Constraints on jet quenching in p-Pb collisions at $\mathbf{\sqrt{s_{NN}}}$ = 5.02 TeV measured by the event-activity dependence of semi-inclusive hadron-jet distributions

The ALICE Collaboration reports the measurement of semi-inclusive distributions of charged-particle jets recoiling from a high-transverse momentum trigger hadron in p-Pb collisions at $\sqrt{s_{\rm NN}} =5.02$ TeV. Jets are reconstructed from charged-particle tracks using the anti-$k_{\rm T}$ algorithm with resolution parameter $R=0.2$ and $0.4$. A data-driven statistical approach is used to correct the uncorrelated background jet yield. Recoil jet distributions are reported for jet transverse momentum $15<p_{\rm T,jet}^{\rm ch}<50$ GeV/$c$ and are compared in various intervals of p-Pb event activity, based on charged-particle multiplicity and zero-degree neutral energy in the forward (Pb-going) direction. The semi-inclusive observable is self-normalized and such comparisons do not require the interpretation of p-Pb event activity in terms of collision geometry, in contrast to inclusive jet observables. These measurements provide new constraints on the magnitude of jet quenching in small systems at the LHC. In p-Pb collisions with high event activity, the average medium-induced out-of-cone energy transport for jets with $R=0.4$ and $15<p_{\rm T,jet}^{\rm ch}<50$ GeV/$c$ is measured to be less than 0.4 GeV/$c$ at 90% confidence, which is over an order of magnitude smaller than a similar measurement for central Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. Comparison is made to theoretical calculations of jet quenching in small systems, and to inclusive jet measurements in p-Pb collisions selected by event activity at the LHC and in d-Au collisions at RHIC.


Introduction
The collision of heavy nuclei at high energies generates a Quark-Gluon Plasma (QGP), a dense, highly inviscid, strongly-coupled fluid governed by sub-nucleonic degrees of freedom [1].While the structure and dynamical behavior of the QGP arise at the microscopic level from the interactions between quarks and gluons that are described by Quantum Chromodynamics (QCD), the QGP also exhibits emergent collective behavior.Current understanding of the properties of the QGP is based primarily on two phenomena observed in high energy nuclear collisions and their comparison to theoretical calculations: strong collective flow [2], and jet quenching, which arises from interaction of energetic jets with the medium [3].
Measurements of asymmetric p-Pb collisions at the LHC and of light nucleus-Au collisions at RHIC reveal evidence of collective effects that are similar in magnitude to those observed in symmetric collisions of heavy nuclei [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48].These measurements in asymmetric systems are reproduced both by model calculations that incorporate a locally thermalized hydrodynamic medium in the final state, and by calculations without QGP but with large fluctuations in the initial-state wavefunctions of the projectiles (see [49] and references therein).This raises the question whether a QGP is in fact generated in such light asymmetric systems, which were initially thought to be too small for the formation of a quasiequilibrated fireball of matter in the final state [49].Additional measurements, in particular to explore jet quenching in p-A collisions, will help to resolve this picture and to clarify the nature of equilibration in strongly-interacting matter.
There are several theoretical calculations currently available of jet quenching effects in p-Pb collisions at the LHC, which differ in their predictions.The calculation in [50] estimates the size of the region of high energy density to have a radius that is a factor 2 smaller in p-Pb than in central Pb-Pb collisions, with jet transport parameter q, assumed to be proportional to charged multiplicity, to be a factor 7 smaller.Jet energy loss, which is proportional to q and depends on path length of the jet in the medium, is consequently expected in this calculation to be much smaller in p-Pb than in central Pb-Pb collisions.In contrast, a model calculation based on one-dimensional Bjorken hydrodynamics predicts large initial energy density in high multiplicity pp and p-Pb collisions [51]; this energy density corresponds to jet energy loss of several GeV, which is similar in magnitude to jet energy loss measured in central Pb-Pb collisions [22].A calculation based on pQCD at next-to-leading order (NLO) finds negligible jet quenching effects for inclusive jet production in p-Pb collisions at √ s NN = 5 TeV [52].Finally, a QCD calculation of initial-state energy loss in cold nuclear matter (CNM) finds significant suppression of inclusive jet production for small-impact parameter p-Pb collisions at √ s NN = 5 TeV [53].
Experimental searches for jet quenching effects in d-Au collisions at RHIC and in p-Pb collisions at the LHC have been carried out with high-p T hadrons and reconstructed jets.These studies utilize both Minimum Bias (MB) events and more-differential event selection, in which events are characterized in terms of "event activity" (EA) based on forward charged-particle multiplicity, transverse energy, or zero-degree neutral energy in the direction of the heavy nuclear projectile.
Inclusive hadron measurements in d-Au collisions at RHIC [54,55] exhibit yield enhancement in the region 2 < p T < 5 GeV/c, which is commonly attributed to multiple scattering in the initial state, with no significant yield modification at higher p T and with no significant difference observed between the MB and EA-selected distributions.For inclusive hadron measurements in p-Pb collisions at the LHC, ALICE does not observe significant yield modification for p T > 8 GeV/c in both MB and EA-selected events [56,57] while ATLAS and CMS observe significant yield enhancement for p T greater than ∼ 30 GeV/c in MB events [58,59], and ATLAS observes additional dependence on EA [58].
For inclusive jet production, no significant yield modification has been observed in MB p-Pb collisions at the LHC and MB d-Au collisions at RHIC [60][61][62][63].In contrast, measurements at both RHIC [62] and the LHC [63] find apparent yield enhancement in EA-selected event populations thought to be biased towards large impact parameter ("peripheral collisions"), with compensating suppression for event populations assigned small impact parameter ("central collisions").
Measurement of jet quenching effects with inclusive processes requires scaling of the inclusive yield from a reference collision system (usually pp) by the nuclear overlap function T pA , with the angle brackets . . .indicating an average over the event population.For an EA-selected population, T pA is calculated by correlating EA with collision geometry and applying Glauber modeling [64].However, the correlation of EA with collision geometry in p-Pb collisions is obscured by large fluctuations in the EA observables [57], and can be biased by conservation laws and by dynamical correlations when measuring high Q 2 processes [65][66][67][68][69][70].Color fluctuations in the proton wavefunction may induce a bias in soft particle production for p-Pb events tagged by a hard process, thereby biasing the correlation between EA and collision geometry [71][72][73][74].A model calculation shows that selection bias can modify the scaling factor for jet production in peripheral A + A relative to pp collisions, generating an apparent suppression of jet production in peripheral A + A collisions if the Glauber calculation does not take this effect into account [75]; similar considerations apply to asymmetric collision systems.
While Glauber modeling for peripheral d-Au collisions at RHIC has been validated experimentally for moderate Q 2 processes using a proton-stripping process and knowledge of the deuteron wavefunction [54], no such check is possible with the proton beam at the LHC.It is therefore crucial to measure the EA-dependence of jet quenching effects in p-Pb collisions at the LHC with observables that do not require the interpretation of EA in terms of collision geometry.
In this paper we present measurements sensitive to jet quenching in p-Pb collisions at √ s NN = 5.02 TeV, based on the semi-inclusive distribution of charged jets recoiling from a high-p T trigger hadron [76].The observable used in this analysis has been measured in pp collisions at √ s = 7 TeV and compared to calculations based on PYTHIA and on pQCD at NLO, with PYTHIA providing a better description [22] The semi-inclusive recoil jet distribution is equivalent to the ratio of inclusive cross sections [22]; comparison of such self-normalized coincidence distributions for p-Pb event populations with different EA therefore does not require scaling by the nuclear overlap function T pPb .Measurement of this observable in p-Pb collisions is sensitive to jet quenching effects, and indeed does not require interpretation of the EA in terms of p-Pb collision geometry.This approach thereby avoids potential bias due to Glauber modeling when interpreting the measurement.
We report charged recoil jet distributions reconstructed with the anti-k T algorithm [77] in the range 15 < p ch T,jet < 50 GeV/c, for jet resolution parameters R = 0.2 and 0.4.Correction of the jet yield for background uncorrelated with the triggered hard process, including multi-partonic interactions (MPI), is carried out statistically at the level of ensemble-averaged distributions, using the data-driven method first applied in [22].EA in p-Pb collisions is characterized by two different observables, forward chargedparticle multiplicity and neutral energy along the beam axis, both measured in the direction of the Pbbeam [57].Jet quenching effects are measured by comparing distributions in different EA classes.The results are compared to other jet quenching measurements and to theoretical calculations of jet quenching in asymmetric collision systems.
The paper is organized as follows: Sect. 2 describes the data set and analysis; Sect. 3 describes event selection based on trigger hadrons and event activity; Sect. 4 describes jet reconstruction; Sect. 5 discusses the semi-inclusive observable and presents the raw data; Sect.6 discusses corrections; Sect.7 discusses systematic uncertainties; Sect.8 presents results and discussion; Sect.9 compares the results to other measurements; and Sect. 10 is the summary.

Data set and analysis
The ALICE detector and performance are described in [78,79].The data used in this analysis were recorded during the 2013 LHC run with p-Pb collisions at √ s NN = 5.02 TeV.The Pb-going direction has rapidity y > 0 and pseudorapidity η > 0. The per-nucleon momenta of the beams in this run were imbalanced in the laboratory frame, with the nucleon-nucleon center-of-mass at rapidity y NN = −0.465.The acceptance of tracks and jets in this analysis are specified in terms of y * = y LAB − y NN , where y LAB denotes the rapidity measured in the laboratory frame.
Events were selected online by an MB trigger, which requires the coincidence of signals in the V0A and V0C forward scintillator arrays.The V0A array has acceptance 2.8 < η < 5.1 and the V0C array has acceptance −3.7 < η < −1.7, both covering the full azimuth.Offline event selection also utilizes the Zero-Degree Calorimeters (ZDC), which are neutron calorimeters at zero degrees relative to the beam direction, located at a distance 112.5 m from the vertex diamond.The ZDC in the Pb-going direction is labeled ZNA.
Jet reconstruction in this analysis uses charged-particle tracks.Tracks are measured by the Inner Tracking System (ITS), a six-layer silicon vertex tracker, and the Time Projection Chamber (TPC).The tracking system acceptance covers |η| < 0.9 over the full azimuth, with tracks reconstructed in the range 0.15 < p T < 100 GeV/c.Primary vertices are reconstructed offline by extrapolation of these tracks to the beam axis.Primary tracks are defined as reconstructed tracks with Distance of Closest Approach to the primary vertex in the transverse plane DCA xy < 2.4 cm.
The analysis uses high-quality primary tracks that include at least one track point in the Silicon Pixel Detector (SPD), which comprises the two innermost layers of ITS.The azimuthal distribution of such high-quality tracks is non-uniform, however, due to the non-uniform acceptance of the SPD in this run.Azimuthal uniformity in the tracking acceptance is achieved by supplementing the high-quality tracks with complementary tracks that do not have a hit in the SPD, which constitute 4.3% of all primary tracks.The momentum resolution of complementary tracks, without an additional constraint, is lower than that of high-quality tracks.Complementary tracks are therefore refit, including the reconstructed primary vertex as a track point.Tracking efficiency for primary tracks is about 81% for p T > 3 GeV/c.Primary-track momentum resolution is 0.7% at p T = 1 GeV/c, 1.6% at p T = 10 GeV/c, and 4% at p T = 50 GeV/c.Further details on the track selection and tracking performance in this analysis are given in [20,61].
The MB trigger efficiency for non-single diffractive (NSD) collisions is 97.8 ± 3.1% [61,80].Since this is a correlation analysis, no correction is applied for the trigger inefficiency.Timing cuts on the V0 and ZDC signals, which are applied offline, remove background events with vertices outside of the nominal p-Pb interaction region that arise from beam-gas interactions and interactions with satellite beam bunches [79].Event pileup, due to multiple interactions in the triggered bunch crossing, is suppressed by rejecting events with multiple primary vertex candidates based on SPD hits.Events accepted for further analysis must have only one primary vertex, with that vertex having |z vtx | < 10 cm relative to the nominal center of the ITS along the beam axis.After all event selection cuts, the number of events in the analysis is 96 × 10 6 , corresponding to an integrated luminosity of 46 µb −1 .
Simulations are used to correct the raw data for instrumental effects, and to compare the corrected measurements to expectations from an event generator.Simulated events were generated for pp collisions at √ s = 5.02 TeV using PYTHIA 6.425 with the Perugia 11 tune [81].These events, labeled "particlelevel," include all primary charged particles as defined in [82].Following the procedure in [60], instrumental effects are calculated by passing particle-level events through a detailed model of the ALICE detector based on GEANT3 [83].These events are reconstructed with the same procedures that are used for real data; the output of this process is labeled "detector-level."Comparison to data also uses a particle-level simulation of pp collisions at √ s=5.02TeV generated with PYTHIA 8.215 Tune 4C [84].All simulations take account of the nucleon-nucleon center-of-mass rapidity shift of the p-Pb data.

Event selection
This analysis is based on the semi-inclusive distribution of jets recoiling from a high-p T trigger hadron.Event selection requires the presence of a high-p T charged track, called the Trigger Track (TT), in a specified p T,trig interval.Two exclusive event sets are defined, based on different TT intervals: 12 < p T,trig < 50 GeV/c, denoted TT{12,50}, and 6 < p T,trig < 7 GeV/c, denoted TT{6,7}.
The choice of the upper TT interval limits is driven by two competing factors: the hardening of the recoil jet p T -spectrum with increasing p T,trig , and the decrease of the inclusive hadron production cross section for increasing p T,trig .The choice of TT{12,50} provides the optimum kinematic reach and statistical precision of the normalized recoil jet spectrum for this dataset.The criteria for the lower TT interval, TT{6,7}, are that it be significantly lower in p T,trig , with correspondingly softer recoil jet spectrum, while still in the region in which inclusive hadron production can be well-described perturbatively using collinear fragmentation functions [85,86].
The fraction of such events in the MB population is 6.9 × 10 −4 for TT{12,50} and 6.4 × 10 −3 for TT{6,7}.However, an event may satisfy both the TT{6,7} and TT{12,50} selection criteria, since fragmentation of an energetic jet can generate hadrons in both TT selection intervals.An additional procedure is therefore required to ensure exclusive, statistically independent datasets for the two TT-selected populations.In addition, optimization of the statistical precision of the analysis requires similar number of events in the two TT classes.The MB population was therefore divided randomly into two subsets, whose sizes are inversely proportional to the relative rate of the two TT selections: 90% of MB events are assigned to the TT{12,50} analysis, with the remaining 10% assigned to the TT{6,7} analysis.
An event can also contain multiple hadrons within a single TT interval, likewise arising from jet fragmentation.For events with at least one hadron satisfying TT{6,7}, the relative rate of two or more hadrons in an event satisfying TT{6,7} is 2.3%; the corresponding relative rate of multiple hadrons satisfying TT{12,50} is 5.3%.If an event contains more than one track in the assigned TT interval, the trigger hadron is chosen as the candidate with the highest p T .The resulting p T -distribution of trigger tracks is consistent with the shape of the inclusive hadron distribution within 2%.After the TT event selection procedure there are 63k events accepted that satisfy TT{6,7} and 60k events accepted that satisfy TT{12,50}.
A different procedure was employed in [22] for the case of multiple trigger candidates in a TT interval, where the trigger track was chosen randomly amongst the candidates.However, the analysis reported here has a wider range in p T for the upper TT class, and random selection results in reduced level of agreement (∼10%) of the trigger track p T -distribution with the inclusive hadron spectrum shape.The full analysis was also carried out for this choice of procedure for trigger selection, and all resulting physics distributions agree with those of the primary analysis within the uncertainties.
Measurement of EA uses signals from V0A and ZNA.Classification of events in percentile intervals of the V0A and ZNA signal distributions is discussed in [57].About 5% of accepted events do not have a ZNA signal above the detector threshold; however, the distribution of mid-rapidity track multiplicity for these events resembles closely that for events with low but observable ZNA signal, and these events are therefore assigned to the bin with lowest ZNA signal.Fig. 1: Distribution of event activity EA in decile bins measured in ZNA (left) and V0A (right), for the MB event population and for event populations selected with the requirement of a high-p T trigger hadron in the intervals 6 < p T,trig < 7 GeV/c (TT{6,7}) and 12 < p T,trig < 50 GeV/c (TT{12,50}).Large EA is to the left, with the 0-10% bin representing the largest EA, or highest amplitude signal in ZNA or V0A.

ZNA percentile
Figure 1 shows the distribution of EA measured by ZNA and V0A, in decile bins of signal amplitude.The decile bin limits are determined from their distributions in the MB population, with MB events therefore distributed uniformly in this projection by construction.The figure also shows V0A and ZNA distributions for event populations selected by the TT{6,7} and the TT{12,50} criteria.Requiring the presence of a high-p T hadron trigger in an event is seen to induce a bias towards larger EA, corresponding to larger amplitude in both ZNA and V0A.A small dependence on the TT class (i.e. on p T,trig ) is also observed, with magnitude less than 10% of the overall bias, and with the TT-dependence slightly larger for V0A than for ZNA. Figure 1 shows significant correlation between EA and the presence of a hard process in the central region, providing new constraints on model calculations of p-Pb collisions and the interpretation of EA in terms of collision geometry.
For further analysis, events were assigned to wider percentile bins in ZNA or V0A, based on their MB distributions: 20% of the MB population with largest signal ("0-20%"), the next 30% ("20-50%"), and the remaining 50% with the lowest signal ("50-100%").The bias imposed by TT selection, shown in Fig. 1, corresponds to different fractions of the TT-biased population: the nominal 0-20% ZNA interval corresponds to 0-35% of the TT-biased population; the nominal 20-50% ZNA interval corresponds to 35-74% of TT-biased; and the nominal 50-100% ZNA interval corresponds to 74-100% of TT-biased.Similar modification of percentile fractions due to TT bias is observed for the V0A signal.
The same events are used for the ZNA and V0A selections, so that the analyses using the two different EA metrics are not statistically independent.

Jet reconstruction
Several types of jet are used in the analysis, which we distinguish by the notation for jet p T : p raw,ch T,jet refers to the output of the jet reconstruction algorithm; p reco,ch T,jet is p raw,ch T,jet after subtraction of an estimated contribution to jet p T of uncorrelated background; and p ch T,jet refers to the fully corrected jet spectrum.For simulations, p part T,jet refers to reconstructed charged-particle jets at the particle-level, and p det T,jet refers to reconstructed charged-particle jets at the detector-level.
Jet reconstruction is carried out using the k T and anti-k T algorithms [77] with the boost-invariant p T recombination scheme [87], using all accepted charged tracks with p T > 0.15 GeV/c.Jet area A jet is calculated using the Fastjet algorithm [88] with ghost area 0.005.
Two jet reconstruction passes are carried out for each event.The first pass estimates the level of uncorrelated background energy in the event, while the second pass generates the set of jet candidates used in the physics analysis, with adjustment of their p T using the estimated background level from the first pass.
In the first pass, the p raw,ch T,jet distribution reconstructed by the k T algorithm with R = 0.4 is used to estimate ρ, the magnitude of background energy per unit area [89], where the median is calculated by excluding the jet which has the trigger hadron as a constituent.A different ρ estimator [90] is utilized to assess the systematic uncertainties of this procedure.
The second jet reconstruction pass is carried out using the anti-k T algorithm with R = 0.2 and 0.4.The value of p raw,ch T,jet for each jet candidate from this step is then adjusted for the estimated background energy density [89], A jet candidate from the second pass is accepted for further analysis if its area satisfies A jet > 0.6πR 2 [20, 22], and its jet axis lies within |η jet | < 0.9 − R and an azimuthal interval situated back-to-back with respect to the TT, ∆ϕ recoil > π − 0.6, where ∆ϕ = ϕ TT − ϕ jet and 0 < ∆ϕ < π.An event may have multiple accepted jet candidates.
For further analysis we follow the procedure used in [22], in which no rejection of individual jet candidates is carried out.Recoil jet distributions are accumulated for the selected event populations, and corrections for uncorrelated jet yield and for smearing and residual shift of p ch T,jet due to uncorrelated background are carried out at the level of the ensemble-averaged distributions, as discussed below.
Jet energy resolution due to instrumental effects (JER) and jet energy scale (JES) uncertainty are similar to those in [22].The JER is determined by comparing simulated jets at the particle and detector levels.The distribution of (p det T,jet − p part T,jet )/p part T,jet is asymmetric, with a sharp peak centered at zero and a tail to negative values [17].Fit of a Gaussian function to the sharp peak gives σ 2-3%, while the full distribution has RMS 25%, with both quantities having no significant dependence on p part T,jet and R. The JES uncertainty, which is due predominantly to uncertainty in tracking efficiency, is 4%, likewise with no significant dependence on p ch T,jet and R.However, these values of JER and JES uncertainty, while helpful to characterize the jet measurement, are not used in the analysis.Corrections are carried out utilizing the full response matrix, which incorporates detailed distributions of all contributions to JER and JES uncertainty.The systematic uncertainties (Tab. 1) likewise take such factors fully into account.

Observable and raw data
The semi-inclusive h+jet distribution corresponds to the p T -differential distribution of recoil jets normalized by the number of trigger hadrons, N trig , All accepted jets contribute to the distribution on the LHS.This distribution is equivalent to measurement of the ratio of two cross sections, as shown on the RHS: the coincidence cross section for both trigger hadron and recoil jet to be in the acceptance, divided by the inclusive production cross section for trigger hadrons.This expression applies to both the MB event population, and to event subsets selected by EA.The features of this observable and its theoretical calculations are discussed in detail in Refs.[17,22].Here we consider two specific aspects of this distribution.
The first aspect is the bias imposed by the high-p T hadron trigger.For collision systems in which jet quenching occurs, selection of high-p T hadrons is thought to bias towards the fragments of jet that have experienced little quenching, due to the combined effect of jet energy loss and the shapes of the inclusive jet production and the jet fragmentation distributions [91][92][93][94][95][96][97][98].If that is the case, then the hadron trigger bias in this measurement would be independent of EA.This conjecture is supported by ALICE measurements of inclusive hadron production in p-Pb collisions that find no significant yield modification in the trigger p T -range of this measurement, for both the MB and EA-selected event populations [56,57].The picture provided by current ATLAS and CMS hadron production measurements [58,59] is more complex, however.Further study of this conjecture requires additional measurements of inclusive hadron production in pp and p-Pb collisions, together with theoretical calculations incorporating jet quenching that accurately reproduce these measurements.
The second aspect is the effect of trigger hadron efficiency on the equality in Eq. 3. As noted in Sect.3, the analysis requires selection of a single trigger hadron in each event.However, in a few percent of events there are multiple hadrons satisfying the TT selection criteria, of which only one is chosen as trigger.Consequently, not all hadrons that would contribute to measurement of the inclusive hadron cross section (first term on the RHS of Eq. 3) also contribute to N trig (first term on the LHS of Eq. 3).However, as noted above, the shape of the trigger hadron p T -distribution is consistent with that of the inclusive hadron spectrum within 2%.In other words, the trigger distribution used in practice samples the inclusive hadron distribution with efficiency less than unity but without p T -dependent bias, within a precision of 2%.This same inefficiency also applies to the h+jet coincidence process in the second term on the LHS of Eq. 3, and it therefore cancels identically in the ratio.Equation 3 therefore remains valid for trigger selection efficiency less than unity.
The study of jet quenching using inclusive yields requires comparison of the inclusive distribution measured in heavy ion collisions to a reference distribution measured in a system in which quenching effects are not expected, usually pp collisions at the same √ s NN .Such comparisons must account for the effect of multiple nucleon-nucleon collisions in each collision of heavy nuclei, which arises due to nuclear geometry.For inclusive distributions in p-Pb collisions this is accomplished by scaling inclusive cross sections for pp collisions by T pPb , which is calculated by modeling based on Glauber theory under the assumption that EA is correlated with the collision geometry [54][55][56][57][58][59][60][61][62][63][64].
For the semi-inclusive distribution in Eq. 3, the reference distribution without nuclear effects is 1 Since the scaling factors T pPb in the numerator and denominator cancel identically, the reference distribution for this observable has no dependence on T pPb .In other words, this distribution is selfnormalized, and measurement of jet quenching using this observable does not require Glauber modeling for the reference spectrum.In particular, the assumption that event activity is correlated with the collision geometry is not required.
Figure 2, left panels, show recoil-jet distributions for R = 0.2 and 0.4 with the 0-20% ZNA event selection.Distributions selected with V0A and with other ZNA EA intervals are similar [100].The distributions have non-zero yield for p reco,ch T,jet < 0, because regions of an event can have energy density less than ρ [22].These distributions are significantly narrower in the region p reco,ch T,jet < 0 than those observed in central Pb-Pb collisions, where the uncorrelated component of the event is significantly larger [22].
Figure 2, right panels, show the ratio of recoil jet distributions for the two TT classes.For p reco,ch T,jet ∼ 0 the two distributions agree within ∼ 10% for both values of R.This is consistent with the expectation that yield in this region arises predominantly from processes that are uncorrelated with the trigger hadron [22].At larger p reco,ch T,jet , the distribution for TT{12,50} exceeds that for TT{6,7}.This dependence of the recoil distribution on p T,trig is expected from QCD-based considerations, since higher p T,trig biases towards hard processes with higher Q 2 on average.This hardening of the semi-inclusive recoil jet distribution with increasing p T,trig has indeed been observed in pp collisions at √ s = 7 TeV, and in theoretical calculations based on NLO pQCD and on PYTHIA [22].
The distribution of jet candidates that are uncorrelated with the trigger is independent of p T,trig by definition.The distribution of correlated recoil jets can therefore be measured using the ∆ recoil observable, which is the difference of the two normalized recoil distributions [22], where TT Sig and TT Ref refer to Signal and Reference TT intervals, in this analysis corresponding to TT{12,50} and TT{6,7} respectively.∆ recoil is normalized per unit η jet , notation not shown.
The Reference spectrum in ∆ recoil is scaled by the factor c Ref to account for the invariance of the jet density with TT-class, as indicated by comparison of the spectrum integrals in Fig. 2  We note that the TT Ref distribution includes correlated recoil jet yield, so that the subtraction in Eq. 5 removes both the trigger-uncorrelated yield and the TT Ref -correlated yield.The ∆ recoil observable is therefore a differential, not absolute, measurement of the recoil spectrum [22], though the TT Ref component is significantly smaller than that in the TT Sig component over most of the p reco,ch T,jet range.The ∆ recoil distributions in Fig. 2 lie significantly below the TT-specific distributions for p reco,ch T,jet < 5 GeV/c but agree with the TT{12,50} distribution within 15% for p reco,ch T,jet > 15 GeV/c.These features indicate that the region of negative and small positive p reco,ch T,jet is dominated by uncorrelated jet yield, while the region for large positive p reco,ch T,jet is dominated by recoil jet yield that is correlated with TT Sig .One contribution to uncorrelated background is jet yield due to Multiple Partonic Interactions (MPI), which can occur when two independent high-Q 2 interactions in the same p-Pb collision generate the trigger hadron and a jet in the recoil acceptance.Since the two interactions are independent, the recoil jet distribution generated by MPI will be independent of p T,trig , by definition, and will be removed from ∆ recoil by the subtraction.No correction of ∆ recoil for the contribution of MPI is therefore needed in the analysis.
The raw ∆ recoil distributions, such as those in Fig. 2, must still be corrected for jet momentum smearing due to instrumental effects and local background fluctuations, and for jet reconstruction efficiency.Jet quenching effects are measured by comparing the corrected ∆ recoil distributions for different EA classes, and at different R.

Corrections
Corrections for instrumental effects and local background fluctuations are carried out using unfolding methods [101][102][103].The measured distribution ∆ M recoil is related to the true distribution ∆ T recoil by a linear transformation, where eff(p part T,jet ) is the jet reconstruction efficiency and R full is the cumulative response matrix excluding jet reconstruction efficiency.The explicit specification of jet reconstruction efficiency in this expression, distinct from the unfolding step, makes interpretation of the unfolding procedure more transparent.R full (p reco,ch T,jet ,p part T,jet ) is further assumed to factorize as the product of separate response matrices for background fluctuations and instrumental response, The matrix R full is can be close to singular, in which case the solution of Eq. 6 via direct inversion of R full generates large fluctuations in central values and large variance due to the statistical variation in ∆ M recoil (p reco,ch T,jet ) and R full [101].An approximate solution of Eq. 6 that is physically more meaningful is obtained by regularized unfolding, which imposes a smoothness constraint on the solution.Unfolding in this analysis is carried out using approaches based on Singular Value Decomposition (SVD) [102] and on Bayes' Theorem [103], as implemented in the RooUnfold package [104].
The instrumental response matrix, R instr , is calculated from the simulated detector response applied to events generated by PYTHIA for pp collisions at √ s = 5.02 TeV.Jets at the particle-level and detectorlevel are matched in (η, φ ) space by selecting the detector-level jet that is closest to the particle-level jet, and vice versa.An entry in R instr is made for every matched pair.The R instr matrix is normalized such that, for each bin in p part T,jet , the sum over all bins in p det T,jet is unity.In practice, however, the matching probability is less than unity, which is accounted for in Eq. 6 by the efficiency factor eff(p part T,jet ).The background response matrix, R bkgd , is calculated by embedding single tracks with transverse momentum p embed T into real p-Pb events that contain a TT [22].The relative azimuthal angle between the embedded track and the TT is in the range [π/4, 3π/4], to minimize overlap of the embedded track with the jet containing TT and with true recoil jets.These hybrid events are analyzed with the same procedures used for real data, and the jet containing the embedded track is identified.Smearing of jet candidate p T due to background fluctuations is quantified by the distribution of where p reco,ch T,jet refers to the jet containing the embedded track.R bkgd , the probability distribution of δ p T , is calculated separately for the MB population and for the various event populations selected by EA.Embedding of PYTHIA-generated jets rather than single tracks yields very similar δ p T distributions.
Unfolding follows the procedure described in [20].The input to unfolding is the measured distribution ∆ M recoil (p reco,ch T,jet ) in the range 1 < p reco,ch T,jet < 90 GeV/c.The unfolding procedure requires specification of a prior distribution.For the primary analysis, the prior is the ∆ recoil distribution calculated with PYTHIA8 tune 4C [84] for pp collisions at √ s = 5.02 TeV.Regularization of SVD unfolding utilizes a statistical test to determine the transition between random fluctuations and statistically significant components of the d-vector [102], which is achieved typically with regularization parameter k = 4.For regularization of Bayesian unfolding, convergence is determined by the stability of the unfolded solution for successive iterations, which is achieved typically by the second iteration.
For both unfolding approaches, consistency of the solution is checked by backfolding, i.e. smearing the unfolded distribution with R full and comparing the result with the ∆ M recoil distribution.Since regularization suppresses oscillating components of the solution, the backfolded and ∆ M recoil distributions will in general not be identical.Consistency of unfolding is imposed by requiring that the difference between the backfolded and ∆ M recoil distributions in each bin be less than 3σ , based on ∆ M recoil statistical errors; otherwise, the solution is rejected.
Closure of the unfolding procedure was verified by a test in which the response matrix, the ∆ recoil distribution, and the prior were generated by statistically independent sets of PYTHIA-generated events for pp collisions at √ s = 5.02 TeV.The response matrix and the spectrum were generated using PYTHIA6 Perugia-11, while the prior was generated using PYTHIA8 tune 4C.The ∆ recoil distribution from this test agrees with the input particle-level distribution to better than 5%.
Correction for jet reconstruction efficiency is applied after the unfolding step by scaling the unfolded ∆ recoil distribution by 1/eff(p ch T,jet ).The value of eff(p ch T,jet ) is 0.96 at p ch T,jet = 15 GeV/c and 0.98 at p ch T,jet = 60 GeV/c.

Systematic uncertainties
The systematic uncertainties of the ∆ recoil distribution are assessed by varying the components of the correction procedure.The most significant systematic uncertainties are due to the following: -Regularization of unfolding: for SVD, vary k by ±2 relative to its value in the primary analysis; for Bayesian unfolding, use the first three iterations; -Unfolding prior: generate prior distributions with PYTHIA6 and PYTHIA8; for additional variation take the difference between the priors from the two PYTHIA versions and vary them by its magnitude but with opposite sign; use the unfolded solution based on the iterative Bayesian approach as prior for SVD-based unfolding; -Binning of distributions: use three different choices of binning, with corresponding variation in spectrum limits; -Calculation of ρ: utilize a modified procedure [60,90,105] that accounts for sparse regions of the event, instead of the area-based approach (Eq.1); -c Ref variation: use as upper limit c Ref = 1, in which the reference recoil jet spectrum is not scaled.The correction for secondary vertex tracks makes a smaller contribution to the systematic uncertainty than the above sources.
Statistical fluctuations of the raw data influence the quantitative assessment of the systematic uncertainties arising from these sources.We utilize the following procedure to minimize such effects.For each source of uncertainty, several randomized instances of the raw ∆ recoil spectrum are generated by variation about the measured central value in each bin using a Gaussian distribution, with σ equal to the uncorrelated statistical error in the bin.Each randomized instance is analyzed using (i) corrections for the primary analysis (see Sect. 6), and (ii) corrections that include a systematic variation.For each randomized instance, the ratio of corrected ∆ recoil spectra resulting from (ii) and (i) is formed.The systematic uncertainty in each p ch T,jet -bin is defined as the median of the distribution of ratios obtained from all randomized instances.Table 1 gives representative systematic uncertainties for R = 0.4 in MB events.The cumulative systematic uncertainty is calculated by adding contributions from all systematic sources in quadrature.Similar uncertainties are obtained for event selection using the various EA-selected populations, and for R = 0.2.For p ch T,jet = 15-20 GeV/c, several components contribute with similar magnitude.For p ch T,jet = 40-50 GeV/c, the cumulative uncertainty is due predominantly to the uncertainty in tracking efficiency.
The systematic uncertainty of the ratio of ∆ recoil distributions was obtained similarly, taking into account the correlated uncertainties of numerator and denominator.The PYTHIA-generated distributions for pp collisions are presented only for comparison and are not utilized in the jet quenching analysis.Figure 3, lower panels, show the ratio of the measured p-Pb MB and PYTHIA-generated pp distributions to the fit distribution.The central values of the PYTHIAgenerated distributions for pp collisions lie below those of the p-Pb data, with a difference of 25% for p ch T,jet < 20 GeV/c.PYTHIA 8 tune 4C agrees better with the p-Pb data, notably at the highest p ch T,jet and for R = 0.4.For pp collisions at √ s = 7 TeV, PYTHIA-generated ∆ recoil distributions have central values that are in good agreement with data [22].We note, however, that the p T,trig intervals in the two analyses are different: this analysis uses TT{12,50}, whereas that in ref.

Results
[22] used TT{20,50}.Reanalysis of the pp 7 TeV data with the trigger selection TT{12,50} shows a similar level of agreement with PYTHIA as that seen in Fig. 3 [100].We also note that at present there are significant uncertainties in the light hadron fragmentation functions at LHC energies [85,86], which may affect hadron trigger selection in the PYTHIA calculation and thereby contribute to the differences between PYTHIA and data seen in the figure .The ∆ recoil distributions for EA-selected event populations and for the MB population shown in Fig. 3 are all qualitatively similar.Measurement of the dependence of the ∆ recoil distribution on EA selection   is therefore carried out using the ratios of such distributions, denoted R EA , to maximize the sensitivity to variations with EA.
Figure 4 shows ratios of the ∆ recoil distributions for EA-selected event populations, with R = 0.2 and 0.4.Since the numerator and denominator come from different, exclusive intervals in EA, they are statistically independent in each panel.However, some systematic uncertainties are correlated between numerator and denominator, which has been taken into account in the systematic uncertainty of the ratio.Note that the same dataset is used for R = 0.2 and R = 0.4, and for the ZNA and V0A selections, so that the results shown in the different panels are correlated.
Jet quenching may result in transport of jet energy out of the jet cone, resulting in suppression of the ∆ recoil distribution at fixed p ch T,jet .Under the assumptions (i) that jet quenching is more likely to occur in events with larger EA, and (ii) that the hadron trigger bias is independent of EA (Sect.5), this effect corresponds to suppression below unity of the ratios in Fig. 4.However, in all panels the ratio is consistent with unity within the statistical error and the systematic uncertainty at all p ch T,jet , indicating that jet quenching effects are negligible relative to the uncertainties.These data can nevertheless provide a limit on the magnitude of medium-induced energy transport to large angles.In order to extract a limit, we parameterize the 0-20% and 50-100% EA-selected ∆ recoil distributions with the exponential function used in Fig. 3, and assume that the slope parameter b is the same for the two distributions.We also assume that the average magnitude of energy transported out-   of-cone is independent of p ch T,jet , which is consistent with the observation that the ratios R EA in Fig. 4 are independent of p ch T,jet within uncertainties.The assumption that the average magnitude of out-of-cone radiation is independent of p ch T,jet is likewise consistent with ∆ recoil measurements in Pb-Pb collisions at 2.76 TeV [22].Consideration of a more complex dependence on p ch T,jet is beyond the scope of this phenomenological study.
The ratios R EA are then expressed in terms of an average shift s in p ch T,jet between low and high EA events, where s = −b • ln (R EA ).Fits to ∆ recoil for R = 0.4 over the range 15 < p ch T,jet < 50 GeV/c give b = 9.26 ± 0.33 GeV/c for 50-100% ZNA and b = 9.05 ± 0.30 GeV/c for 50-100% V0A.Fits to the ratios in Fig. 4 then give s = (−0.12± 0.35 stat ± 0.03 syst ) GeV/c for 0-20% ZNA, and s = (−0.06± 0.34 stat ± 0.02 syst ) GeV/c for 0-20% V0A, both of which are consistent with zero within uncertainties.Fits to narrower ranges in p ch T,jet give similar results.
These values are to be compared with the shift s = (8±2 stat ) GeV/c measured in central Pb-Pb collisions at √ s NN = 2.76 TeV for R = 0.5 [22], indicating significant medium-induced energy transport to large angles in that collision system.This comparison of out-of-cone energy transport in p-Pb and Pb-Pb collisions supports theoretical calculations which predict much smaller jet quenching effects in p-Pb relative to Pb-Pb collisions [50,52], and disfavors the calculation which predicts strong jet quenching in small systems [51].
The measured value of s provides a constraint on the magnitude of out-of-cone energy transport due to jet quenching in p-Pb collisions.We calculate this constraint as the linear sum of the central value of s, the one-sided 90% confidence upper limit of its statistical error, and the absolute value of its systematic uncertainty.For jets with R = 0.4 in the range 15 < p ch T,jet < 50 GeV/c, the medium-induced charged energy transport out of the jet cone for events with high V0A or high ZNA is less than 0.4 GeV/c, at 90% confidence.The red line in each panel of Fig. 4 shows the ratio for a p T -shift of −0.4 GeV/c of the high-EA distribution relative to the low-EA distribution.

Comparison to other measurements
The EA-selected ∆ recoil distribution ratios in Fig. 4 are consistent with unity in the range 15 < p ch T,jet < 50 GeV/c.These distributions therefore have no significant dependence on EA, in contrast to measurements of inclusive jet production in d-Au collisions at √ s NN = 200 GeV [62] and p-Pb collisions at √ s NN = 5.02 TeV [63], which exhibit strong dependence on EA.In this section we explore whether these inclusive and coincidence measurements can provide a consistent picture of jet quenching in asymmetric systems.
We first note that these measurements differ in several aspects, and that their detailed comparison requires calculations based on theoretical models of jet quenching that are beyond the scope of this paper.Here we explore a more limited question, whether the inclusive jet measurements are also consistent with a p T -independent limit of out-of-cone charged-energy transport of 0.4 GeV/c.We do so by comparing the effect of a p T -independent shift of the inclusive spectra to the measured EA-dependence of R CP , which is the ratio of inclusive jet spectra for event populations identified as "central" and "peripheral", with the spectra scaled by T pPb or T dAu .Since the inclusive spectra are measured with fully-reconstructed jets, including neutral energy, we increase the 90% confidence limit for out-of-cone energy transport to the value 0.6 GeV/c.Note in addition that the choice of percentile binning differs in the various measurements, which cannot be accounted for directly in the comparison; this difference should also be borne in mind when comparing the measurements.
The effect of the p T -shift on jet yield depends upon the inclusive spectrum shape.In order to assess this effect we select a representative spectrum for each data set, impose a p T -independent shift of −0.6 GeV/c on this spectrum, and calculate R * CP , the ratio of distributions with and without the shift.Since R * CP represents a 90% confidence limit, no uncertainty is assigned to it.
Table 2 compares R * CP to the values of EA-selected R CP measured in asymmetric collisions at RHIC and the LHC.While some values are in agreement, R * CP and R CP have opposite dependence on p T,jet for both datasets.Within the limits of this comparison, a p ch T,jet -independent out-of-cone charged-energy transport of 0.4 GeV/c is not consistent with measurements of R CP for inclusive jet production in EA-selected d-Au collisions at RHIC and p-Pb collisions at the LHC.
Effects other than jet quenching in the final state can modify jet yields in nuclear collisions, in particular the initial-state effects of shadowing and energy loss in cold matter [53,106].In addition, calculation of the Glauber scaling factor for inclusive measurements may be affected by fluctuations and dynamical correlations between a high Q 2 process and the soft observables used to tag EA [57,[65][66][67][68][69][70][71][72][73][74][75].Such non-quenching effects could be the origin of the inconsistency observed here in the EA-dependence of  inclusive and coincidence jet measurements, since inclusive and coincidence observables have different sensitivity to initial-state effects, and Glauber scaling is required only for inclusive observables.

Summary
We have reported measurements of the semi-inclusive distribution of charged jets recoiling from a highp T hadron trigger in p-Pb collisions at √ s NN = 5.02 TeV, selected by event activity in forward (Pbgoing) charged multiplicity and zero-degree neutral energy.This observable provides a new probe of jet quenching in small systems, whose interpretation does not require the assumption that event activity is correlated with collision geometry.These measurements of jet quenching in p-Pb collisions are thereby systematically different than quenching measurements based on inclusive jet production.No significant difference is observed in recoil jet distributions for different event activity.This measurement provides a limit on out-of-cone energy transport due to jet quenching in p-Pb collisions at the LHC of less that 0.4 GeV/c at 90% confidence for jet radius R = 0.4.Comparison of this measurement to theoretical calculations favors models with little or no energy loss in small systems.Comparison to inclusive jet measurements in small systems at RHIC and LHC indicates that the inclusive jet yield modification observed in EA-selected populations is not consistent with jet quenching.Future p-Pb measurements at the LHC, with higher statistical precision and greater kinematic reach, will provide more stringent limits on jet quenching in light systems.

Fig. 2 :
Fig. 2: Uncorrected semi-inclusive distributions of charged jets recoiling from a high-p T hadron trigger in p-Pb collisions at √ s NN = 5.02 TeV with EA selection of 0-20% in ZNA, for R = 0.2 (upper panels) and R = 0.4 (lower panels).The acceptance for TT and recoil jets in the CM frame are denoted y *TT and y * jet , respectively.Left panels: raw distributions for TT{12,50} (red circles) and TT{6,7} (blue boxes), and the corresponding ∆ recoil distribution (Eq.5, black circles).Right panels: ratio of yields for TT{12,50}/TT{6,7}.The arrow indicates the 0-1 GeV/c bin which is used to calculate c Ref .
and the larger yield of Signal spectrum at high p reco,ch T,jet [22].The value of c Ref in this analysis is taken as the ratio of the Signal and Reference spectra in the bin 0 < p reco,ch T,jet < 1 GeV/c, as shown by the arrow in Fig. 2, right panels.The value of c Ref lies between 0.92 and 0.99 for the various spectra.Additional variation in the value of c Ref was used to assess systematic uncertainties.
For the lower limit, double the value of (1 − c Ref ) from the primary analysis, giving c Ref = 0.95 for R = 0.2 and c Ref = 0.90 for R = 0.4.The systematic uncertainty band corresponds to the largest deviation from all such variations of the unfolded spectrum, relative to the spectrum resulting from the c Ref choice of the primary analysis; -Tracking efficiency: vary ±4% relative to nominal value [60]; -Track momentum resolution: extract systematic uncertainty of momentum resolution from azimuthal variation of the inclusive charged-track distribution; vary R instr accordingly.

Figure 3 ,
Figure 3, upper panels, show the corrected ∆ recoil distributions for p-Pb collisions at √ s NN = 5.02 TeV for the MB event population and for populations selected by EA using ZNA and V0A, and for pp collisions at √ s = 5.02 TeV simulated by PYTHIA.The upper panels also show the result of a fit to the p-Pb MB distributions by an exponential function, a • exp −p ch T,jet /b .

Fig. 3 :
Fig. 3: Corrected ∆ recoil distributions measured for p-Pb collisions at √ s NN = 5.02 TeV, for the MB and EAselected populations.The acceptance for TT and recoil jets in the CM frame are denoted y * TT and y * jet , respectively.Left panels: R = 0.2; right panels: R = 0.4.Also shown are ∆ recoil distributions for pp collisions at √ s = 5.02 TeV simulated by PYTHIA 6 Tune Perugia 11 and PYTHIA 8 Tune 4C.The solid line in the upper panels is the fit of an exponential function to the p-Pb distribution, with fit parameters as specified.Lower panels: ratio of p-Pb MB and pp distributions to the fit function.

Fig. 4 :
Fig. 4: Ratio of ∆ recoil distributions for events with high and low EA measured in p-Pb collisions at √ s NN = 5.02 TeV.Left panels: V0A 0-20% / 50-100%; right panels: ZNA 0-20% / 50-100%.Upper panels: R = 0.2; lower panels: R = 0.4.The grey boxes show the systematic uncertainty of the ratio, which takes into account the correlated uncertainty of numerator and denominator.The red line indicates the ratio for a p T -shift of the high-EA distribution of −0.4 GeV/c.

Table 1 :
Contributions to the relative systematic uncertainty of the ∆ recoil distribution for R = 0.4 in MB events.

Table 2 :
Comparison of R CP and R * CP for inclusive jet production in asymmetric collisions at RHIC and the LHC.See text for details.