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Search for excited quarks in the photon + jet final state in proton
proton collisions at 13 TeVAvailable on the CERN CDS information
server CMS PAS EXO-16-015
CMS Physics Analysis Summary
Contact: [email protected] 2016/08/04
Search for excited quarks in the γ + jet final state in proton proton collisions at
√ s = 13 TeV
The CMS Collaboration
Abstract
The study presents a search for excited quarks (q?) decaying into a γ + jet final state at √
s = 13 TeV with the CMS experiment, using the dataset corresponding to an integrated luminosity of 2.7 fb−1 collected during 2015 data taking at the LHC. High transverse momentum photons and jets are selected to search for a resonance peak in the continuous invariant mass distribution of γ + jet. The 95% confidence level upper limits on cross section times branching ratio are evaluated as a function of excited quark mass (Mq?). We exclude at 95% CL excited quarks with mass 1.0 < Mq? < 4.37 TeV and coupling strength f = 1.0, and present exclusions of excited quark mass as a function of coupling strength.
1
1 Introduction The standard model (SM) of strong and electroweak interactions has been tested for the last few decades at many experiments with unprecedented accuracy. Although the SM has been re- markably successful in describing experimental observations so far, there are still fundamental questions which it leaves unanswered, and thus the SM may well be an effective Lagrangian to a more fundamental theory. The increase in colliding energy at the LHC and improvement in detector technology make it possible to search for extensions of the SM. Many such extensions of the SM predict quark substructure or composite quarks [1–3].
A compelling signature for substructure of quarks would be the discovery of an excited state of a quark (q?). Excited quarks may couple to the ground state quark via gauge transitions described by the Lagrangian [1],
Lint = 1
[ gs fs
] qL + h.c., (1)
where Ga µν, Wµν and Bµν are the field-strength tensors of the SU(3), SU(2) and U(1) gauge
fields; λa, τ, Y are the corresponding gauge structure constants and gs, g, g′ are the gauge coupling constants; Λ denotes the typical scale of these interactions, and fs, f , f ′ are unknown dimensionless constants determined by the compositeness dynamics, representing the cou- pling strength and naively assumed to be of order unity. In proton-proton collisions excited quarks would be produced predominantly by quark-gluon annihilation (qg), and would then decay into a quark and a gauge boson (g, W, Z, γ). Many searches for their existence have been performed in different decay channels previously [4–9], and no evidence of their existence has been found. This analysis searches for the single process qg → q? → qγ shown in Fig. 1. The signal model considered includes the dominant production modes of excited quarks (u? and d?) with spin- 1
2 [2, 3]. The compositeness scale and mass of the excited quarks are set to be equal in the signal model, i.e., Λ = Mq? .
g
q
q*
γ
q
Figure 1: Signal for production of an excited quark in the s−channel and subsequent decay into a quark and a photon.
This paper presents the first results of a search for resonances in the γ+ jet final state at √
s = 13 TeV at CMS. The dataset used in this study corresponds to an integrated luminosity of 2.7 fb−1
collected by the CMS experiment during the pp collision run at the LHC in 2015.
A final state with a photon and a jet are produced in the SM mainly by qg→ qγ, qq→ gγ, QCD multi-jet, and W/Z +γ. Among these the main irreducible backgrounds are the quark-gluon Compton scattering (qg → qγ) and quark-antiquark annihilation (qq → gγ). Although the QCD multi-jet production is two to three orders of magnitude higher, the probability for a jet to fake and be reconstructed as a photon is about 10−3, making it the second largest background.
2 3 Event Reconstruction and Selection
Electroweak production (W/Z+ γ) where W/Z decays to jets, contributes only a small fraction because of low production cross section.
2 The CMS Detector The central feature of the Compact Muon Solenoid (CMS) apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the supercon- ducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electro- magnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudora- pidity [10] coverage provided by the barrel and endcap detectors. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. In the region |η| < 1.74, the HCAL cells have widths of 0.087 in pseudorapidity and 0.087 in azimuth (φ). In the η-φ plane, and for |η| < 1.48, the HCAL cells map on to 5× 5 ECAL crystals arrays to form calorimeter towers projecting radially outwards from close to the nominal interaction point. At larger values of |η|, the size of the towers increases and the matching ECAL arrays contain fewer crystals. Within each tower, the energy deposits in ECAL and HCAL cells are summed to define the calorimeter tower energies, subsequently used to provide the energies and directions of hadronic jets. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [10].
The CMS experiment keeps interesting events using a two-tier trigger system, the Level-1 (L1) and High Level Trigger (HLT). The L1 trigger selects events of interest using information from the calorimeters and the muon system only, and reduces the readout rate from ∼ 40MHz of bunch crossing frequency to below 100 kHz. The HLT is a software-based trigger system and further decreases the event rate to an average of a few 100 Hz. Events are kept if they pass both L1 and HLT level triggers. The data sample used in this analysis consists of those events that either pass a trigger with an Eγ
T threshold of 165 GeV and an additional photon isolation requirement, or pass a trigger with Eγ
T threshold of 175 GeV and no additional isolation require- ment. The combined trigger efficiency is 100% for pγ
T > 190 GeV.
3 Event Reconstruction and Selection Event reconstruction at the CMS experiment is performed using a particle-flow (PF) algo- rithm [11, 12], which reconstructs and identifies individual particles using an optimized combi- nation of all sub-detector information. Photon candidates are identified as energy depositions in the ECAL called superclusters. The energy of charged hadrons is estimated using track momentum and the corresponding ECAL and HCAL energy depositions. These energies are calibrated for the nonlinear response of the calorimeters and zero suppression. The energy of neutral hadrons is obtained from the corresponding calibrated ECAL and HCAL energy.
The jets in each event are formed from PF based reconstructed particles with the infrared- and collinear-safe anti-kT algorithm [13], operated with distance parameter R = 0.4. Jet energies are corrected to establish a uniform calorimetric response in η and an absolute response in pT at the particle level. Jet energy scale (JES) corrections are derived from Monte Carlo (MC) simulations, and a residual correction is derived from the data by measuring the pT balance in γ + jet events and other processes [14].
In offline selection each event is required to have at least one good primary vertex reconstructed
3
within |z| < 24 cm from the center of the detector and with transverse distance less than 2 cm from the z axis.
In each event photons with pγ T > 190 GeV and |ηγ| < 1.4442 (i.e., barrel region), are selected
in the list of the possible photon candidates. The photon with highest transverse momen- tum (leading) amongst the ones which satisfy the photon identification and isolation require- ments [15], is used as the final photon candidate in the event. To select this photon candidate the following PF based isolation and identification requirements are used:
• the energy deposited in the HCAL tower closest to the supercluster position inside a cone of R = 0.15 centered on the photon direction must be less than 5% of the energy deposited in ECAL for that supercluster, where R ≡
√ φ2 + η2.
• the scalar sum ET of photons within a cone of R = 0.3 around the supercluster must be less than 0.81 GeV + 0.0053pγ
T.
• the sum pT of charged hadrons associated to the primary vertex within a cone of R = 0.3 around the supercluster must be less than 3.32 GeV.
• the sum ET of all neutral hadrons within a cone of R = 0.3 around the supercluster must be less than 1.92 GeV + 0.014pγ
T + 0.000019(pγ T)
2.
• the photon candidate should not to be matched with any of the charged tracks iden- tified by the Gaussian Sum Filter algorithm [16] that has no missing hits on the in- nermost tracker layers.
• the photon candidates are required to have an ECAL shower energy profile consis- tent with that of a photon.
The isolation quantities are corrected for effects from overlapping proton-proton interactions (pileup) in the same bunch crossing by subtracting energy calculated from the mean energy density in the event, as computed using the FastJet package [17]. All these photon identifica- tion selection criteria are measured to provide ∼ 82% signal efficiency. A selection is applied on the shower shape variables to remove photon candidates from anomalous calorimeter sig- nals [18].
The jets separated from the selected photon candidate by R > 0.5 and satisfying the tight jet identification criteria [19] are selected as the possible jet candidates. The jet identification criteria have requirements on the number of constituents, and on the fraction of the jet energy held by each constituent type. The jet is required to be within the pseudorapidity region |ηjet| < 2.4 and must have a transverse momentum pjet
T > 190 GeV. If more than one photon or jet candidates exist in the event, the γ + jet invariant mass is calculated using the leading photon candidate and leading jet candidate.
The production of excited quarks considered in this study is an s-channel production which gives an isotropic distribution of final photon and jet. This feature of signal provides a handle to reduce the backgrounds as all backgrounds are predominantly t-channel processes and have an angular distribution peaking in the forward direction. Therefore the |η(γ, jet)| < 1.8 selec- tion is imposed between the selected photon and the jet candidate to reduce the background while keeping large acceptance for the signal. We keep only events with the photon and jet back-to-back in φ, |φ(γ, jet)| > 1.5, because this is the expected event topology of both the signal and background at lowest order. These selections are optimized to get the best signal significance. The invariant mass of the γ + jet system is required to be Mγ,jet > 695 GeV to have full kinematic acceptance for events with the photon and jet pT, η and |η| requirements. The cumulative efficiency for signal events after various selection criteria are given in Table 1.
4 4 Resonance Shape and Background Fit
Selection 2 TeV 4 TeV (%) (%)
Photon ID 81.5 82.0 pγ
T > 190 GeV,|ηγ| < 1.4442 73.5 75.4 Jet ID 73.4 75.4
pjet T > 190 GeV, |ηjet| < 2.4 71.2 74.9
Mγ,jet > 695 GeV 71.0 74.8 |φ(γ, jet)| > 1.5 70.8 74.8 |η(γ, jet)| < 1.8 58.3 60.1
Table 1: The cumulative efficiency for signal event selection for q? resonance mass of 2 TeV and 4 TeV and coupling multiplier f = 1.0.
The signal efficiency goes from about 49% at Mq? = 1 TeV to 58% at Mq? = 2 TeV and 60% at Mq? = 5 TeV
4 Resonance Shape and Background Fit The invariant mass distribution of the γ + jet events in the collected data and MC simula- tion after applying full selection is shown in Fig. 2. The γ + jet and W/Z + γ background MC predictions are generated using MADGRAPH [email protected] program [20] at leading order (LO), with the showering and hadronization carried out by the PYTHIA8 program [21]. The QCD dijet MC predictions are generated using PYTHIA8 event generator. Generated events are processed through a full CMS detector simulation based on GEANT4 [22]. The simulation uses CUETP8M1 underlying event tune [23, 24] and a renormalization and factorization scale µ = pT of the hard-scattered partons and NNPDF2.3LO parton distribution functions [25]. The same event reconstruction is employed both in data and MC simulations. The SM γ + jet pre- dictions from MADGRAPH were corrected in shape using the simulation of the next-to-leading order SM γ + jet from JETPHOX program [26, 27]. The JETPHOX version 1.3.2 is interfaced to LHAPDF 5.8.7 in order to select the CT10 parton distribution function for protons. The BFG-II set of parton-to-parton fragmentation functions are used, and default values of the renormal- ization (µR), initial-state factorization and final-state factorization scales are all set to the pT of the photon. The invariant mass distribution of the γ + jet events at the generator level from MADGRAPH event generator is compared to the invariant mass spectrum from the JETPHOX
program. The reconstructed simulation of γ + jet mass spectrum is then reweighted by mass dependent scale factors, varying between 1.1 at Mγ+jet = 700 GeV and 0.8 for Mγ+jet = 1.1 TeV, derived from comparison of generator level MADGRAPH spectrum and the one obtained using JETPHOX program.
After applying all the selection criteria, the background at these values of γ + jet mass is es- timated via MC simulation to originate predominantly from direct photon production (70%), a small contribution of dijet production where one jet fakes a photon (29%), and a negligible contribution of W/Z + γ production where the W/Z decays hadronically and is reconstructed as a single jet (1%).
The mass distribution shown in Fig. 2 is binned with bin-width approximately equal to the expected γ + jet mass resolution, which varies from about 4.5% at a mass of 1 TeV to 3.6% at 4 TeV. The highest mass event observed in data is at 3.29 TeV. A 3-dimensional view of this event is shown in Fig. 3.
5
E ve
nt s
pe r
bi n
D at
a σ
(D at
a- F
it)
-2
0
2
4
Figure 2: The γ+ jet invariant mass distribution in data (points) and MC (histogram) prediction after full selection. The result of the fit to the data using the parameterization of Eq. (2) is shown with the red dotted curve. The bin-by-bin pull, (data-fit)/σdata, is shown at the bottom. Simulations of excited quark signals (q?) for coupling multiplier f = 1.0 are shown at masses of 1, 2 and 3 TeV (dashed curves).
The expected signal from excited quarks produced via qg fusion is simulated with PYTHIA8 event generator. The reconstructed γ + jet mass distributions for q? model using PYTHIA8, Tune CUETP8M1, and the CMS detector simulation are shown in Fig. 4. The natural width of the resonance peak, at parton level before experimental reconstruction, can be approximated as Γ ∼ 0.03 f 2Mq? . The production cross section is also proportional to f 2.
To search for γ+ jet resonances, the mass distribution of a photon and a jet from the SM sources is modelled using a smooth parameterization:
dσ
dm =
where √
s = 13 TeV and P0, P1, P2, and P3 are four parameters used to describe the shape. This functional form has been widely used in similar previous searches [7–9, 28]. We fit the parameterization to the data after final selection. The fit to the data has a χ2/ndf = 35.9/33, and is shown in Fig. 2. The pull (data - fit/σdata) for each mass bin is shown at the bottom of Fig. 2. The largest differences between the data and the background-only fit are seen at a mass of ∼ 2.0 TeV, where 14 events are expected from the background prediction and 34 data events were observed in a single bin.
In order to examine the presence of a possible systematic bias due to the chosen parametric function, tests are performed using alternate functional forms. For these tests, the background events are estimated using MC simulation and quantified based on the difference between
6 5 Results
Figure 3: Event display of the highest invariant mass γ + jet candidate with mass of 3.29 TeV observed in data in the 3-dimensional plane. The pT, η, and φ values of the photon and jet are indicated.
the true and predicted number of background events in different γ + jet mass windows. The invariant mass distribution obtained from the MC simulation is fitted with alternate test func- tions and the result of the fit, considered as truth model, is used to generate large number of pseudo-data following Poisson distribution with mean as numbers of events observed in data. The pseudo-data are then fitted with the chosen parameteric function, and for each γ+ jet mass window, pull distributions are obtained (where pulls are defined as the difference between the true and predicted number of events divided by the estimated statistical uncertainty). The ab- solute value of the median of this distribution is found to be below 0.5 in the full search region and we conclude that the possible statistical bias from the choice of parameteric function is small as compared to the statistical uncertainty of the fit.
5 Results A Bayesian approach [4] with uniform prior is used for estimating the upper limit on the pro- duction cross section of excited quarks. The data is fitted to the background function plus signal line shape with the signal cross section treated as parameter of interest. A binned likelihood, L, of Poisson type is used and is written as a function of a constant α as
L = ∏ i
where µi = αNi(S) + Ni(B), (4)
where ni is the number of events observed in the ith γ + jet invariant mass bin, Ni(S) is the number of signal events in ith γ + jet invariant mass bin taken from the q? signal shapes, α is
7
[GeV] jetγM 500 1000 1500 2000 2500 3000 3500 4000 4500
N or
m al
iz ed
Y ie
ld /2
0 G
CMS Simulation Preliminary
γ q→q*
q* (1.0 TeV)
q* (2.0 TeV)
q* (3.0 TeV)
q* (4.0 TeV)
Figure 4: The reconstructed resonance mass spectrum generated using PYTHIA8 simulation for γ + jet resonances modeled by qg→ qγ for coupling multipliers f = 1.0 (filled histogram) and f = 0.1 (dotted histogram) having resonance masses ranging from 1.0 to 4.0 TeV.
a constant to scale the signal amplitude, Ni(B) is the number of events expected from back- ground in the same γ + jet invariant mass bin.
The local significance for the largest excess in data is estimated using a likelihood-based signif- icance estimator defined as:
Sig = sgn(S)
√ −2 ln
) (5)
where LB and LS+B are the maximum likelihoods from the best background-only and sig- nal+background fits to the data, respectively. The likelihood function is the same as the one defined in Eq. 3. The local significance does not include the look-elsewhere effect or systematic uncertainties. A fit to the hypothesis of a q? resonance with a mass of 2.0 TeV has a local signif- icance of 3.2σ for f = 1.0 and 3.7σ for f = 0.1, and is sensitive to the choice of f because the excess in data is observed in a single bin. The global significance over a mass range from 1 TeV to 2.5 TeV is found to be 2.36σ for f = 1.0 and 2.84σ for f = 0.1.
Log-normal priors are used to model systematic uncertainties, which are marginalized as nui- sance parameters in the limit setting procedure. We calculate the posterior probability density as a function of signal cross section for various resonance masses. The 95% confidence level (CL) upper limit is calculated from the posterior probability density.
The major sources of systematic uncertainty are jet energy scale (JES) [15], jet energy resolution (JER) [15], photon energy scale (PES) [15], photon energy resolution (PER) [29], background parameters, and luminosity. The uncertainties on the JES and PES are estimated to be 0.5%− 0.8% and 1.0% respectively (as a function of γ+ jet mass). These uncertainties are accounted for by shifting the reconstructed signal mass conservatively by 1.5%. The systematic uncertainty on the JER and PER are estimated to be 10% and 0.5%. The systematic uncertainties from PER and JER translate into a 5% relative uncertainty on the resolution of invariant mass of the γ+ jet
8 5 Results
and is propagated into the results by increasing and decreasing the width of reconstructed mass shape of signal. The uncertainty in photon identification is found to be 2% for photons with pT upto 200 GeV and within 4% in a pT range from 200 GeV to 1 TeV. The estimated systematic uncertainty on the luminosity for the early Run 2 dataset is 2.7% [30], and is propagated to the normalization of the signal cross section. The uncertainty on the signal acceptance due to the choice of PDF [31] is found to be about 2%. For background fit-parameters, the variations of parameters from the best-fit values introduce a systematic uncertainty on the signal strength modelled using flat priors.
The systematic uncertainties in JER, PER, JES, PES, and luminosity are used in the limit setting procedure as nuisance parameters and affect only the signal. The 95% CL upper limit on σ×B as a function of Mq? is shown in Fig. 5. At a mass of 2.0 TeV the observed cross section limit is 45 fb and the expected cross section limit is 19 fb.
The observed limits are compared to the LO theoretical predictions to estimate the lower mass bound on the excited quarks, which is shown in Fig. 5 for f = 1.0, 0.5, and 0.1. A lower bound of 4.37 TeV is obtained for f = 1.0. The corresponding expected limit is found to be 4.33 TeV. The dependence of the σ × B upper limit on f is found to be negligible for f ≤ 1. Using the theoretical predictions for different coupling strengths from 0.1 to 1.0 and the observed limits, a mass region as a function of the coupling strength is excluded as shown in Fig. 6.
q* Mass [TeV] 1 2 3 4 5 6
B [f
b] × σ
Observed limit Expected limit
σ 1±Expected limit σ 2±Expected limit
Excited quark (f = 1.0) Excited quark (f = 0.5) Excited quark (f = 0.1)
(13 TeV)-12.7 fb
γ q→q*
Figure 5: The expected and observed 95% CL upper limits on σ × B for excited quark search in γ + jet final state corresponding to coupling f = 1.0. The limits are also compared with the theoretical predictions for excited quark production, shown for coupling values f = 1.0, 0.5, and 0.1. The uncertainty at 1σ and 2σ levels are shown as green and yellow shaded bands around expected limit.
9
q* Mass [TeV] 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
= f'
] s
(13 TeV)-1 (8TeV) 2.7 fb-119.7 fb
CMS Preliminary
γ q→q*
Figure 6: The observed (yellow filled) and expected (blue dashed line) excluded regions at 95% CL as a function of excited quark mass and the coupling strength for Λ = Mq? (left axis) or the mass divided by compositeness scale for coupling strength of f = 1 (right axis). The excluded region from Run-I is also shown (red shaded).
6 Summary We have presented a search for excited quarks in the γ + jet final state. The data set collected at √
s = 13 TeV corresponds to an integrated luminosity of 2.7 fb−1. The data are found to be consistent with the predictions of the standard model and no evidence is found for an excited quark resonance. The largest excess of events in data is seen at a γ + jet invariant mass of 2.0 TeV.
A 95% CL upper limit is placed on σ×B for q? production in the γ+ jet final state. Comparing these upper limits with the theoretical predictions, an excited quark state with mass 1.0 < Mq? < 4.37 TeV is excluded at 95% CL for f = 1.0. Also, excited quarks with masses 1.0 < Mq? < 3.64 (1.36)TeV are excluded for f = 0.5 (0.1). We also present the excluded mass as a function of coupling strength in Fig. 6.
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4 Resonance Shape and Background Fit
5 Results
6 Summary
CMS Physics Analysis Summary
Contact: [email protected] 2016/08/04
Search for excited quarks in the γ + jet final state in proton proton collisions at
√ s = 13 TeV
The CMS Collaboration
Abstract
The study presents a search for excited quarks (q?) decaying into a γ + jet final state at √
s = 13 TeV with the CMS experiment, using the dataset corresponding to an integrated luminosity of 2.7 fb−1 collected during 2015 data taking at the LHC. High transverse momentum photons and jets are selected to search for a resonance peak in the continuous invariant mass distribution of γ + jet. The 95% confidence level upper limits on cross section times branching ratio are evaluated as a function of excited quark mass (Mq?). We exclude at 95% CL excited quarks with mass 1.0 < Mq? < 4.37 TeV and coupling strength f = 1.0, and present exclusions of excited quark mass as a function of coupling strength.
1
1 Introduction The standard model (SM) of strong and electroweak interactions has been tested for the last few decades at many experiments with unprecedented accuracy. Although the SM has been re- markably successful in describing experimental observations so far, there are still fundamental questions which it leaves unanswered, and thus the SM may well be an effective Lagrangian to a more fundamental theory. The increase in colliding energy at the LHC and improvement in detector technology make it possible to search for extensions of the SM. Many such extensions of the SM predict quark substructure or composite quarks [1–3].
A compelling signature for substructure of quarks would be the discovery of an excited state of a quark (q?). Excited quarks may couple to the ground state quark via gauge transitions described by the Lagrangian [1],
Lint = 1
[ gs fs
] qL + h.c., (1)
where Ga µν, Wµν and Bµν are the field-strength tensors of the SU(3), SU(2) and U(1) gauge
fields; λa, τ, Y are the corresponding gauge structure constants and gs, g, g′ are the gauge coupling constants; Λ denotes the typical scale of these interactions, and fs, f , f ′ are unknown dimensionless constants determined by the compositeness dynamics, representing the cou- pling strength and naively assumed to be of order unity. In proton-proton collisions excited quarks would be produced predominantly by quark-gluon annihilation (qg), and would then decay into a quark and a gauge boson (g, W, Z, γ). Many searches for their existence have been performed in different decay channels previously [4–9], and no evidence of their existence has been found. This analysis searches for the single process qg → q? → qγ shown in Fig. 1. The signal model considered includes the dominant production modes of excited quarks (u? and d?) with spin- 1
2 [2, 3]. The compositeness scale and mass of the excited quarks are set to be equal in the signal model, i.e., Λ = Mq? .
g
q
q*
γ
q
Figure 1: Signal for production of an excited quark in the s−channel and subsequent decay into a quark and a photon.
This paper presents the first results of a search for resonances in the γ+ jet final state at √
s = 13 TeV at CMS. The dataset used in this study corresponds to an integrated luminosity of 2.7 fb−1
collected by the CMS experiment during the pp collision run at the LHC in 2015.
A final state with a photon and a jet are produced in the SM mainly by qg→ qγ, qq→ gγ, QCD multi-jet, and W/Z +γ. Among these the main irreducible backgrounds are the quark-gluon Compton scattering (qg → qγ) and quark-antiquark annihilation (qq → gγ). Although the QCD multi-jet production is two to three orders of magnitude higher, the probability for a jet to fake and be reconstructed as a photon is about 10−3, making it the second largest background.
2 3 Event Reconstruction and Selection
Electroweak production (W/Z+ γ) where W/Z decays to jets, contributes only a small fraction because of low production cross section.
2 The CMS Detector The central feature of the Compact Muon Solenoid (CMS) apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the supercon- ducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electro- magnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudora- pidity [10] coverage provided by the barrel and endcap detectors. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. In the region |η| < 1.74, the HCAL cells have widths of 0.087 in pseudorapidity and 0.087 in azimuth (φ). In the η-φ plane, and for |η| < 1.48, the HCAL cells map on to 5× 5 ECAL crystals arrays to form calorimeter towers projecting radially outwards from close to the nominal interaction point. At larger values of |η|, the size of the towers increases and the matching ECAL arrays contain fewer crystals. Within each tower, the energy deposits in ECAL and HCAL cells are summed to define the calorimeter tower energies, subsequently used to provide the energies and directions of hadronic jets. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [10].
The CMS experiment keeps interesting events using a two-tier trigger system, the Level-1 (L1) and High Level Trigger (HLT). The L1 trigger selects events of interest using information from the calorimeters and the muon system only, and reduces the readout rate from ∼ 40MHz of bunch crossing frequency to below 100 kHz. The HLT is a software-based trigger system and further decreases the event rate to an average of a few 100 Hz. Events are kept if they pass both L1 and HLT level triggers. The data sample used in this analysis consists of those events that either pass a trigger with an Eγ
T threshold of 165 GeV and an additional photon isolation requirement, or pass a trigger with Eγ
T threshold of 175 GeV and no additional isolation require- ment. The combined trigger efficiency is 100% for pγ
T > 190 GeV.
3 Event Reconstruction and Selection Event reconstruction at the CMS experiment is performed using a particle-flow (PF) algo- rithm [11, 12], which reconstructs and identifies individual particles using an optimized combi- nation of all sub-detector information. Photon candidates are identified as energy depositions in the ECAL called superclusters. The energy of charged hadrons is estimated using track momentum and the corresponding ECAL and HCAL energy depositions. These energies are calibrated for the nonlinear response of the calorimeters and zero suppression. The energy of neutral hadrons is obtained from the corresponding calibrated ECAL and HCAL energy.
The jets in each event are formed from PF based reconstructed particles with the infrared- and collinear-safe anti-kT algorithm [13], operated with distance parameter R = 0.4. Jet energies are corrected to establish a uniform calorimetric response in η and an absolute response in pT at the particle level. Jet energy scale (JES) corrections are derived from Monte Carlo (MC) simulations, and a residual correction is derived from the data by measuring the pT balance in γ + jet events and other processes [14].
In offline selection each event is required to have at least one good primary vertex reconstructed
3
within |z| < 24 cm from the center of the detector and with transverse distance less than 2 cm from the z axis.
In each event photons with pγ T > 190 GeV and |ηγ| < 1.4442 (i.e., barrel region), are selected
in the list of the possible photon candidates. The photon with highest transverse momen- tum (leading) amongst the ones which satisfy the photon identification and isolation require- ments [15], is used as the final photon candidate in the event. To select this photon candidate the following PF based isolation and identification requirements are used:
• the energy deposited in the HCAL tower closest to the supercluster position inside a cone of R = 0.15 centered on the photon direction must be less than 5% of the energy deposited in ECAL for that supercluster, where R ≡
√ φ2 + η2.
• the scalar sum ET of photons within a cone of R = 0.3 around the supercluster must be less than 0.81 GeV + 0.0053pγ
T.
• the sum pT of charged hadrons associated to the primary vertex within a cone of R = 0.3 around the supercluster must be less than 3.32 GeV.
• the sum ET of all neutral hadrons within a cone of R = 0.3 around the supercluster must be less than 1.92 GeV + 0.014pγ
T + 0.000019(pγ T)
2.
• the photon candidate should not to be matched with any of the charged tracks iden- tified by the Gaussian Sum Filter algorithm [16] that has no missing hits on the in- nermost tracker layers.
• the photon candidates are required to have an ECAL shower energy profile consis- tent with that of a photon.
The isolation quantities are corrected for effects from overlapping proton-proton interactions (pileup) in the same bunch crossing by subtracting energy calculated from the mean energy density in the event, as computed using the FastJet package [17]. All these photon identifica- tion selection criteria are measured to provide ∼ 82% signal efficiency. A selection is applied on the shower shape variables to remove photon candidates from anomalous calorimeter sig- nals [18].
The jets separated from the selected photon candidate by R > 0.5 and satisfying the tight jet identification criteria [19] are selected as the possible jet candidates. The jet identification criteria have requirements on the number of constituents, and on the fraction of the jet energy held by each constituent type. The jet is required to be within the pseudorapidity region |ηjet| < 2.4 and must have a transverse momentum pjet
T > 190 GeV. If more than one photon or jet candidates exist in the event, the γ + jet invariant mass is calculated using the leading photon candidate and leading jet candidate.
The production of excited quarks considered in this study is an s-channel production which gives an isotropic distribution of final photon and jet. This feature of signal provides a handle to reduce the backgrounds as all backgrounds are predominantly t-channel processes and have an angular distribution peaking in the forward direction. Therefore the |η(γ, jet)| < 1.8 selec- tion is imposed between the selected photon and the jet candidate to reduce the background while keeping large acceptance for the signal. We keep only events with the photon and jet back-to-back in φ, |φ(γ, jet)| > 1.5, because this is the expected event topology of both the signal and background at lowest order. These selections are optimized to get the best signal significance. The invariant mass of the γ + jet system is required to be Mγ,jet > 695 GeV to have full kinematic acceptance for events with the photon and jet pT, η and |η| requirements. The cumulative efficiency for signal events after various selection criteria are given in Table 1.
4 4 Resonance Shape and Background Fit
Selection 2 TeV 4 TeV (%) (%)
Photon ID 81.5 82.0 pγ
T > 190 GeV,|ηγ| < 1.4442 73.5 75.4 Jet ID 73.4 75.4
pjet T > 190 GeV, |ηjet| < 2.4 71.2 74.9
Mγ,jet > 695 GeV 71.0 74.8 |φ(γ, jet)| > 1.5 70.8 74.8 |η(γ, jet)| < 1.8 58.3 60.1
Table 1: The cumulative efficiency for signal event selection for q? resonance mass of 2 TeV and 4 TeV and coupling multiplier f = 1.0.
The signal efficiency goes from about 49% at Mq? = 1 TeV to 58% at Mq? = 2 TeV and 60% at Mq? = 5 TeV
4 Resonance Shape and Background Fit The invariant mass distribution of the γ + jet events in the collected data and MC simula- tion after applying full selection is shown in Fig. 2. The γ + jet and W/Z + γ background MC predictions are generated using MADGRAPH [email protected] program [20] at leading order (LO), with the showering and hadronization carried out by the PYTHIA8 program [21]. The QCD dijet MC predictions are generated using PYTHIA8 event generator. Generated events are processed through a full CMS detector simulation based on GEANT4 [22]. The simulation uses CUETP8M1 underlying event tune [23, 24] and a renormalization and factorization scale µ = pT of the hard-scattered partons and NNPDF2.3LO parton distribution functions [25]. The same event reconstruction is employed both in data and MC simulations. The SM γ + jet pre- dictions from MADGRAPH were corrected in shape using the simulation of the next-to-leading order SM γ + jet from JETPHOX program [26, 27]. The JETPHOX version 1.3.2 is interfaced to LHAPDF 5.8.7 in order to select the CT10 parton distribution function for protons. The BFG-II set of parton-to-parton fragmentation functions are used, and default values of the renormal- ization (µR), initial-state factorization and final-state factorization scales are all set to the pT of the photon. The invariant mass distribution of the γ + jet events at the generator level from MADGRAPH event generator is compared to the invariant mass spectrum from the JETPHOX
program. The reconstructed simulation of γ + jet mass spectrum is then reweighted by mass dependent scale factors, varying between 1.1 at Mγ+jet = 700 GeV and 0.8 for Mγ+jet = 1.1 TeV, derived from comparison of generator level MADGRAPH spectrum and the one obtained using JETPHOX program.
After applying all the selection criteria, the background at these values of γ + jet mass is es- timated via MC simulation to originate predominantly from direct photon production (70%), a small contribution of dijet production where one jet fakes a photon (29%), and a negligible contribution of W/Z + γ production where the W/Z decays hadronically and is reconstructed as a single jet (1%).
The mass distribution shown in Fig. 2 is binned with bin-width approximately equal to the expected γ + jet mass resolution, which varies from about 4.5% at a mass of 1 TeV to 3.6% at 4 TeV. The highest mass event observed in data is at 3.29 TeV. A 3-dimensional view of this event is shown in Fig. 3.
5
E ve
nt s
pe r
bi n
D at
a σ
(D at
a- F
it)
-2
0
2
4
Figure 2: The γ+ jet invariant mass distribution in data (points) and MC (histogram) prediction after full selection. The result of the fit to the data using the parameterization of Eq. (2) is shown with the red dotted curve. The bin-by-bin pull, (data-fit)/σdata, is shown at the bottom. Simulations of excited quark signals (q?) for coupling multiplier f = 1.0 are shown at masses of 1, 2 and 3 TeV (dashed curves).
The expected signal from excited quarks produced via qg fusion is simulated with PYTHIA8 event generator. The reconstructed γ + jet mass distributions for q? model using PYTHIA8, Tune CUETP8M1, and the CMS detector simulation are shown in Fig. 4. The natural width of the resonance peak, at parton level before experimental reconstruction, can be approximated as Γ ∼ 0.03 f 2Mq? . The production cross section is also proportional to f 2.
To search for γ+ jet resonances, the mass distribution of a photon and a jet from the SM sources is modelled using a smooth parameterization:
dσ
dm =
where √
s = 13 TeV and P0, P1, P2, and P3 are four parameters used to describe the shape. This functional form has been widely used in similar previous searches [7–9, 28]. We fit the parameterization to the data after final selection. The fit to the data has a χ2/ndf = 35.9/33, and is shown in Fig. 2. The pull (data - fit/σdata) for each mass bin is shown at the bottom of Fig. 2. The largest differences between the data and the background-only fit are seen at a mass of ∼ 2.0 TeV, where 14 events are expected from the background prediction and 34 data events were observed in a single bin.
In order to examine the presence of a possible systematic bias due to the chosen parametric function, tests are performed using alternate functional forms. For these tests, the background events are estimated using MC simulation and quantified based on the difference between
6 5 Results
Figure 3: Event display of the highest invariant mass γ + jet candidate with mass of 3.29 TeV observed in data in the 3-dimensional plane. The pT, η, and φ values of the photon and jet are indicated.
the true and predicted number of background events in different γ + jet mass windows. The invariant mass distribution obtained from the MC simulation is fitted with alternate test func- tions and the result of the fit, considered as truth model, is used to generate large number of pseudo-data following Poisson distribution with mean as numbers of events observed in data. The pseudo-data are then fitted with the chosen parameteric function, and for each γ+ jet mass window, pull distributions are obtained (where pulls are defined as the difference between the true and predicted number of events divided by the estimated statistical uncertainty). The ab- solute value of the median of this distribution is found to be below 0.5 in the full search region and we conclude that the possible statistical bias from the choice of parameteric function is small as compared to the statistical uncertainty of the fit.
5 Results A Bayesian approach [4] with uniform prior is used for estimating the upper limit on the pro- duction cross section of excited quarks. The data is fitted to the background function plus signal line shape with the signal cross section treated as parameter of interest. A binned likelihood, L, of Poisson type is used and is written as a function of a constant α as
L = ∏ i
where µi = αNi(S) + Ni(B), (4)
where ni is the number of events observed in the ith γ + jet invariant mass bin, Ni(S) is the number of signal events in ith γ + jet invariant mass bin taken from the q? signal shapes, α is
7
[GeV] jetγM 500 1000 1500 2000 2500 3000 3500 4000 4500
N or
m al
iz ed
Y ie
ld /2
0 G
CMS Simulation Preliminary
γ q→q*
q* (1.0 TeV)
q* (2.0 TeV)
q* (3.0 TeV)
q* (4.0 TeV)
Figure 4: The reconstructed resonance mass spectrum generated using PYTHIA8 simulation for γ + jet resonances modeled by qg→ qγ for coupling multipliers f = 1.0 (filled histogram) and f = 0.1 (dotted histogram) having resonance masses ranging from 1.0 to 4.0 TeV.
a constant to scale the signal amplitude, Ni(B) is the number of events expected from back- ground in the same γ + jet invariant mass bin.
The local significance for the largest excess in data is estimated using a likelihood-based signif- icance estimator defined as:
Sig = sgn(S)
√ −2 ln
) (5)
where LB and LS+B are the maximum likelihoods from the best background-only and sig- nal+background fits to the data, respectively. The likelihood function is the same as the one defined in Eq. 3. The local significance does not include the look-elsewhere effect or systematic uncertainties. A fit to the hypothesis of a q? resonance with a mass of 2.0 TeV has a local signif- icance of 3.2σ for f = 1.0 and 3.7σ for f = 0.1, and is sensitive to the choice of f because the excess in data is observed in a single bin. The global significance over a mass range from 1 TeV to 2.5 TeV is found to be 2.36σ for f = 1.0 and 2.84σ for f = 0.1.
Log-normal priors are used to model systematic uncertainties, which are marginalized as nui- sance parameters in the limit setting procedure. We calculate the posterior probability density as a function of signal cross section for various resonance masses. The 95% confidence level (CL) upper limit is calculated from the posterior probability density.
The major sources of systematic uncertainty are jet energy scale (JES) [15], jet energy resolution (JER) [15], photon energy scale (PES) [15], photon energy resolution (PER) [29], background parameters, and luminosity. The uncertainties on the JES and PES are estimated to be 0.5%− 0.8% and 1.0% respectively (as a function of γ+ jet mass). These uncertainties are accounted for by shifting the reconstructed signal mass conservatively by 1.5%. The systematic uncertainty on the JER and PER are estimated to be 10% and 0.5%. The systematic uncertainties from PER and JER translate into a 5% relative uncertainty on the resolution of invariant mass of the γ+ jet
8 5 Results
and is propagated into the results by increasing and decreasing the width of reconstructed mass shape of signal. The uncertainty in photon identification is found to be 2% for photons with pT upto 200 GeV and within 4% in a pT range from 200 GeV to 1 TeV. The estimated systematic uncertainty on the luminosity for the early Run 2 dataset is 2.7% [30], and is propagated to the normalization of the signal cross section. The uncertainty on the signal acceptance due to the choice of PDF [31] is found to be about 2%. For background fit-parameters, the variations of parameters from the best-fit values introduce a systematic uncertainty on the signal strength modelled using flat priors.
The systematic uncertainties in JER, PER, JES, PES, and luminosity are used in the limit setting procedure as nuisance parameters and affect only the signal. The 95% CL upper limit on σ×B as a function of Mq? is shown in Fig. 5. At a mass of 2.0 TeV the observed cross section limit is 45 fb and the expected cross section limit is 19 fb.
The observed limits are compared to the LO theoretical predictions to estimate the lower mass bound on the excited quarks, which is shown in Fig. 5 for f = 1.0, 0.5, and 0.1. A lower bound of 4.37 TeV is obtained for f = 1.0. The corresponding expected limit is found to be 4.33 TeV. The dependence of the σ × B upper limit on f is found to be negligible for f ≤ 1. Using the theoretical predictions for different coupling strengths from 0.1 to 1.0 and the observed limits, a mass region as a function of the coupling strength is excluded as shown in Fig. 6.
q* Mass [TeV] 1 2 3 4 5 6
B [f
b] × σ
Observed limit Expected limit
σ 1±Expected limit σ 2±Expected limit
Excited quark (f = 1.0) Excited quark (f = 0.5) Excited quark (f = 0.1)
(13 TeV)-12.7 fb
γ q→q*
Figure 5: The expected and observed 95% CL upper limits on σ × B for excited quark search in γ + jet final state corresponding to coupling f = 1.0. The limits are also compared with the theoretical predictions for excited quark production, shown for coupling values f = 1.0, 0.5, and 0.1. The uncertainty at 1σ and 2σ levels are shown as green and yellow shaded bands around expected limit.
9
q* Mass [TeV] 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
= f'
] s
(13 TeV)-1 (8TeV) 2.7 fb-119.7 fb
CMS Preliminary
γ q→q*
Figure 6: The observed (yellow filled) and expected (blue dashed line) excluded regions at 95% CL as a function of excited quark mass and the coupling strength for Λ = Mq? (left axis) or the mass divided by compositeness scale for coupling strength of f = 1 (right axis). The excluded region from Run-I is also shown (red shaded).
6 Summary We have presented a search for excited quarks in the γ + jet final state. The data set collected at √
s = 13 TeV corresponds to an integrated luminosity of 2.7 fb−1. The data are found to be consistent with the predictions of the standard model and no evidence is found for an excited quark resonance. The largest excess of events in data is seen at a γ + jet invariant mass of 2.0 TeV.
A 95% CL upper limit is placed on σ×B for q? production in the γ+ jet final state. Comparing these upper limits with the theoretical predictions, an excited quark state with mass 1.0 < Mq? < 4.37 TeV is excluded at 95% CL for f = 1.0. Also, excited quarks with masses 1.0 < Mq? < 3.64 (1.36)TeV are excluded for f = 0.5 (0.1). We also present the excluded mass as a function of coupling strength in Fig. 6.
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4 Resonance Shape and Background Fit
5 Results
6 Summary
