Measurement of the tt charge asymmetry in events with highly Lorentz-boosted top quarks in pp collisions at √ s = 13 TeV

The measurement of the charge asymmetry in top quark pair events with highly Lorentz-boosted top quarks decaying to a single lepton and jets is presented. The analysis is performed using proton-proton collisions at √ s = 13 TeV with the CMS detector at the LHC and corresponding to an integrated luminosity of 138 fb − 1 . The selection is optimized for top quarks produced with large Lorentz boosts, resulting in nonisolated leptons and overlapping jets. The top quark charge asymmetry is measured for events with a tt invariant mass larger than 750 GeV and corrected for detector and acceptance effects using a binned maximum likelihood fit. The measured top quark charge asymmetry of ( 0.42 + 0.64 − 0.69 ) % is in good agreement with the standard model prediction at next-to-next-to-leading order in quantum chromodynamic perturbation theory with next-to-leading-order electroweak corrections. The result is also presented for two invariant mass ranges, 750–900 and > 900 GeV. Published in Physics Letters B as doi:10.1016/j.physletb.2023.137703 .


Introduction
The vast majority of top quarks produced at hadron colliders are from tt pairs that originate via the strong interaction.At the LHC proton-proton (pp) collider, the production stems from gluon fusion about 90% of the time, with qq annihilation making up the rest [1,2].At leading order, the standard model (SM) predicts that tt production from qq annihilation is forwardbackward symmetric.However, higher-order SM effects result in a small (≈6.6%) positive forward-backward asymmetry A FB , such that the top quark (antiquark) is preferentially emitted in the direction of the incoming quark (antiquark).The A FB was measured at the Tevatron proton-antiproton collider by the CDF and D0 collaborations [3] and found to be consistent with the theoretical predictions [4].There is no asymmetry in the gluon fusion tt production that dominates at the LHC, but because valence quarks carry, on average, larger momentum than antiquarks (from the sea), the rapidity distribution of top quarks at the LHC is expected to be broader than that of top antiquarks [5,6].The tt charge asymmetry is defined as where ∆|y| = |y t | − |y t | is the difference between the absolute value of the top quark and antiquark rapidities and N is the number of events.The value of A C is expected to be about 1% in the SM for LHC [5].
Since the relative contribution of valence quarks increases at high momentum transfer [7], we expect that measuring A C in a sample of tt events with highly Lorentz-boosted top quarks will lead to a more stringent probe of quantum chromodynamic (QCD) predictions and higher sensitivity to beyond-the-SM (BSM) physics processes that might alter the charge asymmetry [8].
Several models predict enhancements with respect to the SM prediction in the presence of new particles, including axigluons [9,10], Z ′ bosons [11][12][13], W ′ bosons [10,13,14], scalar isodoublets [15], color triplet scalars [16,17], and color sextet scalars [14,15].These models introduce new spin-0 and spin-1 particles in the interaction, modifying A C by exchanging the new particles through interference terms and dedicated loops.The ATLAS and CMS Collaborations have combined their inclusive and differential measurements of A C [18] at two center-of-mass energies, obtaining A C = 0.005 ± 0.007 (stat) ± 0.006 (syst) and 0.0055 ± 0.0023 (stat) ± 0.0025 (syst) at 7 and 8 TeV, respectively.These combined measurements show good agreement with the respective SM predictions and uniquely restrict the phase space of possible BSM phenomena that would produce large asymmetries [14].Along with specific BSM models, deviations from the SM prediction can also be interpreted through an effective field theory (EFT) approach in which new physics contributions are described via a fixed set of dimension-six operators added to the SM Lagrangian [19].In particular, fits to top quark production and differential distributions, together with Higgs boson, boson pair (diboson), and electroweak precision measurements, are being used in global SM EFT analyses to constrain the operators [20,21].
This Letter presents the first measurement of the tt charge asymmetry that uses pp collision data at √ s = 13 TeV and optimizes the reconstruction of events with tt invariant mass (M tt ) above 750 GeV.The kinematic requirements necessarily imply highly boosted top quarks.We target the single-lepton channel, in which both top quarks decay as t → bW, with one W boson decaying leptonically (W → ℓν, where ℓ is either a muon or electron), and the other hadronically (W → qq ′ ).The charge of the lepton is used to distinguish the top quark from the top antiquark.The highly boosted top quarks yield collimated decay products that appear as partially or fully overlapping energy deposits in our detector.For the top quark decaying to a W boson that decays leptonically (called a top quark leptonic decay), the energy deposits from the lepton overlap with those of the b quark.Dedicated jet and lepton selection requirements at the trigger and offline levels [22] allow us to reconstruct the decay products of the boosted leptonically decaying top quarks by identifying the energy deposits of the leptons without requiring a minimum separation from other signals in the detector.The overwhelming QCD multijet background is controlled with topological requirements.The topology of the top quark decaying to a W boson that decays hadronically (called a top quark hadronic decay) depends on the magnitude of its transverse momentum (p T ).At the high end of the p T spectrum, the top quark decay products have angular distances between partons that result in overlapping energy deposits.In contrast, at the low end of the p T spectrum near the kinematic threshold, the energy deposits from each parton appear separated from the others.For intermediate p T values, the energy deposits of partons originating from the hadronic W boson decay are overlapping, but the b quark is identified separately.All three topologies are considered in this analysis and are referred to as "merged", "semiresolved", and "resolved" for the high, intermediate, and low p T regions, respectively.Tabulated results are provided in the HEPData record for this analysis [23].

The CMS detector and object reconstruction
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections.Forward calorimeters extend the pseudorapidity (η) 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.Events of interest are selected using a two-tiered trigger system [24,25].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. [26].
The offline event reconstruction is based on a particle-flow (PF) algorithm [27], which combines information from each subdetector to identify muons, electrons, photons, and charged or neutral hadrons.To avoid inefficiencies observed in the data for very high p T PF muons, we use muons determined by a different algorithm [28], where muons are reconstructed first in the muon system and then fitted to tracks in the pixel and strip tracker.The primary vertex is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [29].Charged hadrons associated with other vertices are removed from further consideration.The remaining PF candidates are clustered into jets using the anti-k T algorithm [30,31] with a distance parameter of 0.4 (called AK4 jets).The same PF candidates are used to build large-radius (AK8) jets using a distance parameter of 0.8, with the effects of additional pp collisions in the same bunch crossing mitigated through the pileup per particle identification algorithm (PUPPI) [32,33].Any AK4 jet with ∆R = √ (∆η) 2 + (∆ϕ) 2 < 0.8 from the closest AK8 jet, where ϕ is the azimuthal angle, is discarded from the event.The total jet ⃗ p T is given by the sum of the ⃗ p T of its constituents.If a lepton is found within ∆R < 0.4 of an AK4 jet or <0.8 of an AK8 jet, its four-momentum is subtracted from that jet [22].The missing transverse momentum vector ⃗ p miss T is computed as the negative vector sum of the transverse momenta of all the PF candidates in an event, and its magnitude is denoted as p miss T [34].Corrections are applied to improve the jet energy scale and resolution, and the ⃗ p miss T is modified to account for these corrections [35,36].Specialized techniques use AK8 jets and jet substructure information [37], including "soft-drop clustering" [38] and "N-subjettiness" [39], to identify the hadronic decay of boosted top quarks, following the techniques detailed in Ref. [22].Two exclusive categories are considered: hadron-ically decaying top quarks (t tag) in which the three partons are merged into a single AK8 jet, and hadronically decaying W bosons (W tag) in which the two partons from the W boson are merged into a single AK8 jet, but the bottom quark is reconstructed as a separate AK4 jet.The identification of jets originating from the decay of b hadrons (b tag) employs a deep neural network multi-classification algorithm (DEEPJET [40]) that relies on information from the tracker and the calorimeters [41].The b tagging algorithm is applied to each AK4 jet j with p j T > 50 GeV and |η j | < 2.4.The t and W tagging algorithms are applied to AK8 jets with p j T > 400 GeV and |η j | < 2.4.The algorithms are tuned for misidentification rates smaller than 5% and have efficiencies greater than 80%.

Collider data and simulated samples
We analyze data collected by the CMS detector during Run 2 (2016-2018) and corresponding to a total integrated luminosity of 138 fb −1 [42][43][44].Events in the muon channel (µ + jets) are selected with a single-muon trigger that requires p µ T > 50 GeV.Events in the electron channel (e + jets) are selected by either a single-electron trigger with p e T > 115 GeV or a trigger requiring one electron with p e T > 50 GeV and one jet with p j T > 165 GeV [22].The efficiency of these triggers for events in our signal sample is above 95%.As the e + jets trigger was not available during the early running period in 2017, the integrated luminosity available for the 2017 e + jets channel is reduced by 5 fb −1 .
In the offline reconstruction, we select events for the µ + jets (e + jets) channel that contain exactly one muon with p To preserve the identification efficiency of tt decay products in the highly boosted topology, no isolation requirement is imposed on the leptons at either the trigger or offline level.To reduce the background from QCD multijet events, we apply a two-dimensional (2D) selection that requires leptons to satisfy either the condition ∆R min (ℓ, j) > 0.4 or p T,rel (ℓ, j) > 25 GeV, where ∆R min (ℓ, j) is the angular separation between the lepton and the closest AK4 jet, and p T,rel (ℓ, j) is the transverse momentum of the lepton with respect to the axis of the nearest AK4 jet [22].A variety of Monte Carlo (MC) simulated samples are used to model the signal and background contributions.A comprehensive description of the generation parameters used, as well as the MC normalization and associated uncertainties, can be found in Ref. [45].The tt and single top quark (ST) processes are produced with the next-to-leading-order (NLO) POWHEG [46,47] generator.Simulated W + jets, Drell-Yan (DY) Z/γ + jets, and QCD multijet processes are generated with MADGRAPH5 aMC@NLO [48] at NLO.The contribution from diboson events is negligible.All samples are interfaced to PYTHIA8 [49] with the CP5 tune [50] for parton showering and hadronization, and processed through a GEANT4-based simulation [51], which models the propagation of the particles through the CMS detector and the corresponding detector response.The NNPDF 3.1 parton distribution functions (PDFs) [52] are used for all samples, and events in all samples include the simulation of additional inelastic pp interactions (pileup) within the same or nearby bunch crossings.Small corrections are applied to all MC samples to improve the agreement with the observed data, derived from data control samples that are in-dependent of the candidate selection.In particular, the transverse momentum of the top quarks at the generator level is multiplied by the function e (0.0615−0.0005pT,top ) to match the distribution measured in data [45].

Reconstruction of the top quark pair events
The tt system is reconstructed by assigning the four-vectors of the final-state objects to either the leptonic (t ℓ ) or hadronic (t h ) leg of the tt decay.The events are separated into the three topologies discussed earlier based on the presence of t-or W-tagged jets: the merged topology contains events with one t tag and no W tag; the semiresolved topology contains events with one W tag and no t tag; and the resolved topology contains the rest of the events that have no t and no W tag. Events with more than one t or W tag are discarded.For events with a t tag, the t-tagged jet is taken as the t h and only AK4 jets with ∆R > 0.8 from the t h are considered as candidates for the t ℓ .For events with a W tag, the W-tagged jet is assigned to the t h .The AK4 jets with ∆R > 0.8 from the W tag can be assigned to either the t ℓ or the t h , and at least one AK4 jet on each side is required.For events with neither a t tag nor a W tag, all possible assignments of AK4 jets are considered for both the t ℓ and the t h , and again, at least one AK4 jet on each side is required.There is no upper limit on the number of AK4 jets in any of the topologies.Even though each event includes at least one b-tagged jet, the b tagging information for individual jets is not used.The longitudinal component of the neutrino momentum is inferred by constraining the invariant mass of the lepton plus neutrino system to the W boson mass [53].Assuming the W boson is on-shell, a quadratic equation for the z component of the momentum of neutrino can be derived: where p ℓ and p ν are the three momenta of the charged lepton and the neutrino, respectively, with ⃗ p T,ν = ⃗ p miss T , and 2) has either 0, 1, or 2 real solutions.In the absence of a real solution, the real part of the complex solutions is used.If there are two real solutions, both cases are tested, effectively doubling the number of hypotheses for that event.
For each event, one tt hypothesis is selected based on a two-term χ 2 discriminator used to quantify the compatibility of each hypothesis with a tt decay.The discriminator, which was optimized for tt invariant masses greater than 750 GeV, is defined as where M lep and M had are the invariant masses of the reconstructed t ℓ and t h decaying top quark, respectively.The quantities σ M lep and σ M had are the resolutions of the leptonic and hadronic top quark reconstruction, respectively, and ⟨M lep ⟩ and ⟨M had ⟩ are the means of the corresponding mass distributions obtained from simulation for each of the topologies.Because background processes typically result in large values of χ 2 , events with χ 2 > 30 are rejected.Finally, only events with M tt > 750 GeV are retained in our signal candidate sample.Figure 1 shows comparisons between data and MC simulation for kinematic distributions based on events in the candidate sample.The distributions are shown after the likelihood normalization described in Section 6.The boosted nature of the top quarks in the events becomes evident: the M tt range extends to multi-TeV values, events with two and three AK4 jets originating from  the collimated top quark decay products are reconstructed, and events with leptons next to the jet axis are retained.Generally good agreement between data and MC is observed.

Systematic uncertainties
Systematic uncertainties from numerous sources can affect the normalization and the shape of the distributions of physical observables in both signal and background samples.The systematic uncertainties affecting only the normalization come from the SM theoretical cross section values for each process and the luminosity normalization.All MC samples are normalized according to their respective SM cross section values, as has been done in previous analyses including Ref. [45], and assigned a rate uncertainty of 30% for background processes [54] and 5% for the tt signal [55].Additionally, uncertainties in the integrated luminosity vary from year to year: 2.5, 2.3, and 1.2% for 2018 [44], 2017 [43], and 2016 [42], respectively.These include both correlated and uncorrelated components across the three years, while the overall uncertainty for the 2016-2018 period is 1.6%.
All other systematic uncertainties affect both the normalization and shape of the MC distri-butions.Uncertainties from experimental sources are applied to both signal and background samples.All MC samples are reweighted to match the pileup distribution in data, which is generated by using the instantaneous luminosity per bunch crossing for each luminosity section, with a total inelastic cross section of 69.2 mb; an uncertainty of 4.6% is applied to this value [56].
All muons and electrons in the simulated samples have uncertainties associated with the highlevel trigger (HLT), reconstruction (reco), and identification (ID).The uncertainty associated with the possible misidentification of the sign of the lepton electric charge is negligible.These uncertainties are uncorrelated across lepton flavors but correlated across years and are parameterized as a function of the p T and η of the leptons.There is a uniform uncertainty in the efficiency of the 2D selection that rejects QCD background, and this is uncorrelated across lepton flavors and years.Uncertainties in the jet energy corrections (JEC) and resolution (JER) are parameterized in terms of the jet p T and η and considered correlated across years.The uncertainties in the tagging scale factors are parameterized as a function of the jet p T .The uncertainties in t and W tagging are 100% correlated across years, but the uncertainty in b tagging has both correlated and uncorrelated components [57].There are different scale factors to account for the cases when the tagging algorithms incorrectly identify (mistag) some jets, so a separate mistagging uncertainty is also assigned.
In addition to the experimental sources, we consider uncertainties affecting the MC simulations.The uncertainty from the choice of PDF is estimated from the Hessian NNPDF3.1 sets according to the procedure described in Ref. [58].Renormalization (µ R ) and factorization (µ F ) scales at the matrix element level are varied by a factor of 2 or 0.5 to take into account the effect of higher-order corrections in the tt and W + jets simulations.The matrix element and parton shower matching scale (h damp ) regulates the high-p T radiation by damping real emissions from the POWHEG generator; this effect is only taken into account for tt and evaluated using independent simulated samples generated based on parameters derived in Ref. [50].Uncertainties related to the modeling of initial-and final-state radiation (ISR and FSR) are determined by varying the strong coupling constant α S at the scale Q 2 for the tt samples.Finally, an uncertainty in the correction to the top quark p T is evaluated as a one-sided variation computed from the difference between the top quark p T distribution with and without the correction [45].For all these uncertainties, those originating from the same source are considered as 100% correlated between channels and those arising from different sources are considered to be 100% uncorrelated.

Unfolded results
The top quark charge asymmetry is obtained by performing a simultaneous binned maximum likelihood fit to data in all bins and categories of the candidate sample as implemented by the LHC Higgs Combination Group [59].Statistical uncertainties due to the MC sample size are treated separately in each bin with the Barlow-Beeston-lite approach [60].Each source of systematic uncertainty is included in the likelihood as a unique nuisance parameter.For contributions that apply to multiple analysis channels, the nuisance parameters are fully correlated, allowing better constraints to be placed on the systematic uncertainties.For a given channel k in our analysis, the corresponding likelihood function L k is defined as: where • P (n; µ) represents the Poisson probability of observing n events when µ are ex- pected.
• The indexes i and j run over the number of bins at generator level (N gen ) and reconstruction level (N reco ), respectively.In this analysis, we use two bins (N reco = N gen = 2) corresponding to the positive (bin 1) and negative (bin 2) difference between the absolute value of the top quark and antiquark rapidities ∆|y|.
• ⃗ δ u are the nuisance parameters.• A ji is the response matrix, which gives the probability for an event reconstructed in bin j to have been produced in bin i.It is implemented by including the relevant number of reconstructed and generated simulated tt events for each entry, which are subject to the effects of the nuisance parameters.This implementation allows the matrix to account for effects from detector resolution (smearing) as well as detector acceptance and efficiency.
• µ 1 = r pos N gen pos and µ 2 = r neg N gen neg , where r pos and r neg are the signal strengths multiplying the number of signal events at generator level with M gen tt > 750 GeV in which the value of ∆|y| gen is positive (N gen pos ) or negative (N gen neg ), respectively.
• n j is the number of data events in bin j. • b j is the number of background events predicted in bin j.
• N( ⃗ δ u ) are the priors for the nuisance parameters, with the normalization and shape uncertainties assigned a log-normal and Gaussian distribution, respectively.The shape uncertainty nuisance parameters control the vertical interpolation of histograms that represent the up and down one standard deviation shifts from the nominal distribution [61].
Each analysis channel is defined based on reconstruction-level quantities by a range of M tt values and a specific year and lepton flavor.To account for migration of events between mass bins, all simulated events are included, even if the generated mass is outside the reconstructed mass range under consideration.The total likelihood is given by the product of the individual likelihoods from Eq. ( 4), with the index k running over all 12 channels: two lepton flavors (µ + jets and e + jets), 3 years (2018, 2017, and 2016), and two mass regions (750 < M tt < 900 GeV and M tt > 900 GeV).This unfolding approach also has the advantage that the background contributions are constrained by the fit, resulting in smaller systematic uncertainties than those obtained with a direct background subtraction.

The unfolded charge asymmetry at parton level is given by
with r pos and r neg as free parameters in the fit.However, to ensure the uncertainties on A C are properly estimated, we define r pos in terms of r neg and A C , and select r neg and A C as the free parameters.The A C can also be measured in the two mass regions separately.This is achieved combining subsets of the 12 analysis channels according to the reconstructed M tt , while redefining N gen pos and N gen neg as the corresponding number of generated signal events with 750 < M gen tt < 900 GeV or M gen tt > 900 GeV.Table 1 shows the signal and background yields in our candidate sample after the likelihood fit, separated into the two mass regions.The contributions to our candidate sample from background processes (ST, W + jets, DY, and QCD multijet) are taken from simulation and their normalization allowed to change during the likelihood fit.The higher p T thresholds on the lepton and leading jet in the electron channel result in significantly reduced signal acceptance compared to the muon channel.Figure 2 shows ∆|y| for each of these 12 channels both before and after the likelihood normalization.As can be observed, the likelihood fit reduces the total uncertainty significantly and improves the agreement between data and the MC prediction.Table 2 and Fig. 3 show the measured top quark charge asymmetry after unfolding to parton level in the full phase space, compared with the theoretical prediction at next-to-next-to-leading order (NNLO) QCD and NLO EW corrections from Ref. [5].Good agreement between the data and the MC prediction is observed.
Figure 4 shows the ±1 standard deviation (σ) impacts of the systematic uncertainties in the A C measurements for the full signal sample, as well as the effect on the unfolded A C values for up and down variations of the systematic uncertainty.
Table 2: Measured unfolded charge asymmetry compared to the theoretical prediction, including NNLO QCD and NLO EW corrections, from Ref. [5].Results are shown for events with M tt > 750 GeV and for two invariant mass ranges, 750-900 and >900 GeV.The statistical and systematic uncertainties in the data, the MC statistical uncertainty, and the total uncertainty in the measured values are also shown.All values are in percent.

Summary
A measurement of the charge asymmetry in tt events with highly boosted top quarks produced in proton-proton collisions at √ s = 13 TeV is presented based on 138 fb −1 of data collected by the CMS experiment at the LHC.The selection is optimized for top quarks produced with high Lorentz boosts that yield collimated decay products that are partially or fully merged and can result in nonisolated leptons and overlapping jets.The measured top quark charge asymmetry (A C ) is corrected for detector and acceptance effects using a binned maximum likelihood fit.This is the first CMS measurement to use 13 TeV data and a binned maximum likelihood unfolding technique to measure A C directly at parton level in the full phase space.In addition, it is the first result that focuses exclusively on the highly Lorentz-boosted regime, using dedicated reconstruction techniques for the hadronically and leptonically decaying top quarks at both the trigger and offline stages.Since the relative contribution of valence quarks increases at high momentum transfer, A C is especially sensitive to beyond the standard model processes in this highly boosted phase space.
The resulting unfolded charge asymmetry for tt events with invariant masses satisfying M tt > 750 GeV is (0.42 +0.64  −0.69 )%, where the uncertainty includes both statistical and systematic components.The corresponding theoretical prediction at next-to-next-to-leading order in QCD perturbation theory with next-to-leading-order electroweak corrections from Ref. [5] is (0.94 +0.05 −0.07 )%.Good agreement between the measurement and the most precise standard model prediction is thus observed.The result demonstrates that top quark properties can be precisely measured in
Finally, events need to satisfy p miss T > 50 GeV and p miss T + p µ T > 150 GeV (p miss T > 120 GeV) in the µ + jets (e + jets) channel.The larger value of the e + jets p miss T requirement efficiently reduces the larger QCD multijet background in this channel and precludes the need for a separate requirement on p miss T + p e T .To suppress the contribution from the W + jets background, at least one of the AK4 jets must be b tagged.

Figure 1 :
Figure1: Comparison between data and MC simulation for kinematic distributions based on events in the candidate sample (described in Section 4): ∆|y| (upper left), reconstructed M tt (upper right), distance between the lepton and the closest AK4 jet ∆R min (ℓ, j) (lower left), and the number of AK4 jets (lower right).The vertical bars on the points show the statistical uncertainty in the data.The shaded bands represent the total uncertainty in the MC predictions (described in Section 5).The lower panels give the ratio of the data to the sum of the MC predictions.The distributions are shown after the likelihood normalization described in Section 6.

Figure 2 :Figure 3 :
Figure2: Comparison between data and MC simulation for ∆|y| for each of the 12 analysis channels, both before (left) and after (right) the likelihood normalization.The plots in the upper row correspond to 750 < M tt < 900 GeV, and the plots in the lower row to M tt > 900 GeV.The vertical bars on the points represent the statistical uncertainties in the data and the shaded bands give the combined MC statistical and systematic uncertainties.The lower panels display the ratio of the data yields to the sum of the MC predictions.

Figure 4 :
Figure 4: Summary of the dominant systematic uncertainties affecting the A C measurement.The left column lists the sources of systematic uncertainty, treated as nuisance parameters in the fit, in order of importance.In the middle column (Pull), the black points with their ±1 standard deviation horizontal bars show for each uncertainty the difference between the observed best fit value and the nominal value, divided by the expected standard deviation.The right column (Impact on A C (%)), shows the change in the measured A C if a nuisance is varied by one standard deviation (σ) up, in red, and down, in blue.

Table 1 :
The event yields for the candidate sample in data and MC simulations after the likelihood fit for each of the 12 channels (µ + jets, e + jets, 3 years; and two mass regions).The uncertainties in the MC predictions include both statistical and systematic components.