Measurement of the groomed jet radius and momentum splitting fraction in pp and Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

This article presents groomed jet substructure measurements in pp and Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV with the ALICE detector. The Soft Drop grooming algorithm provides access to the hard parton splittings inside a jet by removing soft wide-angle radiation. We report the groomed jet momentum splitting fraction, $z_{\rm g}$, and the (scaled) groomed jet radius, $\theta_{\rm g}$. Charged-particle jets are reconstructed at midrapidity using the anti-kT algorithm with resolution parameters $R = 0.2$ and $R = 0.4$. In heavy-ion collisions, the large underlying event poses a challenge for the reconstruction of groomed jet observables, since fluctuations in the background can cause groomed parton splittings to be misidentified. By using strong grooming conditions to reduce this background, we report these observables fully corrected for detector effects and background fluctuations for the first time. A narrowing of the $\theta_{\rm g}$ distribution in Pb$-$Pb collisions compared to pp collisions is seen, which provides direct evidence of the modification of the angular structure of jets in the quark$-$gluon plasma. No significant modification of the $z_{\rm g}$ distribution in Pb$-$Pb collisions compared to pp collisions is observed. These results are compared with a variety of theoretical models of jet quenching, and provide constraints on jet energy-loss mechanisms and coherence effects in the quark$-$gluon plasma.


Introduction
Ultrarelativistic heavy-ion collisions at the Large Hadron Collider (LHC) are used to study the high temperature deconfined phase of strongly interacting matter known as the quark-gluon plasma (QGP) [1][2][3][4][5].Highly-energetic jets created early in the collisions interact with the QGP medium and through those interactions they can lose energy and their internal structure can be modified.This process, known as jet quenching, can be used to reveal the physical properties of the QGP itself such as its transport coefficients and the quasi-particle nature of its degrees of freedom as a function of scale [6][7][8][9].Experimentally, jet quenching is evaluated by comparing jet measurements in heavy-ion collisions to analogous measurements in pp collisions [10][11][12][13][14][15][16][17][18].Notably, measurements of the jet angularity [16] and jet transverse profile [18], which are sensitive to a combination of the angular and momentum space structure of jets, suggest a narrowing of the jet core in heavy-ion collisions.Nonetheless, up to now, no direct modification of the intra-jet angular distribution alone has been measured.
Jet grooming algorithms provide access to the hard (high-momentum transfer) parton splittings inside a jet by removing soft wide-angle radiation [19][20][21].Access to the hard splittings isolates substructures that are well-controlled in perturbative QCD (pQCD), which in heavy-ion collisions may help constrain various jet quenching effects such as energy loss, transverse-momentum broadening, and color coherence.Measurements of groomed jet observables in heavy-ion collisions have been performed by the ALICE and CMS collaborations [22][23][24], and opened a new avenue in the study of jet substructure in heavy-ion collisions.
The Soft Drop (SD) [19][20][21] grooming algorithm identifies a single splitting by first reconstructing a jet with the anti-k T algorithm and then reclustering the constituents of the jet using the Cambridge/Aachen (C/A) algorithm [25] in order to follow the angular ordering of the QCD parton shower.The splitting is selected from within the history of the reclustering with a grooming condition, z > z cut θ β , where β and z cut are tunable parameters, z is the fraction of transverse momentum (p T ) carried by the sub-leading (lowest p T ) prong, z ≡ p T,subleading p T,leading + p T,subleading , and θ is the relative angular distance between the leading and sub-leading prong, where ∆y and ∆ϕ are the distances measured in rapidity and azimuthal angle, respectively, and R is the jet resolution parameter.The groomed splitting is then characterized by two relevant kinematic observables: the groomed momentum fraction, z g , and the (scaled) groomed jet radius, θ g , which are the values of z and θ of Eq. ( 1) and ( 2) for the identified splitting, as shown in Fig. 1.
In pp collisions, measurements of the θ g and z g distributions were performed at RHIC and the LHC [23,[26][27][28][29].At high-transverse momentum p T , the data are described within uncertainties by pQCD predictions [30].
In heavy-ion collisions, it was proposed that θ g may be sensitive to several important jet-quenching physics mechanisms: the relative suppression of gluon vs. quark jets, transverse-momentum broadening, and the ability of the medium to resolve a color dipole as two independent color charges [31,32].Uncertainty principle arguments suggest that wider splittings are formed earlier in vacuum than narrower splittings (t f ∼ 1/θ 2 g where t f is the splitting formation time).In heavy-ion collisions, this would result in wider splittings traversing a longer path in the medium on average.Complementary to θ g , it has been argued that z g may be sensitive to the modification of the DGLAP splitting function in the QGP, the breaking of color-coherence, and the response of the medium to the jet [33][34][35][36].By measuring both θ g and z g simultaneously, and thereby both the angular and momentum scales of the hard substructure of jets, these jet quenching mechanisms can be further constrained.
p T,leading + p T,subleading y φ Figure 1: Graphical representation of the angularly ordered Cambridge-Aachen reclustering of jet constituents and subsequent Soft Drop grooming procedure [19], with the identified splitting denoted in black and the splittings that were groomed away in light blue.
Up to now, no measurement of θ g has been performed in heavy-ion collisions.Previous measurements of the z g distribution by the CMS [22] and ALICE collaborations [23] indicated significant modification with respect to pp collisions.However, these results were not corrected for background and detector effects, and are difficult to compare directly to theoretical calculations [37].In this letter, we report the first fully corrected measurement of groomed substructure observables in heavy-ion collisions, allowing for a rigorous comparison with theoretical calculations.

Experimental setup and data sets
A description of the ALICE detector and its performance can be found in Refs.[38,39].The pp data set used in this analysis was collected in 2017 during LHC Run 2 at √ s = 5.02 TeV using a minimum-bias (MB) trigger defined by the coincidence of the signals from two scintillator arrays in the forward region (V0 detectors) [40].The Pb-Pb data set was collected in 2018 at √ s NN = 5.02 TeV.Central and semicentral triggers that select events in the 0-10% and 30-50% centrality intervals based on the multiplicity of produced particles in the forward V0 detectors, were used [41,42].The event selection includes a primary-vertex selection and the removal of beam-induced background events and pileup [10].After these selections, the pp data sample contains 870 million events and corresponds to an integrated luminosity of 18.0 ± 0.4 nb −1 [43].The Pb-Pb data sample contains 92 million events in central collisions and 90 million events in semi-central collisions, corresponding to an integrated luminosity of 0.12 nb −1 and 0.06 nb −1 , respectively.This analysis uses charged-particle tracks reconstructed using information from both the Time Projection Chamber (TPC) [44] and the Inner Tracking System (ITS) [45].While track-based observables are collinear-unsafe [46][47][48], they can be measured with greater precision than calorimeter-based observables and recent measurements have demonstrated that for the groomed jet observables considered here, track-based distributions are compatible with the corresponding collinear-safe distributions [49].Tracks with 0.15 < p T < 100 GeV/c were accepted over pseudorapidity range |η| < 0.9.Further details about the track selection are described in Ref. [50].The accepted tracks exhibit approximately uniform azimuthal acceptance and momentum resolution σ (p T )/p T ranging from about 1% at track p T = 1 GeV/c to 4% at track p T = 50 GeV/c.

Analysis method
Jets were reconstructed from charged-particle tracks with FastJet 3.2.1 [51] using the anti-k T algorithm with E-scheme recombination for resolution parameters R = 0.2 and 0.4 [52,53].The pion mass is assumed for all jet constituents.Jets in heavy-ion collisions have a large uncorrelated background contribution due to fluctuations in the underlying event (UE) [54].The event-by-event constituent subtraction method was used, which corrects the overall jet p T and its substructure simultaneously by subtracting UE energy constituent by constituent [55,56].A maximum recombination distance R max = 0.25 was used.After background subtraction, the measured range is 40 < p T, ch jet < 120 GeV/c.The jet axis is required to be within the fiducial volume of the TPC, η jet < 0.9 − R, where η jet is the jet pseudorapidity.
Local background fluctuations in a heavy-ion collision environment can result in an incorrect splitting (unrelated to the hard scattering) being identified by the grooming algorithm.In order to address this issue, the measurement was performed by applying a strong grooming condition, z cut = 0.2 (with β = 0), which better mitigates these effects as compared to softer grooming conditions (e.g.z cut = 0.1) [37].To further reduce the mistagging effects, we report measurements with either a small resolution parameter (R = 0.2 in central collisions) or with more peripheral collisions (30-50% for R = 0.4).
The rate of prong mistagging from residual background effects was evaluated by embedding jets simulated with the PYTHIA8 event generator [57] into measured Pb-Pb data and following the procedure in Ref. [37].The residual background contribution ranges from approximately 5% up to 15% at lower p T , in more central events, and at larger R.This level of background contamination is small enough to allow the results to be unfolded for detector effects and background fluctuations.The impact of the residual background contribution remains one of the main sources of systematic uncertainty [50].
The reconstructed p T, ch jet , θ g , and z g distributions were corrected for effects related to the tracking inefficiency, particle-material interactions, and track p T resolution.Moreover, in Pb-Pb collisions, background fluctuations significantly smear the reconstructed distributions of θ g and z g .To account for these effects, events were simulated with the PYTHIA8 generator using the Monash 2013 tune [57] and the GEANT3 model [58] for the particle transport in the ALICE detectors' material.For the Pb-Pb data, we embedded the simulated events into measured Pb-Pb data to mimic the background effects.A fourdimensional response matrix describing the detector and background response in p T, ch jet and θ g or z g was constructed and used in the two-dimensional unfolding in p T, ch jet , θ g or z g using the iterative Bayesian unfolding algorithm [59,60].

Systematic uncertainties
The largest systematic uncertainties in this measurement originate from the tracking inefficiency, the unfolding procedure, residual mistagged prongs, and the background subtraction procedure.The total systematic uncertainty is calculated as the quadratic sum of all of the individual systematic uncertainties described below.
The systematic uncertainty due to the uncertainty of the tracking efficiency is evaluated using random rejection of additional tracks in jet finding according to the estimated tracking efficiency uncertainty of 4%, based on variations in the track selection criteria and on the ITS-TPC track-matching efficiency uncertainty.The systematic uncertainty arising from the unfolding regularization procedure is evaluated by varying the number of unfolding iterations by ±2 units, scaling the prior distribution, varying the binning, and varying the lower bound in the detector-level charged-particle jet transverse momentum p ch jet T,det range by 5 GeV/c.The systematic uncertainty due to the model-dependence of the generator used to construct the response matrix is estimated by comparing results obtained with PYTHIA [57], HERWIG [61], and JEWEL [62].The systematic uncertainty due to the bias introduced by the constituent subtraction procedure is estimated by varying R max from "under-subtraction" (R max = 0.05) to "oversubtraction" (R max = 0.7), around the nominal value of R max = 0.25.The systematic uncertainty due to a possible residual contamination of mistagged splittings after unfolding is estimated with a closure test.The total relative systematic uncertainty ranges from 3-24% for θ g and 4-10% for z g .See Ref. [50] for more details about the systematic uncertainties used in this measurement.TeV with z cut = 0.2 for 0-10% centrality for R = 0.2 (left) and 30-50% centrality for R = 0.4 (right).The distributions are normalized to the inclusive jet cross section in the 60 < p T, ch jet < 80 GeV/c interval, and f tagged indicates the fraction of splittings that were tagged to pass the SD condition in the selected p T, ch jet interval.The ratios in the bottom panel are compared to the following theoretical predictions: JETSCAPE [63], JEWEL [62,64], Caucal et al. [34,65], Chien et al. [33], Qin et al. [35], and Pablos et al. [36,66,67].Further details can be found in Ref. [50].

Results
We report the θ g and z g distributions in the p T, ch jet interval between 60 and 80 GeV/c for z cut = 0.2 in central (0-10%, R = 0.2) and semi-central (30-50%, R = 0.4) Pb-Pb collisions.The distributions are reported as normalized differential cross sections, where N is the number of jets passing the SD condition with a given p T, ch jet , N jet,inc is the number of inclusive jets, and σ , σ jet,inc are the corresponding cross sections.The analog of Eq. ( 3) also applies for θ g .
The z g and θ g distributions are shown in Fig. 2 and Fig. 3, respectively.The distributions from Pb-Pb collisions are compared with the corresponding distributions from pp collisions, with their ratios displayed in the bottom panels.The relative uncertainties are assumed to be uncorrelated between pp and Pb-Pb collisions, and are added in quadrature in the ratio.In Pb-Pb collisions the precision of the measurements decreases as the jet resolution parameter is increased or the centrality is decreased, as the prong mistagging probability decreases with centrality and with decreasing R.
The fraction of jets that do not contain a splitting which passes the SD condition ( f tagged ) differs by at most 1% between Pb-Pb and pp collisions.Therefore, any modifications in Pb-Pb compared to pp collisions can change the shape of the distribution, but keep the integral approximately the same.
The z g distributions in Pb-Pb and pp collisions are consistent within experimental uncertainties for all jet momenta, jet resolution parameters, and centralities measured.
The situation is remarkably different when comparing the groomed jet radius, θ g , in both systems.For R = 0.2 in central collisions, the data suggests a narrowing of the Pb-Pb distribution relative to the pp distribution is observed.This narrowing persists even in semi-central Pb-Pb collisions for R = 0.4 where quenching effects are expected to be less than in central collisions.TeV with z cut = 0.2 for 0-10% centrality for R = 0.2 (left) and 30-50% centrality for R = 0.4 (right).The distributions are normalized to the inclusive jet cross section in the 60 < p T, ch jet < 80 GeV/c interval, and f tagged indicates the fraction of splittings that were tagged to pass the SD condition in the selected p T, ch jet interval.The ratios in the bottom panel are compared to the following theoretical predictions: JETSCAPE [63], JEWEL [62,64], Caucal et al. [34,65], Pablos et al. [36,66,67], and Yuan et al. [31].Further details can be found in Ref. [50].
We compare the ratio of the measurements in pp and Pb-Pb collisions with several theoretical implementations of jet quenching: -JETSCAPE [63] consists of a medium-modified parton shower with the MATTER model [68] controlling the high-virtuality phase and the Linear Boltzmann Transport (LBT) model describing the low-virtuality phase [69].The version of JETSCAPE used for this calculation employs a jet transport coefficient, q, that includes dependence on parton virtuality, in addition to dependence on the local temperature and running of the parton-medium coupling.
-JEWEL [62,64] consists a Monte Carlo implementation of BDMPS-based medium-induced gluon radiation in a medium modeled with a Bjorken expansion.We consider the impact of medium recoil by including calculations both with and without recoils enabled [70].
-Caucal et al. [34,65] implements a pQCD parton shower with incoherent interactions including both factorized vacuum and medium-induced emissions in a static brick medium.
-Chien et al. [33] (for z g only) applies Soft Collinear Effective Theory with Glauber gluon interactions.
-Qin et al. [35] (for z g only) applies the higher twist formalism with coherent energy loss.
-Pablos et al. [36,66,67] consists of partons produced by a vacuum shower that interact with the medium according to a strongly-coupled AdS/CFT-based model.The parameter L res describes the degree to which the medium can resolve the jet angular structure, where L res = 0 corresponds to full resolution of all jet constituents (fully incoherent), L res = ∞ corresponds to fully coherent energy loss, and L res = 2/πT is an intermediate case, where T is the local medium temperature.
-Yuan et al. [31] (for θ g only) "med q/g" and "quark" consist of medium-modified quark-gluon fractions without any additional effects, where the quark-gluon fractions in the "med q/g" case are extracted in Ref. [71] with a relative suppression factor of approximately four between gluon jets and quark jets.The calculation labeled " qL" includes an implementation of transverse-momentum broadening.
The Pb-Pb-to-pp ratios of the z g distributions are consistent with all theoretical predictions considered.The predicted modifications, which have been constrained by previous measurements [22,23], are small, and the differences between them are yet smaller than the current uncertainty of the data.Nevertheless, these new measurements are the first direct comparisons of predictions to fully corrected data, and limit the possible in-medium modifications of the momentum structure of hard splittings to be less than 10-20% depending on the centrality, jet R, and the grooming settings considered.
Despite employing different microscopic implementations of the jet-medium interactions, the majority of the models capture the qualitative feature of the narrowing seen in the θ g distributions.The theoretical models can be grouped according to three distinct mechanisms by which θ g is modified: incoherent energy loss, coherent energy loss, and transverse broadening.The measurements are consistent with models implementing (transverse) incoherent interaction of the jet shower constituents with the medium.This is illustrated by calculations of Pablos et al.where the data favor the incoherent energy loss (L res = 0) and is also supported by Caucal et al., JEWEL, and JETSCAPE.On the other hand, the Yuan et al. calculation with medium-modified "quark-gluon" fractions indicates that the data could be explained by the stronger suppression of gluon showers, which are on average broader, with fully coherent energy loss.These two physics mechanisms -the degree of incoherent energy loss, and the relative quark/gluon suppression -both lead to a suppression of wide-angle splittings.The prediction by Yuan et al. " qL" exhibits the opposite trend compared to the data, demonstrating that there is no strong transverse broadening in the hard substructure.
The presented measurements indicate that the medium has a significant resolving power for splittings with a particular dependence on the angular (or coherence) scale, promoting narrow structures or filtering out wider jets altogether.

Conclusions
We reported the groomed jet momentum fraction, z g , and the (scaled) groomed jet radius, θ g , of chargedparticle jets measured in pp and Pb-Pb collisions at √ s NN = 5.02 TeV with the ALICE detector.By using stronger grooming conditions in the SD grooming algorithm, we suppressed contamination of mistagged splittings from the underlying event, and unfolded the final distributions for detector and background fluctuation effects.This allows for the first time the direct comparison of groomed jet measurements in heavy-ion collisions with theoretical predictions of jet quenching in the QGP.The z g distributions are consistent with no modification in Pb-Pb collisions compared to pp collisions.The θ g distributions are narrower in Pb-Pb collisions compared to pp collisions, which is the first direct experimental evidence for the modification of the angular scale of groomed jets in heavy-ion collisions.
These new results demonstrate sensitivity to the microscopic structure of the QGP, including its angular resolving power.This marks an important step towards quantitative understanding of the properties of the QGP, and provides a new path for novel differential jet substructure measurements to further elucidate the microscopic nature of the QGP.

Figure 2 :
Figure2: Unfolded z g distributions for charged-particle jets in pp collisions compared to those in Pb-Pb collisions at √ s NN = 5.02 TeV with z cut = 0.2 for 0-10% centrality for R = 0.2 (left) and 30-50% centrality for R = 0.4 (right).The distributions are normalized to the inclusive jet cross section in the 60 < p T, ch jet < 80 GeV/c interval, and f tagged indicates the fraction of splittings that were tagged to pass the SD condition in the selected p T, ch jet interval.The ratios in the bottom panel are compared to the following theoretical predictions: JETSCAPE[63], JEWEL[62,64], Caucal et al.[34,65], Chien et al.[33], Qin et al.[35], and Pablos et al.[36,66,67].Further details can be found in Ref.[50].

Figure 3 :
Figure3: Unfolded θ g distributions for charged-particle jets in pp collisions compared to those in Pb-Pb collisions at √ s NN = 5.02 TeV with z cut = 0.2 for 0-10% centrality for R = 0.2 (left) and 30-50% centrality for R = 0.4 (right).The distributions are normalized to the inclusive jet cross section in the 60 < p T, ch jet < 80 GeV/c interval, and f tagged indicates the fraction of splittings that were tagged to pass the SD condition in the selected p T, ch jet interval.The ratios in the bottom panel are compared to the following theoretical predictions: JETSCAPE[63], JEWEL[62,64], Caucal et al.[34,65], Pablos et al.[36,66,67], and Yuan et al.[31].Further details can be found in Ref.[50].