Measurement of the jet mass in high transverse momentum $Z(\rightarrow b\overline{b})\gamma$ production at $\sqrt{s}= 13$ TeV using the ATLAS detector

The integrated fiducial cross-section and unfolded differential jet mass spectrum of high transverse momentum $Z\rightarrow b\overline{b}$ decays are measured in $Z\gamma$ events in proton-proton collisions at $\sqrt{s} = 13$ TeV. The data analysed were collected between 2015 and 2016 with the ATLAS detector at the Large Hadron Collider and correspond to an integrated luminosity of 36.1 fb$^{-1}$. Photons are required to have a transverse momentum $p_{\mathrm{T}}>175$ GeV. The $Z\rightarrow b\overline{b}$ decay is reconstructed using a jet with $p_{\mathrm{T}}>200$ GeV, found with the anti-$k_{t}$ $R = 1.0$ jet algorithm, and groomed to remove soft and wide-angle radiation and to mitigate contributions from the underlying event and additional proton-proton collisions. Two different but related measurements are performed using two jet grooming definitions for reconstructing the $Z\rightarrow b\overline{b}$ decay: trimming and soft drop. These algorithms differ in their experimental and phenomenological implications regarding jet mass reconstruction and theoretical precision. To identify $Z$ bosons, $b$-tagged $R = 0.2$ track-jets matched to the groomed large-$R$ calorimeter jet are used as a proxy for the $b$-quarks. The signal yield is determined from fits of background templates extracted from the data to the different jet mass distributions for the two grooming methods. Integrated fiducial cross-sections and unfolded jet mass spectra for each grooming method are compared with leading-order theoretical predictions. The results are found to be in good agreement with Standard Model expectations within the current statistical and systematic uncertainties.


Introduction
This Letter presents a measurement of the fiducial and differential jet mass cross-sections of high transverse momentum (p T ) Z bosons that decay into b b pairs and are produced in association with a photon, denoted by Z(→ b b)γ.The analysis uses proton-proton (pp) collision data collected in 2015 and 2016 by the ATLAS detector [1] at the Large Hadron Collider (LHC) at a center-of-mass energy of √ s = 13 TeV.This measurement of the unfolded jet mass spectrum of hadronically decaying Z bosons at the LHC explores the experimental features and phenomenological implications of techniques used to reconstruct boosted bosons -colour singlets -decaying into b b.Similar measurements of gluons -colour octets -decaying into b b pairs have also been made by the ATLAS Collaboration [2].The Z(→ b b)γ process provides a well-defined experimental signature for measuring massive boosted Z bosons using high-p T jets containing pairs of b-quarks.A detailed study of the Z → b b signal is important for assessing systematic uncertainties and identification techniques for the measurement of H → b b in the high-p T range, as well as for potential TeV-scale resonances decaying into dibosons, one of them being a Z boson or a Higgs boson decaying into b b [3,4].
The Z(→ b b)γ channel offers advantages in accessing the Z → b b signal compared to the inclusive channels studied in Run 1 by ATLAS [5] and in Run 2 by CMS [6] since it provides both a useful trigger signature via the photon and an opportunity to directly estimate background processes using the data.Initial modelling results with 13 TeV data in the Z(→ b b)γ channel within ATLAS are presented in Ref. [7].The measurement described in this Letter selects b b decays of a Z boson contained within a single jet, referred to as a Z-jet, with transverse momentum p Z-jet T > 200 GeV and a photon with transverse momentum p γ T > 175 GeV.The high-p T requirement enhances the signal over the dominant γ + jets background production, which has a softer p T spectrum.The candidate Z-jet is reconstructed using a 'groomed' anti-k t [8] jet with radius parameter R = 1.0 (large-R jet).A multivariate algorithm is used to determine whether R = 0.2 track-jets that are associated with the large-R jet are b-tagged, i.e. if they contain b-hadron decay products.The approach to tagging presented in this Letter is built upon a foundation of studies from LHC runs at √ s = 7 and 8 TeV, including extensive studies of jet reconstruction and grooming algorithms [9][10][11] and detailed investigations of track-jet-based b-tagging in boosted topologies [7,12].
Two different definitions of jet grooming are used to perform the measurement: 'trimming' [10], and 'soft drop' [11,13].The experimental and phenomenological implications for jet mass reconstruction and theoretical precision are different for the two grooming algorithms.The trimming algorithm is the default used in ATLAS to study boosted bosons, chosen as a result of optimisation studies performed from LHC runs at √ s = 8 and 13 TeV [14].The soft-drop calculations achieve a different theoretical precision and offer advantages such as the formal absence of non-global logarithms.The distribution of the soft-drop mass for QCD processes has now been calculated both at next-to-leading order (NLO) with next-to-leading-logarithm (NLL) accuracy [15,16] and at leading order (LO) with next-to-next-to-leadinglogarithm (NNLL) accuracy [17,18].This level of precision for a jet substructure observable at a hadron collider is surpassed only by the calculation of thrust in e + e − interactions [19].Similar calculations are not currently available for trimmed jets.
The double differential cross-section of soft-drop jets as a function of the mass and transverse momentum were previously measured by ATLAS [20] and CMS [21] in balanced dijet events at √ s = 13 TeV.The trimmed jet mass distribution in dijet and W/Z+jets events was measured by CMS at √ s = 7 TeV [22].

ATLAS detector
The ATLAS detector at the LHC is a multipurpose particle detector with a forward-backward symmetric cylindrical geometry and a near 4π coverage in solid angle.1It consists of an inner detector (ID) for tracking surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic and hadronic calorimeters, and a muon spectrometer.The ID covers the pseudorapidity range |η| < 2.5.It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors.A new inner pixel layer, the insertable B-layer [23,24], was added at a mean radius of 3.3 cm during the period between Run 1 and Run 2 of the LHC.Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity (|η| < 3.2).The hadronic calorimeter uses a steel/scintillatortile sampling detector in the central pseudorapidity range (|η| < 1.7) and a copper/LAr detector in the region 1.5 < |η| < 3.2.The forward regions (3.2 < |η| < 4.9) are instrumented with copper/LAr and tungsten/LAr calorimeter modules optimised for electromagnetic and hadronic measurements, respectively.A muon spectrometer with an air-core toroid magnet system surrounds the calorimeters.Three layers of high-precision tracking chambers provide coverage in the range |η| < 2.7, while dedicated fast chambers allow triggering in the region |η| < 2.4.The ATLAS trigger system consists of a hardware-based first-level trigger followed by a software-based high-level trigger [25].
1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector.The positive x-axis is defined by the direction from the interaction point to the centre of the LHC ring, with the positive y-axis pointing upwards, while the beam direction defines the z-axis.Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis.The pseudorapidity η is defined in terms of the polar angle θ by η = − ln tan(θ/2).Rapidity is defined as y = 0.5 ln[(E + p z )/(E − p z )] where E denotes the energy and p z is the component of the momentum along the beam direction.The angular distance ∆R is defined as (∆y) 2 + (∆φ) 2 .

Data and Monte Carlo simulation
The data were collected in pp collisions at the LHC with √ s = 13 TeV and a 25 ns proton bunch crossing interval during 2015 and 2016.The full data sample corresponds to an integrated luminosity of 36.1 fb −1 after requiring that all detector subsystems were operational during data recording.The uncertainty in the combined 2015-2016 integrated luminosity is 2.1% [26], obtained using the LUCID-2 detector [27] for the primary luminosity measurements.Collision events were recorded with a trigger selecting events with at least one photon candidate with transverse energy E T > 140 GeV.
Monte Carlo (MC) event samples that include an ATLAS detector simulation [28] based on G 4 [29] are used to model the Zγ signal and the small t t + γ and W γ background contributions.In addition, γ + jets MC event samples are used to study the trigger modelling.In addition to the hard scatter, each event was overlaid with additional pp collisions (pile-up) according to the distribution of the average number of pp interactions per bunch crossing, µ , observed in data.These additional pp collisions were generated with P 8.1 [30] using the ATLAS A2 set of tuned parameters [31] and the NNPDF23LO [32] parton distribution function (PDF) set.Simulated events were then reconstructed with the same algorithms as those run on collision data.
The Zγ signal was modelled using the LO S 2.1.1 [33] generator, with the CT10 NLO [34] PDF set; the sample is flavour inclusive (Z(→ qq)γ).An alternative Zγ sample was produced with M G 5.2 [35], which generated LO matrix elements that were then parton showered with P 8.1 using the NNPDF23LO PDF set and the ATLAS A14 set of tuned parameters [36] for the underlying event.This alternative signal sample is used to determine the systematic uncertainty associated with the signal modelling.
The γ + jets samples were also generated with S 2.1.1 and the CT10 NLO PDF set.The matrix element was configured to allow a photon with up to three partons in the final state.The t t + γ processes were modelled by M G 5.2 interfaced to P 8.1.NLO corrections were applied to the t t + γ cross-section [37].The W γ MC samples with hadronically decaying W bosons were generated using S 2.1.1,with a configuration similar to that used for the Zγ sample.Predictions for W γ production were normalised according to the cross-sections provided by the generator.

Event reconstruction and selection
Events are required to have a reconstructed primary vertex, defined as the vertex with at least two reconstructed tracks with p T > 0.4 GeV and with the highest sum of squared transverse momenta of associated tracks [38].
Hadronically decaying high-p T Z → b b candidates are identified using large-R jets to capture both b-quarks, since they will be very close due to the high Lorentz boost.The two different jet grooming algorithms considered in the analysis, trimming and soft drop, differ in their pile-up mitigation and mass resolution performance.
Trimmed calorimeter jets Trimmed calorimeter jets are reconstructed from noise-suppressed topological clusters (topoclusters) of calorimeter energy deposits calibrated to the local hadronic scale (LC) [39], using the anti-k t algorithm with radius parameter R = 1.0 implemented in F J [40,41].Trimmed calorimeter jets are those jets to which the trimming algorithm [10] is applied.The aim of this algorithm is to improve the jet mass resolution and its stability with respect to pile-up by discarding the softer components of jets that originate from initial-state radiation, pile-up interactions, or the underlying event.This is done by reclustering the constituents of the initial large-R jet, using the k t algorithm [42,43], into subjets with radius parameter R sub = 0.2 and removing any subjet that has a p T less than 5% of the parent jet p T ( f cut ).The jet mass, the main discriminating variable, is defined as the magnitude of the four-momentum sum of constituents inside a jet.It is referred to as the calorimeter-based mass if it is calculated using the topoclusters as constituents, or as the track-assisted jet mass [44] if it is estimated by using tracking information.The jet mass for trimmed jets is defined as the weighted combination of the calorimeter-based mass and the track-assisted jet mass, m comb [44], where each input mass is weighted by a factor proportional to their inverse-squared mass resolution.
Soft-drop calorimeter jets Soft-drop calorimeter jets are formed by the application of the soft-drop algorithm [11] to the anti-k t R = 1.0 jets described above, with additional topological cluster preprocessing that is described below.The soft-drop algorithm is designed to remove soft and wide-angle radiation and also contamination from pile-up.In the first step of the grooming algorithm, the anti-k t R = 1.0 jets are reclustered with the Cambridge-Aachen (C/A) [45,46] algorithm so that the constituents are combined purely according to their angular separation.The soft-drop algorithm then reverses the C/A algorithm clustering history and removes the softer subjet at a specific step of the C/A clustering history unless the soft-drop condition is fulfilled: min(p T1 , p T2 ) where z cut and β are algorithm parameters, p T1 and p T2 are the transverse momenta of the declustered subjets at each history step, ∆R 12 is the distance between the subjets in the (η, φ) space and R 0 is a threshold corresponding to the jet radius.The parameters β = 0 and z cut = 0.1 are used in the analysis, based on the studies in Ref. [47].The final measurement is performed in a fiducial range of the jet mass with m jet > 30 GeV, which implies that any collinear divergence is regulated and the measurement remains protected against collinear singularities.The soft-drop jet mass exhibits a pile-up dependence with the chosen parameters and therefore a special version of pile-up suppressed topological clusters are used to construct the jets that are then groomed with the soft-drop algorithm.Specifically, the SoftKiller (SK) algorithm [48] is used in conjunction with Constituent Subtraction (CS) [49,50] based on the studies presented in Ref. [47].CS is applied before the SK algorithm.The CS is an extension of the pile-up subtraction based on jet area [51] and removes pile-up contributions from the individual topoclusters by uniformly adding soft particles (ghosts) to the event with energy density matching the median energy density of the event.The ghosts are then geometrically matched to the topoclusters and only those within ∆R = 0.25 of the topocluster are considered for the pile-up removal procedure.The algorithm proceeds iteratively though each topocluster-ghost pair in order of ascending ∆R and either corrects the p T of individual topoclusters by subtracting the p T of the ghost or removes the topocluster.The SK algorithm exploits the characteristic that particles originating from pile-up collisions are softer than those from the hard-scattering collision and removes particles that fall below a certain p T threshold, determined on an event-by-event basis.The pile-up suppressed topological clusters after CS and SK are used as input to the soft-drop jet reconstruction.The calorimeter jet mass is used for soft-drop jets.
All groomed jets A dedicated MC-based calibration, similar to the procedure used in Ref. [44], is applied to correct the jet p T and mass of both the trimmed jets and the soft-drop jets to the particle level.To account for semileptonic decays of the b-hadrons, the four-momentum of the closest reconstructed muon candidate within ∆R = 0.2 of the b-tagged track-jet is taken into account in the calorimeter-based component of the jet mass observable (see below for the description of the track-jet definition and b-tagging).Muon candidates are identified by matching ID tracks to full tracks or track segments reconstructed in the muon spectrometer.
Muons are required to have p T > 10 GeV and |η| < 2.4, and to satisfy the loose identification criteria of Ref. [52], which impose quality requirements on the tracks, but no isolation criteria are applied.Muons are calibrated, and reconstruction and identification efficiency scale factors, derived from Z → µ + µ − events [52], are applied to simulation.Large-R jets are required to have p T > 200 GeV and |η| < 2.0.A comparison of the calibrated Z-jet mass distribution for trimmed jets and soft-drop jets is shown in Figure 1.
The jet mass distribution of soft-drop jets is significantly broader than that of trimmed jets for both the reconstructed jet mass, Figure 1(a), and the particle-level jet mass, Figure 1(b), whereas the distribution for trimmed jets is more asymmetric than for soft-drop jets at particle level.Track-jets Small-radius jets formed from charged-particle tracks are used as probes of b-hadrons associated with large-R jets that may contain the candidate Z → b b jets.Track-jets are built with the anti-k t algorithm with a radius parameter of R = 0.2 [12] from at least two ID tracks with p T > 0.5 GeV and |η| < 2.5 [53].Only track-jets with p T > 10 GeV and |η| < 2.5 are used and they are associated with the large-R calorimeter jets via ghost-association [54].Track-jets containing b-hadron decay products are tagged with a multivariate algorithm known as MV2c10, which exploits the presence of large-impact-parameter tracks, the topological decay chain reconstruction and the corresponding displaced vertices from b-hadron decays [55,56].The MV2c10 algorithm is configured to achieve an efficiency of 70% for tagging b-jets in a MC sample of t t events, while rejecting 80% of c-jets and more than 99% of light (quark or gluon) jets in the same sample.This configuration is referred to as the 70% working point (WP).For MC samples, the tagging efficiencies are corrected to match those measured in data [53,57,58].These small-radius track-jets are referred to as b-jets.By using this small-R definition, b-jets can be reliably identified in the dense environment of boosted bosons.Consequently, the number of associated b-jets (N b-jet ) provides an essential criterion for the identification of merged Z → b b decays.
Photons Photon candidates are reconstructed from clusters of energy deposits in the EM calorimeter [59].The photon energy is calibrated by applying the energy scales measured with Z → e + e − decays [60].Identification requirements are applied to reduce the contamination from π 0 or other neutral hadrons decaying into photons.Requirements on the shower shape in the EM calorimeter and on the energy fraction measured in the hadronic calorimeter are used to identify photons.Photons must satisfy the tight identification and isolation criteria defined in Ref. [59], and must have |η| < 1.37 or 1.52 < |η| < 2.37.For MC samples, the photon reconstruction, identification and isolation efficiencies are corrected to match those measured in data [59,60].The photon is required to have p γ T > 175 GeV, which is determined by an optimisation study and to ensure that the trigger is fully efficient.The efficiency of the photon selection ranges between 95% and 98% for photons with p γ T > 175 GeV depending on the pseudorapidity of the photon.These selection criteria are inverted to form a sample of non-tight photons for the background estimate described in Section 5.
Quality requirements are applied to photon candidates to identify those arising from instrumental problems or non-collision background [61], and events containing such candidates are rejected.In addition, quality requirements are applied to remove events containing spurious jets from detector noise or out-of-time energy deposits in the calorimeter from cosmic rays or other non-collision sources [62].
Selected events are required to have at least one groomed large-R jet and at least one photon, with ∆R(jet, γ) > 1.0 from the groomed large-R jet axis.The groomed large-R jet is required to have p

Signal and background estimation
To extract the Z(→ b b)γ signal from the data, signal and background templates obtained from MC simulation and from data are fitted to the observed Z → b b candidate jet mass distribution using a binned maximum-likelihood fit.This procedure is repeated separately for each of the groomed jet definitions used to perform the measurement.The dominant background is γ + jets with gluon to b b splitting.Less significant background contributions are due to t t + γ and W γ processes.Other backgrounds such as multijet and W/Z+jet processes, where a jet is misidentified as a photon, and the associated production of a Higgs boson with a γ are found to be negligible (< 1%).
Templates of the jet mass distribution for the Z(→ b b)γ signal, and for the t t + γ and W γ backgrounds, are determined from MC simulation.In contrast, the template used to estimate the dominant background contribution from γ + jets processes is derived directly from the measured data without input from MC simulation.This approach is referred to as a data-driven technique for estimating this particular background.It is especially important to minimise the reliance on MC simulations for this process, as MC generators have not been tested thoroughly in the relevant region of the b b production phase space for γ + jets.
The data-driven background estimate of the jet mass distribution for the γ + jets process relies on two features of the final state: the b-jet multiplicity (i.e.N b-jet ) and the photon identification criteria (i.e.tight vs non-tight).The b-jet multiplicity requirement is used to isolate the γ + jets process, which dominates in samples with N b-jet = 0 or 1.Furthermore, the ratio of γ + jets yields (N γ+jets ) in events with tight compared with non-tight photons is observed to be approximately independent of N b-jet .These two characteristics are used to model the expected γ + jets yield in the signal region via a transfer-factor (TF) method.This method extrapolates the signal region (SR) yield from control regions (CRs) with N b-jet = 1 and the shape of the jet mass distribution for the γ + jets background from CRs with N b-jet = 2 but non-tight photons.The definitions of the different CRs are summarised in Table 1.In these CRs, the t t + γ and W γ contributions are subtracted from the data, as the mass shape differs from that of γ + jets.
Table 1: Definitions of the control regions (CR) and the signal region (SR) used for the data-driven background estimate of the γ + jets process.
The γ + jets background estimates are constructed in 10 GeV bins of Z → b b candidate jet mass.For each jet mass bin, i, in each CR, the estimated yield of γ + jets events in that bin is calculated as: where N t t+γ CR,i and N Wγ CR,i are the number of t t + γ and W γ events, respectively, taken directly from the MC simulation.The systematic uncertainties for t t + γ and W γ contributions are described in Section 7.There is a negligible contribution from signal events in each of these control regions.
To obtain the estimate of the number of γ + jets events present in each bin of the jet mass distribution in the SR (N γ+jets SR,i ), the jet mass distribution from CR-E (N γ+jets CR−E,i ) is multiplied by a TF determined from the N b-jet = 1 regions: CR-C and CR-D.This procedure may be summarised as where the ratio N γ+jets CR−D,i /N γ+jets CR−C,i is the TF in each bin of the jet mass distribution.The value of the TF varies with jet mass, ranging from 1.2 for jet masses of 30 GeV to 0.8 at 160 GeV, and is within 5% of unity from 50 to 110 GeV.With this TF method, the shape of the jet mass distribution in the signal region is determined from CR-E (with N b-jet = 2) and the normalisation of each bin is determined from the N b-jet = 1 control regions.
The validity of this approach relies on the assumption that the TF does not depend on N b-jet .This is tested in data, using the N b-jet = 0 sample as a cross-check, and in MC simulation using N b-jet = 0, 1, and 2. The differences in the TFs between the N b-jet = 0 and N b-jet = 1 control regions in data are taken as systematic uncertainties in the TFs, as described in Section 7.

Definition of the observable and correction for detector effects
The reconstructed jet mass distributions from the signal regions are corrected to particle level in order to measure the full differential cross-section of the Z → b b candidate jet mass.Unfolding accounts for the effects of detector resolution and inefficiency and allows direct comparisons with particle-level predictions.The particle-level event selection is similar to the detector-level selection described in Section 4. Particle-level jets are built from stable final-state particles (defined as those with proper lifetime τ corresponding to cτ > 10 mm) excluding muons and neutrinos and using the same jet reconstruction algorithms used for calorimeter jets.Similarly to the muon-in-jet correction at reconstruction level described in Section 4, particle-level muons are added to the particle-level jet if they are within ∆R = 0.2 of a b-hadron.Events are required to have at least one particle-level jet with p T > 200 GeV, |η| < 2.0 and two ghost-associated b-hadrons.They are also required to have a particle-level photon with p T > 175 GeV, |η| < 1.37 or 1.52 < |η| < 2.37 and ∆R(jet, γ) > 1.0.
The estimated shape and yield of the background jet mass spectrum is subtracted from the data in the signal region, as discussed in Section 8.The background-subtracted detector-level distribution of the jet mass is then unfolded using an iterative Bayesian technique [63] with one iteration.This technique is implemented in the RooUnfold framework [64].One iteration was chosen to minimise the statistical uncertainties as well as the differences between the particle-level and the unfolded jet mass distribution.The unfolding procedure corrects for bin migrations between the particle-level and the detector-level jet mass distribution using a response matrix that describes the probability for an event with a particle-level jet mass in bin i to be reconstructed in bin j.The response matrix is constructed from events that satisfy the event selection and fiducial region criteria at both the particle level and the detector level.The particle-level jets and detector-level jets are required to be matched within ∆R = 0.75.Furthermore, the unfolding procedure corrects for events that satisfy either the detector-level or the particle-level selection criteria, but not both.The response matrix is obtained from the S Z(→ b b)γ signal MC simulation.The Z → b b candidate jet mass distribution was rebinned in the high jet mass region to improve the correlation between the reconstructed and particle-level jet mass.

Systematic uncertainties
There are various sources of systematic uncertainties that impact the Z → b b candidate jet mass distribution.These are classified into experimental and theoretical uncertainties, and uncertainties related to the background estimate and the unfolding procedure.The systematic uncertainties can have an impact on the shape of the jet mass distribution and on the signal and background yields.Systematic uncertainties are evaluated by varying each source by plus or minus one standard deviation of its uncertainty.The fit is repeated for each variation and the jet mass distribution unfolded to particle level.The jet energy and mass scale uncertainties are treated as correlated while all other sources of systematic uncertainties are treated as uncorrelated.
For groomed large-R jets, the uncertainties in the energy and mass scales are estimated by using the doubleratio technique described in Ref. [44] by comparing the calorimeter jet properties with the measurements of the same jet reconstructed from tracks in the ID.The uncertainties in the jet mass and energy resolutions are assessed by applying additional smearing of the jet observables according to the uncertainty in their resolution measurements.An absolute uncertainty of 2% is used for the jet energy resolution while a relative uncertainty of 20% is used for the jet mass resolution, consistent with previous studies of both the trimmed and soft-drop jet definitions [20,65].
The b-tagging uncertainty is evaluated by varying the data-to-MC corrections in various kinematic regions, based on the measured tagging efficiency and mistag rates.These variations are applied separately to b-hadron jets, c-hadron jets, and light jets, leading to three uncorrelated systematic uncertainties.An additional uncertainty is included to account for the extrapolation to jets with p T beyond the kinematic reach of the data calibration [53,57,58].
The impact of the systematic uncertainties on the photon reconstruction, identification and isolation efficiencies is studied by varying the scale factors, used to correct the respective efficiencies in simulation to match those observed in data, within their uncertainties.The uncertainties are determined from data samples of Z → + − γ (with = e, µ), Z → e + e − , and inclusive photon events, using the methods described in Ref. [59].Uncertainties in the photon energy scale and resolution are also taken into account [60].
The uncertainties associated with the muon momentum calibration and resolution, and the reconstruction and identification efficiency scale factors, are derived from Z → µ + µ − events [52].
The uncertainty associated with the modelling of pile-up in the simulation is assessed by varying the reweighting of the pile-up in the simulation within its uncertainties.This uncertainty covers the difference between the ratios of predicted and measured inelastic cross-section values [66].
The efficiency of the photon trigger is 100% for photons with E γ T > 175 GeV, with an uncertainty of 0.5% that is propagated through the unfolding.
The systematic uncertainties associated with the data-driven background template are estimated by deriving the bin-by-bin normalisation from CR-A and CR-B with N b-jet = 0 instead of from the N b-jet = 1 CRs as described in Section 5.An additional uncertainty in the bin-by-bin normalisation of the background template is derived by varying the jet mass distributions in CR-C and CR-D (with N b-jet = 1) within their statistical uncertainty.
The signal and background yields are estimated by performing a simultaneous fit to the data.The uncertainty in the normalisation of the background template, arising from the statistical uncertainty in the data, is referred to as the fit uncertainty in the following.
The modelling uncertainties affecting the W γ process are derived by comparing the nominal S 2.1.1 sample with one produced using the M G [35] generator interfaced to P 8.For the t t + γ background, three different sources of modelling uncertainties are considered: the uncertainty due to the parton shower and hadronisation is estimated by comparing the nominal samples produced using M G interfaced to P 8, with M G interfaced to H 7 [67,68]; the uncertainty due to different initial-and final-state radiation conditions is estimated by using P 8 tuned parameters with high or low QCD radiation activity; and the uncertainties due to the choice of renormalisation and factorisation scales are estimated by using alternative samples with the scales varied independently by factors of 2 and 0.5.
For the signal process, the modelling uncertainty is derived by replacing the nominal sample with the alternative M G sample, interfaced to P 8.The fit is repeated with the alternative MC signal sample and then unfolded using the response matrix, signal efficiency and fake fraction from this alternative signal sample.Uncertainties in the signal efficiency and response matrix are already covered by experimental systematic errors outlined earlier.
The systematic uncertainty due to the dependence of the unfolding on the prior signal distribution, as obtained from MC simulations, is evaluated through a data-driven 'closure test'.The simulated signal sample is reweighted at particle level such that the distribution of the fully simulated detector-level jet mass more closely matches the observed data.Pseudo-data from the reweighted signal MC sample are then unfolded using the response matrix from the original unweighted signal MC sample, and the unfolded result is compared with the reweighted particle-level distribution.Differences observed in this comparison are taken as systematic uncertainties in the unfolding, and are referred to as non-closure uncertainties in the following.The uncertainty due to the dependence on the number of unfolding iteration steps is negligible.The statistical uncertainties in the signal MC sample and background templates are also considered.
A bootstrapping procedure [69] is used to ensure that the systematic uncertainties are statistically significant.For each systematic uncertainty considered, pseudo-experiments are constructed from the data or MC simulation by assigning each event a weight taken from a Poisson distribution with unit mean.The statistical uncertainty in the systematic variation is taken as the RMS across the pseudo-experiments.The jet mass distribution for each of the systematic variations is then rebinned until a target significance of 1.5 standard deviations is achieved.
The impact of the systematic uncertainties on the integrated fiducial cross-section measurements, grouped by source, is summarised in Table 2.The dominant systematic uncertainties arise from the uncertainties in the fit, the signal modelling, the data-driven background estimate, the jet mass and energy scales, and the jet mass resolution.The uncertainty in the pile-up modelling in MC simulation is found to be negligible.

Results
Results of the measurement of the jet mass distribution in Z(→ b b)γ events are reported in the following three subsections; fit results and the calculation of the significance of the signal above the background, the unfolded fiducial cross-section measurement using the full measured jet mass spectrum, and the unfolded differential spectrum of the jet mass itself.

Fit results and significance estimate
The signal yield is extracted by simultaneously fitting the signal and the background templates described in Section 5 to the observed Z → b b candidate jet mass distribution.A binned maximum-likelihood fit is performed in the mass range between 30 and 160 GeV using a bin width of 10 GeV.The upper mass bound is chosen to exclude the mass region near the top quark mass while the lower mass bound is chosen to exclude the region of jet mass for which the uncertainty in the calibration is large and to protect against collinear singularities, as discussed in Section 4. The result of the fit to the detector-level Z → b b candidate jet mass distribution is shown in Figures 2(a) and 2(b) for trimmed and soft-drop jets along with their corresponding background-subtracted data distributions in Figures 2(c) and 2(d).The fitted signal yield is 215 ± 61 events for trimmed jets and 167 ± 73 events when using soft-drop jets as shown in Table 3.
Table 3: The number of data events observed in the signal region, along with the composition of these events after the fit in the 30 < m The 13 bins of the Z → b b candidate jet mass distribution are combined in a profile likelihood fit [70] to extract the expected and observed significances.Systematic uncertainties are included in the fit as nuisance parameters and are assumed to be gaussian distributed.The expected and observed significances of the Standard Model prediction fitted to the observed data for the Z(→ b b)γ production are summarised in Table 4.For each jet definition, the observed significance is consistent with the expectation.Differences in the significance between the two jet definitions are related to the differences in both the jet mass resolution and the effective fiducial cross-sections between trimmed and soft-drop jets, which affect the signal and background yields in the 30-160 GeV mass window.

Integrated fiducial cross-section measurement
The measured integrated fiducial cross-sections in the boosted (high p T ) Z → b b region are listed in Table 5.The integrated fiducial cross-section is extracted from the ratio of the unfolded yield of signal events and the total integrated luminosity.The measurements are compared with the S 2.1.1 and M G +P 8 LO predictions described in Section 3. M G +P 8 predicts around 30% less events than the samples generated with S .Within the current uncertainties on the measurement, both predictions are consistent with the measured cross-sections for soft-drop jets.For trimmed jets, larger differences can be observed between the M G +P 8 prediction and the measured cross-section.The uncertainties in the measured integrated fiducial cross-section results are summarised in Table 2.The dominant source of systematic uncertainty is the fit uncertainty for both jet definitions.The uncertainty in the normalisation of the background template has a large impact on the cross-section measurement because of the order of magnitude difference between the estimated numbers of signal and background events.

Differential fiducial cross-section measurement
The differential fiducial cross-section of Z(→ b b)γ production as a function of the Z → b b jet mass, obtained from the unfolded data in the signal region, is shown in Figure 3 for trimmed and soft-drop jets.As a comparison, the prediction from S 2.1.1 at LO is also shown.The observed slope in the data-to-prediction ratio in the unfolded measurement for trimmed jets is fitted with a linear function and the slope is found to be consistent with zero within two standard deviations.Statistical uncertainties are significant for the differential fiducial cross-section measurement in the tails of the jet mass distribution.

Conclusion
The fully unfolded differential jet mass spectrum for the high-p T Z → b b signal using the Zγ final state and the fiducial production cross-section are measured in 36.1 fb −1 of pp collisions at The integrated fiducial cross-section measurements and the differential cross-section of the jet mass of the boosted Z → b b decay are found to be in agreement with the LO predictions from S and M G +P 8 (integrated), and from S (differential), respectively, within the current statistical and systematic uncertainties.
Switzerland.e Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona; Spain.f Also at Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisboa; Portugal.

Figure 1 :
Figure 1: Comparison of (a) the calibrated reconstructed Z-jet mass distribution and (b) the particle-level jet mass distribution of soft-drop (dashed line) and trimmed jets (solid line) in the signal region in the Zγ sample.

>
200 GeV to capture both of the decay products of the Z → b b decay, i.e. both jets from the b-quarks should be fully contained in the groomed large-R jet.In the signal region, the jets identified as candidate Z → b b decays must contain at least two ghost-associated track-jets, and the two with the highest p T must be tagged as b-jets (N b-jet = 2).

Figure 2 :
Figure 2: The reconstructed jet mass distribution in the signal region (a, b) after fitting the S 2.1.1 signal model and background templates to the data and (c, d) the corresponding background-subtracted distributions for (a, c) trimmed and (b, d) soft-drop jets.The ratio of data to the fitted signal plus background is shown at the bottom in Figures (a) and (b).The background-subtracted jet mass distributions in data are compared with the reconstructed signal jet mass distributions in the nominal Monte Carlo simulation.The error bars on the background-subtracted data distribution are statistical only.The S signal model and background template are scaled to fit the data as described in Section 5.

Figure 3 :
Figure 3: Unfolded distribution of the Z → b b candidate jet mass from background-subtracted data in the signal region along with the predictions from S 2.1.1.Results for (a) trimmed and (b) soft-drop jets are shown.The error bars correspond to the statistical uncertainty while the hatched band corresponds to the total systematic uncertainty in the measurement.The statistical uncertainty in the S signal is negligible and not shown in the figure.

√ s = 13
TeV recorded in 2015 and 2016 by the ATLAS detector.The high-p T Z → b b signal is reconstructed using large-R jets and jet substructure techniques, including double subjet b-tagging.Two different grooming algorithms are used in this analysis: trimming and soft drop.Within the fiducial regions defined for each jet definition the production cross-sections are measured to be: σ trimming Z(→b b)γ = 17.0 ± 5.0 (stat.)± 3.6 (syst.)fb, σ soft drop Z(→b b)γ = 12.5 ± 4.9 (stat.)± 3.1 (syst.)fb.

Table 2 :
The uncertainties in the integrated fiducial cross-section measurement from data in the signal region for trimmed and soft-drop jets.Multiple independent components are combined into groups of systematic uncertainties.
Z-jet < 160 GeV mass range.Numbers are presented for trimmed and soft-drop jets.Statistical and systematic uncertainties are added in quadrature.Systematic uncertainties are described in Section 7.

Table 4 :
Expected and observed significance values (in numbers of standard deviations) for trimmed and soft-drop jets for a mass range between 30 and 160 GeV.
Also at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah; United Arab Emirates.h Also at Department of Financial and Management Engineering, University of the Aegean, Chios; Greece.i Also at Department of Physics and Astronomy, Michigan State University, East Lansing MI; United States of America.j Also at Department of Physics and Astronomy, University of Louisville, Louisville, KY; United States of America.k Also at Department of Physics and Astronomy, University of Sheffield, Sheffield; United Kingdom.l Also at Department of Physics, California State University, East Bay; United States of America.m Also at Department of Physics, California State University, Fresno; United States of America.n Also at Department of Physics, California State University, Sacramento; United States of America.o Also at Department of Physics, King's College London, London; United Kingdom.p Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg; Russia.q Also at Department of Physics, Stanford University, Stanford CA; United States of America.r Also at Department of Physics, University of Adelaide, Adelaide; Australia.s Also at Department of Physics, University of Fribourg, Fribourg; Switzerland.t Also at Department of Physics, University of Michigan, Ann Arbor MI; United States of America.u Also at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow; Russia.v Also at Giresun University, Faculty of Engineering, Giresun; Turkey.w Also at Graduate School of Science, Osaka University, Osaka; Japan.x Also at Hellenic Open University, Patras; Greece.y Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona; Spain.z Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg; Germany.aa Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen; Netherlands.ab Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia; Bulgaria.ac Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest; Hungary. g