Measurement of the centrality dependence of the dijet yield in $p$+Pb collisions at $\sqrt{s_{_\text{NN}}}$ = 8.16 TeV with the ATLAS detector

The measurement of hard scatterings in proton-nucleus collisions has resulted in a greater understanding of both the proton and nuclear structure. ATLAS measured the centrality dependence of the dijet yield using 165 nb$^{-1}$ of $p$+Pb data collected at $\sqrt{s_{_\text{NN}}}$ = 8.16 TeV in 2016. The event centrality, which reflects the $p$+Pb impact parameter, is characterized by the total transverse energy registered in the Pb-going side of the forward calorimeter. The central-to-peripheral ratio of the scaled dijet yields, $R_\mathrm{CP}$, is evaluated, and the results are presented as a function of variables that reflect the kinematics of the initial hard parton scattering process. The $R_\mathrm{CP}$ shows a scaling with the Bjorken-$x$ of the parton originating from the proton, $x_p$, while no such trend is observed as a function of $x_\mathrm{Pb}$. This analysis provides unique input to understanding the role of small proton spatial configurations in $p$+Pb collisions by covering parton momentum fractions from the valence region down to $x_p \sim 10^{-3}$ and $x_\mathrm{Pb}\sim 4\cdot10^{-4}$.

Proton-nucleus (+A) reactions at colliders provide unique opportunities to study the structure of both the proton and the nucleus [1].By measuring high transverse momentum ( T ) probes generated in +A collisions over a wide rapidity range, it is possible to investigate modifications of parton distribution functions (PDFs) in the nuclear environment [2][3][4][5] from small parton fractional momenta () up to the valence quark dominance region.Inclusive jet production rates were measured in +Pb collisions at the LHC [6][7][8][9] and in +Au collisions at RHIC [10].ALICE also measured the jet production cross-sections and nuclear modification of charged jets at 5.02 TeV [6].None of these results observed a substantial modification of jet rates relative to the geometrical expectation constructed from proton-proton ( ) collisions, i.e., for +A, scaling with the atomic mass number A:  +A ≃  +  .ATLAS [9] and PHENIX [10] analyzed the centrality dependence of the jet production.In this context, centrality is an experimental classification of the collision geometry based on a measurement of the underlying event (UE) activity in a rapidity region entirely separated from the hard-scattering measurement.In /+A collisions, centrality is sensitive to the multiple interactions between the projectile and the nucleons in the nucleus, with more central (peripheral) events characterized by a higher (lower) average number of nucleon-nucleon (NN) collisions.Both Refs.[9] and [10] observed a suppression of the jet yield in central events, and an enhancement in peripheral events.ATLAS found the relationship between the suppression and the enhancement to be a function of only the total jet energy.However, the initial hard parton-parton kinematics in each measurement were not fully constrained by the measurement of a single jet.To test for a trivial dependence on the kinematics of an NN collision, ATLAS also performed a measurement of the forward transverse energy in   collisions [11], and found only a weak correlation between  of the proton beam, and the transverse energy in the opposite direction, a trend that is at odds with the +Pb results.This implied that the scaling observed in +Pb collisions was not a property of the NN collision itself.CMS measured a shift in the Pb beam direction of the mean dĳet pseudorapidity as a function of the total forward transverse energy [7], which is dominated by the energy deposited by the Pb debris.The inclusive measurement was observed to be consistent with predictions based on nuclear parton distribution functions (nPDFs), but the relative changes with centrality were found to be much larger than those expected from model predictions using nPDFs [12].While this result had qualitative similarities to those reported by ATLAS [9], it covered a more limited kinematic range in only a single dĳet  T interval, making it difficult to assess more quantitatively.
[13] and [14] were able to partially reproduce the ATLAS data [9], but were strongly disfavored by the results of Ref. [11].In Ref. [15], the authors were able to reproduce inclusive jet results at both RHIC [10] and LHC [9] energies using a model based on a color fluctuations-related [16] interpretation.The interaction strength of the proton, as well as its transverse size, are treated as dynamic quantities that depend on the instantaneous partonic configuration, considered frozen during the propagation of the proton through the nucleus.Due to QCD color screening, the overall interaction strength of a color-neutral configuration is expected to vary with the transverse area subtended by its color charges [17], which is smaller in hadrons where one parton carries a considerable fraction of the momentum.Therefore, hard +Pb scatterings involving configurations of the proton with a large- parton, typical of the valence quark dominance region, are characterized by a smaller than average size and interaction strength of the projectile.These configurations have a reduced number of soft interactions with the nucleus, resulting in lower underlying event activity and thus shifting the event into a more peripheral centrality interval.This can be interpreted as a manifestation of color transparency phenomena [17][18][19][20].Triple differential measurements of the dĳet production as a function of centrality would allow for connecting these effects directly to the kinematics of the parton scattering, providing crucial input to advance the understanding of small proton configurations and their relation to the suppression of the overall interaction strength in +A collisions.resultant ⟨ AB ⟩ values and associated uncertainties are (0.205±0.013) mb −1 and (0.043±0.009) mb −1 for central and peripheral collisions, respectively.Nuclear modification effects are typically characterized by the ratio of the hard scattering rates in the presence and absence of a nuclear environment.In this analysis, the dĳet yield was measured in different centrality intervals to construct the central-to-peripheral ratio,  CP , defined as: where  dĳet ) represent the number of sampled minimum-bias and dĳet events in central (peripheral) collisions, respectively.The  CP quantifies the deviations in the dĳet yield in more central collisions from geometric expectations relative to peripheral collisions, assuming little to no nuclear final state modification in the latter.An  CP of unity implies no centrality-dependent modifications.
The +Pb data used in this analysis were required to satisfy detector and data-quality requirements, and to contain at least one reconstructed primary vertex and at least two reconstructed jets.A set of central and forward single-jet triggers [28], characterized by different  T thresholds, were chosen to provide full  T coverage over a wide pseudorapidity range, corresponding to −2.8 <  < 4.5.The leading jet was required to have passed the trigger that sampled the largest luminosity and was 99% efficient for the given jet  and  T .The leading (sub-leading) jet was further required to have  T > 40 (30) GeV.Events were discarded if either of the jets fell in the acceptance of the disabled HEC region.To define a rejection criterion for the analysis, the disabled region was increased by an additional 0.4 margin in both the pseudorapidity and azimuthal angle.Pileup events were rejected using vertex and track requirements.The exclusion of events in the 90-100% centrality interval, combined with a rapidity gap requirement [29] in the Pb-going direction, effectively rejected any contribution from ultra-peripheral collisions.
Jets used in this measurement were reconstructed using the anti-  algorithm [30] as implemented within the FastJet software package [31].Jets with  = 0.4 were formed by clustering four-vectors corresponding to massless calorimeter towers with size Δ × Δ = 0.1 × (/32).The background energy arising from the UE was subtracted from each tower.An iterative procedure was used to estimate the UE average transverse energy density, (), while excluding regions of the detector populated by jets [32].The UE evaluation was additionally corrected for - dependent non-uniformities of the detector.
The performance of the jet reconstruction was evaluated using Geant4 [33,34] to simulate the detector response and a Pythia8 [35] MC sample consisting of dĳet events from 8. 16 TeV   collisions, including the boost in rapidity relative to the lab frame that is present in data.The MC sample was generated using Pythia8 with the A14 set of tuned parameters [36] and the NNPDF2.3loparton distribution functions [37].Events from the dĳet sample were overlaid with minimum-bias +Pb collisions recorded by ATLAS during the same data-taking period as the analyzed data, ensuring a proper UE description in the MC sample.
To correct for the effects of detector response on the measurement, the dĳet yield was unfolded in  T,Avg using a one-dimensional Bayesian procedure [38], implemented within the RooUnfold package [39].For each  b ,  * , and centrality interval, a response matrix was filled using pairs of true and reconstructed jets from the Pythia8 overlay MC sample.The statistical uncertainty on the dĳet yield was evaluated using a bootstrapping method [40] to generate statistically correlated response matrices.
An efficiency correction was included during the unfolding to account for reconstructed dĳets that migrated between  b and  * bins, or out of the measurement phase space at the detector level due to energy resolution effects.Dĳets impacted by the disabled HEC region exclusion were also accounted for with this correction.The size of the efficiency correction on the yields is significant only in the pseudorapidity region corresponding to the disabled HEC, where it reaches approximately a factor of three.It is on the order of a few percent in the remaining phase space due to migration between  b and  * bins and energy resolution effects.
To estimate the systematic uncertainty on the jet energy scale (JES), jet energy resolution (JER), and unfolding procedure, the difference between the nominal result and that obtained by repeating the analysis with modified response matrices was calculated.The JES and JER smearing factors were obtained via in situ studies [41], as well as by accounting for reconstruction and calibration differences [32] between this measurement and 13 TeV   data, where components of the uncertainty were derived.An additional component accounting for MC modeling of the quark and gluon jets is included in the JES uncertainty.The total systematic uncertainty on the dĳet yield is dominated by the JES uncertainty, which is approximately 10% in all kinematic intervals.The JER uncertainty is sub-dominant, reaching up to ∼10% only for the highest  * values.The uncertainty on the unfolding procedure is related to its sensitivity to the choice of prior, which was reweighted to have better data-MC agreement.To address this, an approach similar to one found in Ref.
[9] was used to vary the reweighting, producing modified response matrices.The systematic uncertainty on the unfolding is at the sub-percent level for all bins.
The systematic uncertainty associated with the disabled HEC exclusion was evaluated by increasing the fiducial cuts by 0.1 in all directions in azimuth and pseudorapidity, and repeating the analysis procedure.The resultant uncertainty was found to be on the order of 1-2% in the majority of the measurement's phase space.
Correlations in the JES, JER, and HEC uncertainties between central and peripheral bins were accounted for in the propagation of the uncertainties to the  CP .The partial cancellation of the resulting systematic uncertainties from these sources results in considerably smaller uncertainties on the  CP compared with those on the dĳet yield.The normalization uncertainty on the  CP corresponding to the  AB is +12% / −19%, and is independent of jet  T and .
The measured central and peripheral dĳet yields are used to construct the  CP as a function of  T,Avg .The  CP values are then plotted against the approximated kinematics of the hard parton scattering, constructed using Eqs. 2 and 3 as where ⟨ b ⟩ and ⟨ * ⟩ are the average values of the dĳet boost and half-rapidity separation in each given kinematic bin, respectively.The level of accuracy of this approximation was evaluated via Pythia8 MC simulations and found to be accurate within the bin widths used for the measurement.
Figure 1 shows the results as a function of ⟨  ⟩ (left) and ⟨ Pb ⟩ (right).A distinct   -scaling of the  CP (  ) is observed in the valence quark dominance region, characterized by a log-linear decreasing trend.No similar scaling is observed for smaller values of   , or for any region when expressed as a function of  Pb .Recently, the analysis of forward dĳet production in +Pb collisions at LHC energies was proposed in order to search for the onset of gluon-saturation [42] at low values of  Pb .The saturation scale in the nuclear environment is expected to be enhanced by a factor A 1/3 .The lack of monotonic scaling with decreasing  Pb observed in Figure 1 suggests that gluon saturation is not the dominant source of the observed effect.These observations can be expected from the color fluctuations-related interpretation discussed at the beginning of this Letter.The measured suppression of the  CP is qualitatively consistent with an   -dependent decrease in the interaction strength of proton configurations containing high- partons, resulting in a modification of the UE activity and, therefore, the centrality.Centrality estimates for events with hard scatterings have been found to be biased by modifications in soft processes, an effect that is typically enhanced with small pseudorapidity separations, Δ, between a hard probe and the centrality detector acceptance [23,43,44].The effect is strongly reduced at large Δ, and is expected to have negligible impact on the  CP   -scaling reported in Figure 1.
The   -scaling observed in Figure 1 is qualitatively similar to that observed in the 5.02 TeV Run 1 inclusive jet analysis [9] as a function of the jet energy.A direct comparison between the results could clarify whether or not they are connected by the same underlying physics.The measurements can be compared by making use of the Feynman scaling variable,  F [45]. Figure 2 shows the dĳet results as a function of the approximated  F computed in each kinematic bin as ⟨ F ⟩ = ⟨  ⟩ − ⟨ Pb ⟩.The mapping of the  CP to ⟨ F ⟩ allows for factoring out the beam energy from the results, while isolating the dependence of the dĳet yield on the parton momentum fractions characterizing the hard-scattering.Large positive (negative) values of ⟨ F ⟩ are associated to scatterings dominated by the longitudinal momentum of the parton originating from the proton (nucleus).In inclusive jet measurements,  F can also be constructed as a property of the final state, i.e.,  F = 2  / √  NN , where   is the longitudinal momentum of the measured jet.Assuming the jet mass to be small compared to its transverse momentum, and considering  c.m. values large enough that sinh  c.m. ≃ ± cosh  c.m. , with the positive (negative) sign corresponding to  c.m. > 0 ( c.m. < 0): Therefore, because the results in Ref.
[9] were reported as a function of  T × cosh  c.m. , a comparison to the results presented in this Letter can be achieved using the relation: , where the sign of the left-hand of the equation corresponds to the sign of  c.m. .This comparison is shown in Figure 3.A striking agreement is observed between the results obtained at positive  c.m. and  b , corresponding to the high-  region.This comparison shows that the physics mechanism responsible for the  CP suppression in this kinematic region is the same in the two analyses, and the scaling behavior observed at 5.02 TeV as a function of the jet energy is effectively governed by the proton configuration.The agreement between the data progressively worsens when moving toward the negative rapidity region, where the majority of the momentum in the hard scattering is contributed by the parton from the Pb nucleus.These results provide new input to further parameterize color fluctuation effects in +A collisions.Improvements in the understanding of these effects will also pave the way for future studies of color transparency at the electron-ion collider [46].These new dĳet data can also be used to provide further interpretation of the dĳet pseudorapidity measurement as a function of the forward transverse energy carried out by CMS [7].Analyzing the rapidity dependence of the results in Figure 1, a more substantial  CP suppression is associated with larger values of  b , corresponding to higher values of   .This observation is directly linked to a shift in the ⟨ b ⟩ dependence of the dĳet yield measured in central and peripheral events, refer to the Appendix for more details.Thus, these results can be used to recast the observations reported by CMS as a manifestation of the   -related scaling reported in this Letter.
In summary, this Letter presents the measurement of the centrality dependence of the dĳet yield over a wide range of  T,Avg ,  b and  * .The measured  CP is reported in terms of approximated kinematics of the hard parton-parton scattering.In the valence quark dominance region of the proton, a striking   -scaling of the  CP is observed.Such scaling behavior is not present when the  CP is analyzed as a function of  Pb .By making use of the Feynman variable,  F , and a few kinematic considerations, the results are compared with those obtained by ATLAS for the centrality dependence of inclusive jet production at 5.02 TeV [9].The comparison between the two measurements strongly suggests that the observed  T × cosh  c.m. scaling at 5.02 TeV is driven by the kinematics of the parton originating from the proton.The outcome of this analysis provides new input to explain the systematic shift in the mean ⟨ b ⟩ measured by CMS at 5.02 TeV [7].These results are qualitatively in agreement with the   -dependent color fluctuation effects described in Ref. [15], directly related to small configurations of the proton characterized by a reduced interaction strength.The measurement presented in this Letter represents an essential step forward in the understanding of jet production in +Pb collisions in terms of the hard-scattering kinematics.

Appendix
The measured triple differential dĳet yields can also be used to study the centrality dependence of the ⟨ b ⟩ distribution.Figure 4 shows the results as a function of ⟨ b ⟩ for central and peripheral intervals in a few representative  T,Avg and  * selections.A shift from zero of the two distributions is observed in all the kinematic bins.This deviation is found to be monotonically decreasing as a function of  T,Avg for peripheral yields in all the  * ranges.Conversely, central yields show a shift from zero decreasing in magnitude with increasing  T,Avg only in 0 <  * < 1.A moderate increase with  T,Avg is observed in 1 <  * < 2, while in 2 <  * < 4 the shift goes from positive (low  T,Avg ) to negative (high  T,Avg ).These kinematic dependencies are directly reflected in the   -scaling of the  CP reported in Figure 1.

Figure 1 :
Figure 1:  CP plotted as a function of approximated   (left panel) and  Pb (right panel), constructed using ⟨ b ⟩ and ⟨ * ⟩.An inset legend is included, showing the ( b ,  * ) bins, and their corresponding markers.The proton-going direction is defined by  b > 0. Shaded rectangles represent the total systematic uncertainty, while the vertical error bars represent the statistical uncertainty.The solid rectangle on the left-side of each panel represents the uncertainty on the  AB .

Figure 2 :
Figure 2:  CP plotted as a function of approximated  F , here indicated with ⟨ F ⟩ and constructed using ⟨ b ⟩ and ⟨ * ⟩.An inset legend is included, showing the ( b ,  * ) bins, and their corresponding markers.The proton-going direction is defined by  b > 0. Shaded rectangles represent the total systematic uncertainty, while the vertical error bars represent the statistical uncertainty.The solid rectangle on the left-side of the panel represents the uncertainty on the  AB .

Figure 3 :
Figure 3: Dĳet  CP results from this Letter compared with inclusive jet  CP at 5.02 TeV measured by ATLAS [9].The dĳet results are denoted by full markers and are reported as a function of ±⟨ F ⟩ × 4080 GeV, for positive (+, left panel) and negative (−, right panel)  b ( c.m. ) results, respectively.An inset legend is included, showing the ( b ,  * ) bins, and their corresponding markers.The inclusive jet results are displayed as a function of  T × cosh(⟨ c.m. ⟩) and use open markers.Shaded rectangles represent the total systematic uncertainty, while the vertical error bars represent the statistical uncertainty.The uncertainties on the  AB on the dĳet (inclusive jet) results are reported using the left (right) solid rectangle on the right side of each panel.The 5.02 TeV data for −0.3 <  c.m. < 0.3 was omitted since it belongs to the transition region between the two panels.