Search for low-mass resonances decaying into two jets and produced in association with a photon or a jet at $\sqrt{s}=13$ TeV with the ATLAS detector

A search is performed for localized excesses in the low-mass dijet invariant mass distribution, targeting a hypothetical new particle decaying into two jets and produced in association with either a high transverse momentum photon or a jet. The search uses the full Run 2 data sample from LHC proton-proton collisions collected by the ATLAS experiment at a center-of-mass energy of 13 TeV during 2015-2018. Two variants of the search are presented for each type of initial-state radiation: one that makes no jet flavor requirements and one that requires both of the jets to have been identified as containing $b$-hadrons. No excess is observed relative to the Standard Model prediction, and the data are used to set upper limits on the production cross-section for a benchmark $Z'$ model and, separately, for generic, beyond the Standard Model scenarios which might produce a Gaussian-shaped contribution to dijet invariant mass distributions. The results extend the current constraints on dijet resonances to the mass range between 200 and 650 GeV.


Introduction
The Standard Model of particle physics (SM) successfully describes a wide range of phenomena across many orders of magnitude of energy at colliders, astrophysical observatories, and other experiments [1].Nevertheless it fails to account for many observed phenomena, such as the presence of dark matter (DM) [2][3][4] and the imbalance of matter over antimatter in the observable universe [5].While there are a wide range of proposed models of physics beyond the SM (BSM) to explain these effects [6][7][8][9][10][11][12][13][14][15][16][17], this paper focuses on a search for a hadronically decaying resonance.
′ bosons are hypothetical spin-1 vector bosons that are singlets under electric and color charge [1], predicted in a variety of BSM models as a potential mediator to dark matter particles [14,[17][18][19][20][21][22].Direct  ′ searches have shown to be an effective way of constraining BSM models [19][20][21].Searches at the Large Hadron Collider (LHC) for  ′ decays into pairs of charged leptons set strong constraints [21,23], but may be eluded by choosing the couplings of the  ′ such that it is leptophobic, meaning it does not couple to SM leptons.However, constraints from searches for hadronically decaying  ′ resonances cannot be avoided in this way, since the same  ′ -- decay vertex would also be responsible for  ′ production at the LHC for any kind of resonance or search for topologies with a single reconstructed object recoiling against a large missing transverse energy.Additionally, the  ′ -- vertex would be necessary for the dark matter self-annihilation cross-section that drives the relic-density for weakly interacting massive particles [2].
The ATLAS and CMS Collaborations at the LHC have published several searches that are sensitive to hadronic  ′ production using a variety of strategies.Searches for excesses in the invariant mass of the two jets with the highest transverse momentum ( T ) in the event constrain  ′ production at high masses [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].The lower reach of these searches are limited by the bandwidth available to single-and multĳet triggers, and so different strategies must be used to gain sensitivity to  ′ masses below around twice the  T threshold where these triggers become fully efficient, around 1 TeV.One strategy is to record only minimal information, but at a higher rate than the standard triggers, enabling lower trigger thresholds [31,39].A complementary approach, explored in this paper, relies on the production of high- T initial-state-radiation (ISR), such as a jet or a photon, which recoils against the  ′ , enabling access to lower dĳet masses without trigger bias.This type of search was performed by the ATLAS and CMS Collaborations in topologies where the two  ′ decay products can be resolved as individual jets [40,41] and the case where the decay products are sufficiently boosted to be reconstructed into a single large-radius jet [42][43][44][45][46].This paper explores the resolved case, where the resonance decay products are reconstructed into two jets, covering a resonance mass range of 200 GeV to 650 GeV.In total, four different channels are studied, based on the type of ISR particle and the flavor composition of the  ′ decay products.The first channel,   , selects events in which the ISR is a photon and applies an inclusive selection on the jets that form the  ′ .The second channel, , focuses on the case where the ISR is a photon and both jets are identified as containing -hadrons (-tagged).The third and fourth channels focus on the case where the ISR is a jet, both in the inclusive case (   ), and the case where both jets from the candidate resonance decay are -tagged (  ).While -tagging requirements impose assumptions on the  ′ decay products, they also provide significant background suppression, resulting in a more powerful search for some models.The cross-sections for the    and   processes are higher than for    and .However, the    channel has the additional challenge of identifying which jets might correspond to the  ′ decay products, and which correspond to the ISR.Furthermore, different trigger thresholds apply for recorded events triggered by a photon or a jet.Hence a different kinematic acceptance is imposed on the ISR object for the various channels.The two channels where the ISR is a photon are collectively called the photon channels, while the two where the ISR is a jet are referred to as the trĳet channels.
In addition to the increased luminosity, this analysis features several improvements over the previous analysis targetting the same signature [40], including a better -tagging algorithm that reduces the background and the inclusion of the trĳet channels.The dominant backgrounds for this search are multĳet and single-photon production, which are estimated from data using a functional form fit to the  jj distribution.For each channel, estimates for background and signal are combined into a likelihood function, where the signal yields are controlled by a free multiplicative parameter.The signal is interpreted as either a  ′ boson or a generic narrow resonance producing a Gaussian-shaped bump in the measured mass spectrum.
The paper is organized as follows.The ATLAS detector at the LHC and the data and simulated samples used in this search are described in Sections 2-3.The object and event selection for the four channels are summarized in Section 4. The methodology of the search is introduced in Section 5 and the systematic uncertainties are discussed in Section 6.The results are presented in Section 7 and conclusions are drawn in Section 8.

The ATLAS detector
The ATLAS detector [47] at the LHC covers nearly the entire solid angle around the collision point. 1 It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadron calorimeters, and a muon spectrometer incorporating three large superconducting air-core toroidal magnets.
The inner-detector system is immersed in a 2 T axial magnetic field and provides charged-particle tracking in the range of || < 2.5.The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track, the first hit normally being in the insertable B-layer installed before Run 2 [48,49].It is followed by the silicon microstrip tracker , which usually provides eight measurements per track.These silicon detectors are complemented by the transition radiation tracker (TRT), which enables radially extended track reconstruction up to || = 2.0.The TRT also provides electron identification information based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to transition radiation.
The calorimeter system covers the pseudorapidity range || < 4.9.Within the region || < 3.2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering || < 1.8 to correct for energy loss in material upstream of the calorimeters.Hadron calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within || < 1.7, and two copper/LAr hadron endcap calorimeters.The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimized for electromagnetic and hadronic energy measurements respectively.
The muon spectrometer comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by the superconducting air-core toroidal magnets.The field integral of the toroids ranges between 2.0 and 6.0 T m across most of the detector.Three layers 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the -axis along the beam pipe.The -axis points from the IP to the center of the LHC ring, and the -axis points upwards.Cylindrical coordinates (, ) are used in the transverse plane,  being the azimuthal angle around the -axis.
of precision chambers, each consisting of layers of monitored drift tubes, cover the region || < 2.7, complemented by cathode-strip chambers in the forward region, where the background is highest.The muon trigger system covers the range || < 2.4 with resistive-plate chambers in the barrel, and thin-gap chambers in the endcap regions.
Interesting events are selected by the first-level trigger system implemented in custom hardware, followed by selections made by algorithms implemented in software in the high-level trigger [50].The first-level trigger accepts events from the 40 MHz bunch crossings at a rate below 100 kHz, which the high-level trigger further reduces to record events to disk at about 1 kHz.
An extensive software suite [51] is used in data simulation, in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment.

Data and Monte Carlo simulated samples
This analysis is performed using data from proton-proton ( ) collisions at √  = 13 TeV at the LHC, collected during 2015-2018 with the ATLAS detector.The total integrated luminosity of this data sample is 140 fb −1 [52], obtained using the LUCID-2 detector [53] for the primary luminosity measurements.Due to the high instantaneous luminosity and the large total inelastic   cross-section, there are, on average, 33.7 collisions in each bunch crossing.The additional collisions not selected as the hard-scatter process are referred to as pileup collisions.Data in this analysis are required to satisfy standard quality requirements [54].
Samples of Monte Carlo (MC) simulated signal and background events are used in this analysis for optimization, estimate of possible signal contributions, and validation of background estimation strategies.
The main benchmark model is a simplified leptophobic  ′ axial-vector mediator signal, which is used to test the sensitivity to potential resonant signals.The choice of this benchmark signal is motivated by the role that dĳet resonance searches play in constraining possible interactions between dark matter and SM particles.This simplified model considers an -channel mediator with axial-vector interactions, as described in Refs.[18,55].Two relevant parameters of this model in the dĳet search are the  ′ mass, and the coupling of the  ′ to quarks (  ), which affect the intrinsic width of the resonance.The mass of the dark matter fermion is set to be much heavier than the  ′ mass, such that the decay width into dark matter is zero.In all channels, signal samples are generated for  ′ masses between 200 GeV and 650 GeV, with the coupling of the mediator to non-top-quarks set to 0.2, regardless of the quark flavor.Such a choice for the coupling value is a benchmark model already used in other analyses [40].Also, given the  ′ intrinsic width for   = 0.2 is much smaller than the experimental resolution, such a sample is adequate to also model the shape of signals with slightly different or smaller   values.Signal samples are generated separately for a  ′ decaying into ,, and  quark flavors and  ′ decaying into -quarks, in order to enhance the signal statistical precision for the -tagged channels.
The signal samples are simulated using the MadGraph generator [56] at leading-order (LO) in perturbative quantum chromodynamics (QCD) with the NNPDF2.3loparton distribution function (PDF) set [57].The events are interfaced to Pythia8.244 [58,59] to model the parton shower, hadronization, and underlying event, with parameter values set according to the A14 tune [60].EvtGen [61] is used to model decays of heavy flavor hadrons.To further increase statistical precision in the    channel, a generator-level filter is applied on the photon  T .Two sets of samples are produced: one set with this filter defined to be  T, ≥ 130 GeV and a second with the filter at  T, ≥ 65 GeV.For the trĳet channels, a generator-level jet filter of 370 GeV is applied on the leading- T  = 0.4 jet, which is fully efficient for the reconstructed jet  T threshold.The generator-level filters are chosen based on the triggers used in the two different analyses, to ensure high statistical precision for each mass point without introducing kinematic biases.
While the final background estimate is performed using a data-driven approach, background multĳet and photon-plus-jets samples are used to optimize the event selection and validate the background estimation strategy.For the photon channels, prompt single-photon production is simulated with the Sherpa 2.2 [62] generator.In this arrangement and thanks to the Comix [63] and OpenLoops [64][65][66] libraries, matrix elements for up to two partons are calculated to next-to-leading-order (NLO) accuracy, while matrix elements for up to four partons are calculated at LO in QCD.They are matched with the Sherpa parton shower [67] using the MEPS@NLO prescription [68][69][70][71] with a dynamic merging scale cut [72] of 20 GeV.Photons are required to be isolated according to a smooth-cone isolation criterion [73].Samples are simulated using the NNPDF3.0nnloPDF set [74], along with the dedicated set of tuned parton-shower parameters developed by the Sherpa authors.
For the trĳet channels, background samples of simulated multĳet processes are generated using Pythia 8.230 with the 2 → 2 matrix element, and additional jets are produced through the parton shower.Events are simulated using the A14 tune [60], the Lund string hadronization model and the NNPDF2.3loPDF set.The Pythia parton shower algorithm uses a dipole-style  T -ordered evolution, and its renormalisation and factorisation scales are set to the geometric mean of the squared transverse masses of the outgoing particles.
The generated background and signal events are passed through a detailed detector simulation [75] based on Geant4 [76].Additional minimum-bias interactions simulated using Pythia8 with the A3 tune [77] and the NNPDF2.3loPDF set [57] are overlayed to the backgrond and signal events, to model pileup interactions.The distribution of the average number of pileup interactions in simulation is reweighted during data analysis to match that observed in Run 2 data.

Object reconstruction
While the four different channels use different combinations of objects, the object reconstruction is standardized across all of the different channels.Three different objects are used: jets, -tagged jets, and photons.
Selected events are required to contain a primary vertex with at least two associated tracks with transverse momentum  T > 0.5 GeV [78].The vertex with the highest sum of  2 T of the associated tracks is taken as the primary vertex.
Jets in this analysis are reconstructed from particle flow objects [79] using the anti-  algorithm [80] as implemented in FastJet [81], using a jet radius parameter  = 0.4.The ATLAS particle flow algorithm combines measurements from the ATLAS inner detector and calorimeter systems [82] to improve the jet energy resolution, reduce sensitivity to pileup effects, and improve jet reconstruction efficiency, especially at low jet  T .The jet energy scale of particle flow jets is calibrated with a combination of simulation-based and in situ corrections [83].Calibrated jets are required to have a  T > 25 GeV and satisfy || < 2.5.To reduce the effects of pileup, jets with  T < 60 GeV and || < 2.4 are required to satisfy the "tight" working point of the jet vertex tagger criteria [84], which selects jets originating from the selected primary vertex.
A set of quality criteria is also applied to reject events containing at least one jet arising from non-collision sources or detector noise [85].
Reconstructed jets are -tagged using the DL1r multivariate algorithm [86].Jets are considered -tagged if they satisfy the 77% -tag efficiency working point, as measured in inclusive  t events.The corresponding rejection factors for gluon/light-quark jets and charm-quark jets are approximately 200 and 5, respectively.This working point was found to result in optimal signal sensitivity for both the  and   channels.
Photons are reconstructed from energy deposits in the electromagnetic calorimeter [87].Reconstructed photon candidates are required to have  T > 25 GeV, and only central photons with || < 2.5 are considered, excluding the barrel/endcap calorimeter transition region (1.37 < || < 1.52).Only photons that satisfy the tight identification requirement are considered, and additional tight isolation requirements are imposed to further suppress contamination from jets [87].
An overlap removal procedure is applied to avoid any double-counting between the reconstructed photons and jets, by removing any jet with an angular distance √︁ Δ2 + Δ 2 < 0.4 to any photon.

Photon channel selection
The two photon channels (   and ) are required to satisfy the singel-photon trigger [88] with the lowest threshold where all events passing it are saved (unprescaled), and a single photon with  T > 150 GeV is required in order for the trigger selection to be fully efficient.In addition, the event is required to have two reconstructed jets passing the selection in Section 4.1, and the two highest- T (leading) jets are used to reconstruct the resonance candidate.Several dĳet and -jet kinematic variables were studied to enhance the  ′ →  q signal over the expected background, and the strongest discriminating variable was found to be the asymmetry

2
, where  1 and  2 are the rapidities of the two selected jets.It is expected that a signal from  ′ production produces isotropic jets while forward jets are more common in background events, causing the signal to have smaller values of  * than the background.The shape of the  * variable is found to be well described by the background simulation, with maximum differences of a few percent.A cut of  * < 0.825 is applied to maximize the signal sensitivity across the different mass ranges.For the  channel, in addition to satisfying the selection for the    channel, the two leading jets in the event are required to satisfy the -tagging requirements described in Section 4.1.

Trĳet channel selection
In both the    and   channels, events are required to have at least three reconstructed jets, where the leading jet is required to be above 475 GeV to be fully efficient for the lowest unprescaled single jet trigger [89].When considering only the three leading- T jets in a given event, there are three possible choices to assign two jets as corresponding to the resonance decay product candidates. 2In the case where the resonance decays into two -quarks, the combinatorial problem can be in principle trivially solved by identifying the two -tagged-jets in the event.While possible, this causes challenges in background modeling, and so this trivial solution is not used.To illustrate the combinatorial problem more clearly, Figure 1 shows the particle-level dĳet mass spectrum of different jet pairs for three different  ′ signal samples.Each jet is assigned a number based on its  T ordering, e.g.,  12 is the dĳet mass distribution ( jj ) of the leading and subleading jets.For lower  ′ mass, the  23 contribution clearly peaks near the  ′ mass, while at higher  ′ mass, contributions from  13 become more important.
The combinatorial challenge is further complicated by the background estimate, which relies on a functional fit to a smoothly falling  jj spectrum, meaning that any additional selection to solve the combinatorial problem must also result in a smooth  jj spectrum.The dominant background for these channels may be simplistically modeled as balanced high- T dĳet events where one jet emits a softer jet, resulting in a trĳet event.Since the emitting jet loses some energy to its emission, the three jets are roughly  T ordered from low to high as the emitted jet, the emitting jet, and the non-emitting jet, it is possible to roughly map  23 to  emitted,emitting ,  13 to  non-emitting,emitted and  12 to  non-emitting,emitting .In reality, this description of the background does not fully describe the observed background.Multiple emissions may occur, and various detector effects can spoil the  T balance of the reconstructed jets, meaning that the assumption that  23 corresponds to the mass of the emitting and emitted jet may not hold in some events.
The mass spectra of the three possible pairings have different shapes, since different underlying physics contributes to each of them.This is illustrated in Figure 2 the spectrum, roughly corresponding to the turn-ons in these different pairings.Hence instead of pairing jets based solely on  T -ordering, a different pairing method based on the kinematics of the three leading jets need to be used in the analysis.
Three similar options for choosing the dĳet pairing were compared to determine which one results in the smoothest spectrum, each roughly corresponding to the mass of the emitting and emitted jet: the secondand third-leading jets (as described above), the jet pair with the minimum |Δ|, and the pair of jets with the lowest mass.The smoothness of the  jj spectrum at low masses determines the fit range therefore limiting the lowest  ′ mass reach covered by the search.The signal efficiencies of these three  jj selection options are similar.However, selecting jet pairs with the minimum |Δ| between them results in the smoothest low-mass spectrum in studies of multĳet MC simulation.
One final aspect to consider is that in dĳet-like topologies, where one of the high- T jets radiates a low- T gluon reconstructed as a jet, the gluon radiation tends to happen at small angles, while the two high- T jets are produced back-to-back.This means that the |Δ| selection tends to identify the radiating jet and the gluon.Depending on which jet radiates the gluon, this selection can identify either the secondand third-leading jets or the first-and third-leading jets.In a small fraction of events, the |Δ| selection identifies the two leading jets in the events as trĳets, but where the underlying topological assumptions break down.These events, comprising around 0.2% of background events, do not produce a smooth  jj spectrum, as shown in Figure 2(b).Based on this, events where the |Δ| selection identifies the two leading jets are rejected to avoid biasing the fit.
To summarize, the algorithm selected to identify the  ′ decay candidates takes the jet pair with the minimum |Δ| between them and rejects the event if such jets correspond to the two  T -leading jets.The pair of jets passing such requirements are referred to as the selected jets and, as explained above, produces the smoothest low-mass spectrum in studies of multĳet MC simulation.No additional background suppression is applied, since cuts on observables such as  * can sculpt the background distribution.For the   channel, in addition to passing the same jet requirements as the    channel, the two jets with the minimum |Δ| between them are also required to be -tagged.The resulting signal  jj distributions after the event selection are shown for each channel in Figure 3.The    channel, at higher masses, has a clear tail in the  jj distribution resulting from the incorrect selection of the dĳet pair.This tail is less pronounced for the   channel, owing to the additional -tagging requirement imposed on the selected jets.The signal efficiency for the   selection gets smaller at high masses, as the selected dĳet pair is often not -tagged there.Such an effect is considered less relevant than obtaining a smoothly falling  jj distribution for the background at lower  jj values, as the more energetic part of the  jj spectrum is better studied by other analyses [31, 39].

Methodology
The numbers of signal and background events are estimated channel-by-channel by binned profile likelihood fits of a signal-plus-background model to the measured  jj distributions.The number of selected events as a function of  jj is parameterized in the fit as: where   and   are the number of signal and background events, respectively, and   ( jj ) and   ( jj ) are their probability distribution functions.All the distributions entering the fit are binned finely in bins of 1 GeV width, to minimize the loss of information and the typical biases of binned likelihood fits [90].

Signal templates
The likelihood fit results are interpreted using model-independent and model-dependent strategies.For the model-independent limits, the signal probability distribution functions are taken as Gaussian distributions, with a mean equal to the resonance mass, with widths ranging from 5% to 15%.The upper end of the template width is determined based on the results of the spurious signal test and signal injection test described in Section 5.2.
For the model-dependent limits, the shape of the  jj distributions from simulated samples are used directly.Signal samples are produced with a limited set of signal masses, and these templates are used as inputs to an interpolation between mass points to provide a finer signal grid using the method described in Ref. [91].

Background estimate
The selected jets in non-resonant QCD processes, which constitute the SM background for this search, result in dĳet systems with smoothly-falling invariant mass distributions.In order to estimate this background in the search regions, a class of parametric functions is fit to the  jj distributions: where  =    / √ , and  1 ,  2 ,  3 ,  4 ,  5 , and  6 are the fitted parameters.For an -parameter fit, only the first  parameters are allowed to vary, while the higher- terms are fixed to zero.Such functions were successfully used by a wide variety of dĳet and multĳet resonance searches by the CDF, CMS, and ATLAS Collaborations [25, 27,32,34,[92][93][94][95][96][97].
The data-driven background fitting procedure employs a 5-parameter function and was validated using several cross-checks, including spurious signal tests and signal injection tests.These tests were performed using simulated samples, with a subset of checks performed on a partial data sample.
The spurious signal test evaluates whether the fitting procedure is biased such that it produces a non-zero extracted signal when fitting a data sample with no true signal.This test is performed using many pseudodata distributions which are generated from background-only fits to the simulated  jj distribution with a 6-parameter function, which has more flexibility than the final fit function.Each distribution is tested by performing signal+background fits with a 5-parameter fit function and various signal hypotheses.Gaussian-shaped signals with widths ranging from 5 to 15% of the signal mean are tested, as well as using the signal templates from the  ′ simulated samples directly.For each pseudodata distribution and signal hypothesis   is determined, and the median value and standard deviation of the   distribution are taken to be  spur and  spur respectively.To satisfy the spurious signal requirements,  spur / spur is required to be less than 0.5 for every signal hypothesis mass point.This requirement is satisfied for all channels for  ′ masses between 250 GeV and 650 GeV.While the fits extend to  jj values beyond 650 GeV, higher signal masses do not always satisfy the spurious signal tests, and are not considered further.In addition, for the    channel, the signal shape degrades significantly at higher signal masses, since the selected jets often do not correspond to the resonance decay products.Finally, the   channel passes this requirement for resonance masses down to 200 GeV, which is possible since the  jj spectrum in this channel is smooth down to lower masses than the other channels.
The signal injection test is performed to ensure that the fit is able to extract a signal component with the expected signal strength.Simulated signal models, with both Gaussian shapes and in a range of widths and signal templates, are included in the fitted background distribution with a given signal cross-section selected to be in the range 0 − 5, where  =   / √   and the number of signal and background events are determined using a 2 window around the injected signal peak in each test.The injected signals in this study were extracted for pseudodata distributions, with the requirement that the median of the extracted significances is within 0.5 of the injected significance, for all the signal hypotheses and mass points individually.These tests were satisfied for all channels for the same range of resonance masses and widths as with the spurious signal tests, while they failed for Gaussian-shaped signals with widths above 15%.
The fitted  jj region is determined separately for each channel.For the chosen range, the fit quality, spurious signal, and signal injection tests are must be satisfied for the MC simulation.The fitted  jj region is chosen to prioritize a fit that starts as low in  jj as possible while maintaining a wide enough fit range to study the relevant signal models.The lowest part of the  jj spectrum does not have a smoothly falling shape because of trigger inefficiency and analysis selection effects, such as the  * cut, and such a behavior cannot be fit by the class of functions considered.The    and  channels are found to have a smoohly falling behavior starting from  jj = 200 GeV, while the    and   channels from  jj = 225 GeV and  jj = 160 GeV respectively.The upper fit ranges are defined from the edges of bins defined by the  jj resolution, and are taken to be the highest among those where the background fit functions to the simulated  jj distributions have a  2 -value above 0.05.The procedure to determine the fit range is repeated on the measured data, to ensure the fit ranges estimated from the MC simulation are adequate.If they are not, the upper limit of the fit range is reduced by one  jj resolution bin, and all the tests are repeated.
For the  channel, the background estimate is further validated using an ABCD method with simulated samples, following the strategy of Ref. [40].Such method allows a test of the background estimate in the  channel with a higher statistical precision than available in the existing simulated sample and also serves as a test for potential biases in the  jj spectrum introduced by -tagging.The ABCD re-weighting method defines different regions based on whether events satisfy or fail to meet the  * selection and the -tagging requirements, providing an estimate for the -tagged spectrum which is based on the un-tagged distribution.The ABCD-reweighted  jj spectrum is found to be compatible with the one obtained by applying the  event selection, within the statistical precision of the re-weighted and high-statistics spectrum.Given the level of agreement, no uncertainty related to -tagging is considered to affect the background fit.The resulting distribution is found to satisfy the spurious signal and signal injection tests described above, providing further confirmation of the fit strategy.Since this method relies on the  * selection, the technique cannot easily be applied to the   channel, but the conclusions on the possible -tagging biases from  apply to the   channel as well.

Systematic uncertainties
When interpreting the analysis in terms of candidate signal models, the impact of various experimental and theoretical sources of uncertainty is considered.
Luminosity.The uncertainty in the combined 2015-2018 integrated luminosity is 0.83% [52], obtained using the LUCID-2 detector [53] for the primary luminosity measurements.It is treated as a single normalization uncertainty applied as a scale factor to the signal models.
Jets.Systematic uncertainties in the  = 0.4 jet energy scale and resolution are evaluated using a series of in situ measurements and simulation-based techniques, thoroughly documented in Ref. [83].The most significant source of uncertainty in the JES originates from uncertainties on the flavor of the jet.Uncertainties on the JVT are also included, but are negligible, since the uncertainties are applied only to the signal.For the photon channels, these uncertainties have a negligible impact on the efficiency, and around a 2% impact on the location of the  ′ mass.For the trĳet channels, the impact on the location of the  ′ mass is around 1%, while the impact on the selection efficiency is around 3%.
Photons.The systematic uncertainties in the photon identification and isolation efficiencies are estimated following the prescriptions in Ref. [87].They are evaluated by varying the correction factors for photon selection efficiencies in simulation by the corresponding uncertainties and affect the diphoton selection efficiency.The experimental uncertainties in the photon energy scale and resolution are obtained from Ref. [87], and are only applied to the    and  channels.These systematic uncertainties primarily impact the selection efficiency of the signal events, with a total impact on the efficiency of around 2%.

B-tagging.
For final states with requirements on the number of -tagged jets, additional systematic uncertainties are applied.The systematic uncertainty in the -tagging efficiency is measured using data enriched in  t events for jet  T < 400 GeV and extrapolated to higher  T regions using a method similar to the one described in Ref. [98].The impact of this systematic uncertainty in the efficiency of the event selection of signal events ranges from 2-3%.

Parton distribution functions.
The theoretical uncertainty envelope associated with the NNPDF2.3loPDF set is propagated through the analysis, where their impact is primarily on the normalisation of the signal events.The change in analysis selection efficiency is recalculated for each provided PDF variation, and the standard deviation of all such variations is taken as a measure of the systematic uncertainty due to PDFs.This uncertainty affects signal samples and ranges from 1-5% across the different channels, with larger effects on the photon channels than on the dĳet channels.
Background modeling A systematic uncertainty to cover potential biases in modeling the background shape is accounted for using the spurious signal  modeling .The value of  modeling is determined as the envelope of | spur | over  jj and is considered to cover features of the  jj background spectrum which are not modeled by the background parametrisation chosen.This is implemented in the likelihood fit as an additional signal contribution, such that where  signal (  ′ ) is the number of extracted signal events at a given   ′ , , , , and L are the signal cross-section, acceptance, signal branching ratio, and integrated luminosity, respectively; and  modeling is a nuisance parameter associated with the background modeling uncertainty.The signal acceptance is defined as the fraction of simulated events at detector level that pass the analysis selection cuts.
The spurious signal uncertainty is found to be, together with the statistical uncertainty, the leading source of uncertainty on the extracted number of signal events.

Results
The dĳet invariant mass distributions in data, together with the corresponding fitted background estimates, are shown in Figure 4 for all four channels.The data are well described by the 5-parameter fit function in all channels, and the global  2 -value ranges from 0.10 to 0.42 for the different channels.Fit ranges are chosen such that the fits satisfy the tests explained in Section 5.2.For the photon channels, the background fit spans the  jj range of 200 GeV to 875 GeV for the    channel and of 200 GeV to 854 GeV for the  channel, while for the    and   channels, the fit spans 225 GeV to 1000 GeV and 160 GeV to 700 GeV respectively.
The BumpHunter [99,100] algorithm, as implemented in pyBumpHunter [101,102], is used to measure the statistical significance of localized excesses of the measured data relative to the estimated background in the  jj distributions, which could be due to the presence of resonant signals.This is done using mass bins with a bin width determined by the mass resolution of  jj as a function of the mass, where the mass resolution is determined using a Gaussian function fit to the  jj response distribution.Windows are allowed to have a width of up to three mass-resolution bins, hence corresponding to three times the  jj resolution, and for each scanned window BumpHunter evaluates the statistical significance of the observed difference between the data distribution and the background fit.The BumpHunter -value is defined as the smallest observed probability for the data in a given window to deviate from the background prediction by the observed amount due to a Poissonian fluctuation of the background, using pseudoexperiments generated from the background prediction, and without considering systematic uncertainties.The most significant localized excesses identified by the BumpHunter algorithm are found at 348 GeV with a local significance of 1.9 for the    channel, at 380 GeV with a local significance of 1.8 for the  channel, at 404 GeV with a local significance of 1.8 for the    channel and at 522 GeV with a local significance of 1.5 for the   channel.
As no significant deviation from the background expectation is observed, upper limits are set on the signal production rate as a function of the hypothesized resonance mass.The numbers of signal and background events are estimated from maximum-likelihood fits of the signal-plus-background models to the corresponding  jj distributions.Systematic uncertainties described in Section 6 are included in the fits via nuisance parameters constrained by Gaussian-distributed penalty terms.Systematic uncertainties affecting the signal shape have only a small impact on the result, and the dominant uncertainties arise from the statistical and spurious signal uncertainties.The -value is determined from a profile-likelihood-ratio-test statistic [103].The local -value for compatibility with the background-only hypothesis when testing a given signal hypothesis ( 0 ) is evaluated based on the asymptotic approximation [103].Global significance values are computed from background-only pseudo-experiments to account for the trial factors due to scanning both the signal mass and the width hypotheses.The expected and observed 95% confidence level (CL) exclusion limits on the product of the cross-section, branching ratio, and acceptance are computed using a modified frequentist-approach [104], in an asymptotic approximation to the test-statistic distribution [103].
Figure 5 shows the 95% CL upper limits on the  ×  × BR of the  ′ axial-vector dark-matter mediator as a function of its mass, derived using the signal templates.Results are interpolated linearly in the log of the cross-section.Similar results are shown in Figure 6 for generic signals with Gaussian function shapes with 5%, 7%, 10%, 12%, and 15% signal widths.
Given the relation between couplings and cross-section, the limits on the  ′ cross-sections can be translated to contraints on the   coupling, by taking into account the values of the simulated sample cross-sections and the analysis acceptance.A comparison of the limits on the   coupling as a function of the  ′ mass for all channels is shown in Figure 7.For the flavor-inclusive channels, the cross-section combines the contributions from the signal samples where the  ′ decays are restricted to light flavors with the samples where the  ′ decay products decay into -quarks.While the limits on  ×  × BR are much stronger for the  and   channels than for the    and    channels, the cross-sections and branching ratios are much lower, meaning that the limits on   are more similar across channels.Overall, the    and    channels set the strongest limits on the   coupling.
The limits on the   coupling obtained from the    and    channels are similar in value and there is only a small overlap in the selected events across the two categories.Hence a combination of the two channels can further strengthen the constraints on   .No combination of the -tagged channel is considered, as the constraints on   from such channels are weaker than the flavor-inclusive ones.
Events passing both the    and    selections are removed from the    channel, to have two statistically independent measurements.Such double-counted events amount to 0.2% of all the   -selected events and their impact on the    channel fits were found to be negligible.A combined likelihood function, which Figure 6: Expected and observed 95% CL upper limits on the product of the cross-section, acceptance and branching ratio ( ×  ×BR) for the (a)   , (b) , (c)   , and (d)   channels with the background and signal contributions modeled by a 5-parameter fit function and Gaussian distributed signal templates with a mass  G and width  G , respectively.Observed limits are indicated with markers and a solid line, and expected limits are indicated with a dashed line.Observed and expected limits corresponding to different choices of template widths (5%, 7%, 10%, 12% and 15%) are indicated as different sets of markers or line styles, respectively.The shaded bands around the expected limit for templates with 5% width indicate the (darker band) 1 and (lighter band) 2 uncertainty range.is the product of the    and    likelihood functions, is used to obtain 95% CL upper limits on   .In the combined likelihood, the jet and luminosity systematic uncertainties are taken as correlated among the channels.Spurious signal and PDF systematic uncertainties are instead taken as uncorrelated, as the background fit functions and production mechanisms of the two processes are independent across channels.Photon systematic uncertainties only affect the    part of the combined likelihood.The combination improves the limits on   relative to the individual channels, as shown in Figure 8, with both the expected and observed limits excluding coupling values down to 0.05-0.07.

Conclusion
Dĳet resonances with a width up to 15% of the mass, produced in association with a photon or jet, were searched for in 140 fb −1 of LHC   collisions recorded by the ATLAS experiment at √  = 13 TeV.This search expands on previous similar searches by using the full Run 2 data samples, and by including the case where the initial-state radiation is a jet.It considers the cases where no flavor requirements are placed on the resonance decay products, and the case where both of the decay products are required to be -tagged, resulting in four channels, depending on the type of initial-state radiation and the flavor requirements.In all four channels, the observed  jj distribution is well-described by a smooth functional fit without contributions from such resonances.No significant excess of events beyond the Standard Model expectation is observed, and so upper limits are set on two models:  ′ axial-vector dark-matter mediators and Gaussian-shape signal contributions for resonant masses between 200 GeV and 650 GeV.Relative to already published results using a similar analysis technique, this search improves the limits on the  ′ -- coupling   by up to 50%, with the most stringent limits on   set by the    channel for lower  ′ candidate masses and by the    channel for higher  ′ masses.A further combination of the    and    channels is performed, which set limits on   down to 0.05-0.07.

Figure 1 :
Figure 1: Distributions of particle-level dĳet mass in simulated  ′ →  events corresponding to different combinations of two jets, where jets 1,2 and 3 correspond to the leading, sub-leading and third-leading jets.Signal events generated with (a)   ′ = 250 GeV, (b)   ′ = 450 GeV and (c)   ′ = 650 GeV are shown.

Figure 2 :
Figure 2: (a) Distributions of reconstructed dĳet mass in simulated background events corresponding to different combinations of two jets, where jets 1,2 and 3 correspond to the leading, sub-leading and third-leading jets, and (b) comparison of the shape of the normalized selected dĳet  jj spectra in the case where the selected jets are the second and third leading jets ( min|Δ | =  23 ), the first and third leading jets ( min|Δ | =  13 ), or the first and second leading jets ( min|Δ | =  12 ).Events are simulated with Pythia.

Figure 3 :
Figure 3: Distributions of reconstructed dĳet mass in simulated  ′ →  events with different   ′ values in the (a)   , (b) , (c)   , and (d)   channels after full event selection.

Figure 4 :
Figure 4: Dĳet invariant mass distributions data compared to the fitted background estimates for the (a)   , (b) , (c)   , and (d)   channels.Bottom panel shows the fit residuals in terms of standard deviations ().The distributions are shown here with the  jj resolution binning.

Figure 5 :
Figure 5: Expected and observed 95% CL upper limits on the product of the cross-section, acceptance and branching ratio ( ×  × BR) as a function of the  ′ mass for the (a)   , (b) , (c)   , and (d)   channels with the background and signal contributions modeled by a 5-parameter fit function and templates from the signal samples, respectively.Observed limits are indicated with markers and a solid line, and expected limits are indicated with a dashed line.The shaded bands around the expected limit indicates the (darker band) 1 and (lighter band) 2 uncertainty range.The dotted line represents the expected  ×  × BR assuming   = 0.1, as obtained from the MadGraph signal samples.

Figure 7 :
Figure 7: Expected and observed 95% CL upper limits on the   coupling as a function of the  ′ mass on the   , ,   , and   channels with the background and signal contributions modeled by a 5-parameter fit function and templates from the signal samples, respectively.Observed limits are indicated with markers and a solid line, and expected limits are indicated with a dashed line.

Figure 8 :
Figure 8: Expected and observed 95% CL upper limits on the   coupling as a function of the  ′ mass on the    channel, the    channel and the combination of the two.The background and signal contributions are modeled by a 5-parameter fit function and templates from the signal samples, respectively.Observed limits are indicated with markers and a solid line, and expected limits are indicated with a dashed line.The shaded bands indicate the (darker band) 1 and (lighter band) 2 uncertainty range on the combined result.