( t(xx 1 100))
10-50a 200 400 600 800 1000 1200 1400 1600 10-50 200 400 600 800 1000 1200 1400 1600
(a) PγT (GeV) (b) PTjet (GeV)

Signal Signal
-11 pb 101 WγZQ C+( (j jDjJ)j) e+ d+t iγ jγe ( tx(x 1 100)) -11 pb 101 WγZQ C+( (j jDjJ)j) e+ d+t iγ jγe ( tx(x 1 100))
12 / 10-1 12 / 10-1
0. 0.
s / s /
nt10-2 nt10-2
e e
v v
E E
o of 10-3 o of 10-3
N N
10-4 10-4
10-5 -4 -2 0 2 4 10-5 -4 -2 0 2 4
(c) ηγ (d) ηjet

Signal 10
-1V / 1 pb 101 QWγZ C+( (j DjjJ)j) e + d+t iγ jγe ( t(xx 1 100)) -1ns / 1 pb 1
No of Events / 10.00 Ge11110000----4321 No of Events / 0.01 radia11110000----4321 γZQS iC +(g j jDn J) a e+ dl t iγ j e ( tx 1 0 )
W (jj) + γ (x 10)
10-5 500 1000 1500 2000 2500 3000 3500 4000 10-50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(e) Mγ-jet (GeV) (f) |Cosθ*|γ-jet
FIG.7: Kinematicvariabledistributionsafter200GeVpre-selectioncutonPT (a)PTγ distribution(b)PTjet distribution(c)ηγ
distribution (d) ηjet distribution (e) Mγ−jet distribution and (f) cosθ∗ γ−jet. The signal corresponds to Mq∗ =1TeV.
| |
partonic subprocess center of mass frame through geometricalacceptencesfortheCMSdetectorforvarious
backgrounds and signal of Mq∗ =1, 4 and 5 TeV against
1 x
η(γ)= ln 1 +η∗(γ) the total generated events.
2 x
(cid:18) 2(cid:19)
where x are the momentum fractions of the incom-
i
ing partons. For small sˆ values (hence lower ckin(3) VIII. ISOLATION VARIABLES
cuts)thepartondensitiesaremaximizedwhenthe(anti-
)quark acquire small(large) momentum fractions respec- In a detector, a photon candidate is reconstructed by
tively. This leads to a considerably large contribution to summingtheelectromagneticenergydepositioninECAL
ηγ from the boost, thereby smearing the original double towers in a limited region of space, with the sum being
peakedηγ distributionintocentrallypeakedone. Onthe required to be above a certain ET threshold. For the
contrary, for typically high sˆ (ckin(3) 1 TeV) values sakeofsimplicity,thislimitedregioncanbevisualizedas
≥
the x tend to be not too different thereby reducing the a cone in ∆η ∆φ space given by ∆R ∆φ2+∆η2,
i
− ≡
smearing on this account. andcontainingmostoftheenergyoftheelectromegnetic
p
In Table III we show the pre-selection efficiencies and object.
9
10-2
Signal 10-3 Signal
QCD dijet QCD dijet
-11 pb10-3 ZWγ +( j( jjJ)j )e+ +t γ γ ( (xx 1 100)) -11 pb10-4 WγZ +( (j jjJ)j) e+ +t γ γ ( (xx 1 100))
V / 10-4 V /
Ge Ge10-5
0 10-5 0
0 0
s / 10.10-6 s / 10.10-6
nt nt
Eve10-7 Eve10-7
of of
No 10-8 No 10-8
10-9 1000 1500 2000 2500 3000 3500 4000 4500 10-9 1000 1500 2000 2500 3000 3500 4000 4500
(a) PγT (GeV) (b) PjTet (GeV)
10-2 10-2
Signal Signal
QCD dijet QCD dijet
-1Events / 0.12 / 1 pb11110000----6543 γZW +( j( jjJ)j )e+ +t γ γ ( x(x 1 100)) -1Events / 0.12 / 1 pb11110000----6543 WγZ +( (j jjJ)j) e+ +t γ γ ( (xx 1 100))
o of 10-7 o of 10-7
N N
10-8 10-8
10-9-3 -2 -1 0 1 2 3 10-9-3 -2 -1 0 1 2 3
(c) ηγ (d) ηjet
10-3
Signal 10-3
-1No of Events / 10.00 GeV / 1 pb1111100000-----87654 QWγZ C+( (j DjjJ)j) e + d+t iγ jγe ( t(xx 1 100)) -1No of Events / 0.01 radians / 1 pb1111100000-----87654 WSZQγ iC+ ( g (j jDjn J)j ) a e + d+l t iγ jγ e ( t(x x 1 1 0 0 ) )
10-9 2000 3000 4000 5000 6000 7000 8000 10-90 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(e) Mγ-jet (GeV) (f) |Cosθ*|γ - jet
FIG. 8: As in Fig.7 but with a 1 TeV pre-selection cut on PT and a signal corresponding to Mq∗ =5TeV instead.
Ajetfragmentingintoneutralandchargehadronswith the scalar sum of transverse energy (E ) in-
TSUM
a π0 γγ (with overlapping photons) carrying max- • side a cone around the photon. Although, in a
→
imum momentum can also lead to fake single-photon full detector simulation the E is measured
TSUM
candidates. To remove such events, photons are re- separately for ECAL and HCAL, but working at
quired not to have associated charged tracks within a the generator level, we combine them into a sin-
cone of size R . This is implemented by requiring that gle variable with all kinds of electromagnetic and
iso
the scalar/vector sum of energy/transverse momentum hadronic objects around the photon being taken
within R should be below a certain threshold. For ex- into account.
iso
ample, the DØ and the CDF experiments demand that
the E due to chargedtracks within a cone of ∆R=0.4
T
around the photon should be less than a certain value. A. Track Isolation
In this anlaysis,we closely follow the CMS detector sim-
ulation studies [44] and consider the following isolation Forthepurposeoftrackisolation,only‘stable’charged
variables: particles e.g. π±, K±, e± and P± were considered. The
other particles were found to have only a negligible con-
thenumberoftracks(N )aboveacertainthresh- tribution. Indeed,π± alonecontributemorethan80%of
trk
•
old inside a cone around the photon candidate. thechargedtracks. Fig 9showsthedistributionofnum-
10
ber of charged tracks (Ntrk) around the leading photon 1
awsitwheinllaascfoonrethoefstioztea∆lbRac≤kg0r.o3u5nfdo.rSainMceq∗th=e1leTadeVingsipghnoa-l 10-1 Riso≤ 0.35 SQiCgDna dl(i j1eTteV)
tonisthetruephotonforsignalevents,mostofthemare
associated with zero tracks (N =0) and the distribu-
trk s10-2
tionfallsoffveryrapidlyforlargerNtrk values. Forback- nit
U
g8raonudndtheevnenftaslltshsolouwghly,.thTehdeisstmriablultriiosenapteaNktsrkat=N0triks∼du7e- bitrary 10-3
to the fact that γ+jet(SM) and W/Z +γ backgrounds Ar10-4
havetruephotonsastheleadingphotonintheeventand
have no tracks around them, while the rising part along
10-5
withtheextendedtailismainlycontributedbytheQCD
dijet events where the fake photon typically has a large
10-6
number of tracks around itself. In this study, we accept 0 5 10 15 20 25 30 35 40 45
(a) Highest Ptrk (GeV)
a photon to be an isolated one if there is no track with T
minimum transverse momentum (Ptrk ) within a given
Tmin
cone aroundit. It shouldbe notedthat comparativedis-
tributions of signal and total background, as shown in 10-1 Riso≤ 0.35 Signal (5 TeV)
Fig 9, is not overly sensitive to moderate changes in the QCD dijet
PTtrmkin value (the exact values are discussed at a later 10-2
stage). nits
U
y 10-3
ar
102 R ≤ 0.35 Arbitr10-4
iso Signal (1 TeV)
10
Background 10-5
-1b
p 1
1
vents / 10-1 10-60(b) 5 10 15Hig2h0est 2P5tTrk (G30eV)35 40 45 50
E
er of 10-2 FIG.10: HighestPT trackaroundleadingphotonforthesig-
Numb10-3 TnaelVa.nAdntihsoelaQtiCoDn cboancekgorfosuizned0a.3)5Mhaq∗s b=e1enTuesVedb.)BMotqh∗d=is5-
tributionsarenormalizedtounityforthesakeofcomparison.
10-4
Note that the background differs between the two panels on
account of thediffering requirements on PˆT (videSect.IV).
0 10 20 30 40 50 60
N
trk
FIG.9: Numberoftracks(Ntrk)forthesignal(Mq∗ =1TeV) To optimize the value of Ptrk , it is useful to exam-
and the background eventsaround thephoton. Tmin
ine both the signal and the QCD dijet background in
termsofthedistributionforthehighest-P track. InFig
T
In pp collisions at the LHC, a large number of soft 10(a) and (b) respectively, we display this distribution
tracks (in the range of a few MeVs to a few GeVs) will for the signal for Mq∗ = 1 TeV and 5 TeV. Accompany-
be produced in each event. The main sources of such ing these, in each case, are the corresponding QCD dijet
soft tracks are ISR, FSR, minimum bias and underly- background. For ease of comparision both the distribu-
ing events. For a direct photon emerging from the hard tions are nomralized to unity. As is evident, any tracks
interaction, such soft tracks could actually be in the accompanying the photon in a signal event tend to have
near vicinity of the photon. Labelling such photons as a low P , whereas for the background events, the distri-
T
non-isolatedonescouldpotentiallyreducethesignaleffi- bution is a very wide one. An indicative value for the
ciency,andmanyinterestingevents,suchasthoseinthis optimalPtrk isgivenbythepointofintersectionofthe
Tmin
study,couldbelost. Topreventsuchloss,tracksareusu- two normalised distributions (signal and background).
ally required to pass certain minimum selection criteria, Theoptimalchoicedoesdependonthesignalprofile(de-
withaminumumthresholdonthetransversemomentum termined, in a large measure by the typical momentum
being a common requirement [29, 44, 45]. Adopting this transfers), as is evident from the crossover points being
strategy, we investigate the dependence of the signal ef- 4(6)GeVforsignalscorrespondingtoMq∗ of1(5)TeV.
∼
ficiency and the signal/background (S/B) ratio on the Thus,characterizingonlythose tracks,aroundaphoton,
chosenPT threshold(PTtrmkin),varyingthe latterbetween with a PT >∼ 4GeV as true tracks (or, in other words,
1-3 GeV. accepting photons with accompanying tracks satisfying