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Transverse momentum balance of dijets in Xe+Xe collisions at the LHC

NUCLEAR PHYSICS AND INTERDISCIPLINARY RESEARCH

Transverse momentum balance of dijets in Xe+Xe collisions at the LHC

Yao Li
Shu-Wan Shen
Sa Wang
Ben-Wei Zhang
Nuclear Science and TechniquesVol.35, No.7Article number 113Published in print Jul 2024Available online 09 Jul 2024
34101

We present a theoretical study of the medium modifications of the pT balance (xJ) of dijets in Xe+Xe collisions at sNN=5.44 TeV. The initial production of dijets was carried out using the POWHEG+PYTHIA8 prescription, which matches the next-to-leading-order (NLO) QCD matrix elements with the parton shower (PS) effect. The SHELL model described the in-medium evolution of nucleus-nucleus collisions using a transport approach. The theoretical results of the dijet xJ in the Xe+Xe collisions exhibit more imbalanced distributions than those in the p+p collisions, consistent with recently reported ATLAS data. By utilizing the Interleaved Flavor Neutralisation, an infrared-and-collinear-safe jet flavor algorithm, to identify the flavor of the reconstructed jets, we classify dijets processes into three categories: gluon-gluon (gg), quark-gluon (qg), and quark-quark (qq), and investigated the respective medium modification patterns and fraction changes of the gg, qg, and qq components of the dijet sample in Xe+Xe collisions. It is shown that the increased fraction of qg component at a small xJ contributes to the imbalance of the dijet; in particular, the q1g2 (quark-jet-leading) dijets experience more significant asymmetric energy loss than the g1q2 (gluon-jet-leading) dijets traversing the QGP. By comparing the ΔxJ=xJppxJAA of inclusive, cc¯ and bb¯ dijets in Xe+Xe collisions, we observe Δ xJ incl.>Δ xJ cc¯>Δ xJ bb¯. Moreover, ρXe, Pb, the ratios of the nuclear modification factors of dijets in Xe+Xe to those in Pb+Pb, were calculated, which indicates that the yield suppression of dijets in Pb+Pb is more pronounced than that in Xe+Xe owing to the larger radius of the lead nucleus.

Heavy-ion collisionsQuark-gluon plasmaJet quenchingTransverse momentum balance
1

introduction

Ultra-relativistic heavy-ion collisions at the Large Hadron Collider (LHC) and Relativistic Heavy Ion Collider (RHIC) provide a unique arena for searching for a new form of nuclear matter, quark-gluon plasma (QGP), in which the degrees of freedom of the quarks and gluons in the protons and neutrons are released [1-5]. The strong interactions between the hard-scattered partons with the medium, referred to as the “jet quenching” phenomenon, open up new avenues to understand the properties of such a strongly-coupled quark matter [6-9] and test the fundamental theory of quantum chromodynamics (QCD) at the extremely hot and dense conditions [10-16]. In the past two decades, a series of tools have been extensively investigated to reveal this partonic strong interaction, such as the suppression factor RAA of high-pT hadron/jet [17-22], the momentum asymmetry of dijets [23-34], correlations of the vector boson associated jets (γ/Z0+jets) [35-40], the global event geometry [41, 42] and the jet substructures [43-52].

Because dijets are the dominant QCD processes in the hadron collisions in the experiment and are less influenced by the underlying background than inclusive jets, they exhibit a unique glamour in jet physics. The back-to-back configurations of the two leading jets in the transverse plane can significantly suppress the contribution of the underlying background of the jet reconstruction in both p+p and A+A collisions. In a vacuum, the parton shower effects and higher-order QCD processes may break the symmetry of the final-state dijets, leading to a deflection from the back-to-back azimuthal angle and an unequal transverse momentum between the leading and subleading jets. In A+A collisions, because the two jets usually experience asymmetric energy loss as traversing the QGP medium, the transverse momentum balance of dijets xJpT,2/pT,1 [53], defined as the ratio of the subleading to leading jet pT, can be further modified by the in-medium interactions and show a different sensitivity to the path-length dependence of jet quenching [25] and jet-by-jet fluctuations of jet-medium interactions [54]. More imbalanced AJ(pT,1pT,2)/(pT,1+pT,2) and xJ distributions of dijets have been observed in Pb+Pb collisions relative to p+p at sNN=2.76 TeV and sNN=5.02 TeV by the ATLAS [23, 53, 55] and CMS Collaborations [28, 56, 57], and in Au+Au collisions at sNN=200 GeV by the STAR Collaborations [58], which have been extensively investigated using theoretical calculations [26, 27, 31-34].

Recently, the ATLAS Collaboration measured the dijet xJ in Xe+Xe collisions at sNN=5.44 TeV for the first time [59] however, timely theoretical studies are still lacking. Because the xenon nucleus has a smaller radius than lead, studying the jet production in different collision systems will deepen our understanding of the system size dependence of the jet quenching effect [53, 55, 60-64]. Furthermore, because dijet events consist of gg, qg and qq components, whereas the jet energy loss is closely related to the flavor of hard partons (ΔEg/ΔEqCA/CF=9/4,CA=3,CF=4/3) [2, 18], it is essential to determine their respective modification patterns and assess the roles they play in the overall medium modifications of dijet xJ. Furthermore, massive heavy quarks are believed to lose less energy than light quarks owing to the “dead-cone” effect [65-68], which leads to a mass hierarchy of partonic energy loss ΔEq>ΔEc>ΔEb [69, 70, 49, 71]. It is of particular interest to explore the mass dependence of the medium modification on the dijet xJ by comparing light- and heavy-flavor (such as cc¯ and bb¯) dijets in high-energy nuclear collisions.

This paper presents the first theoretical study on medium modifications of the dijet pT–balance xJ in Xe+Xe collisions. The initial production of dijets was carried out using the POWHEG+PYTHIA8 prescription, which matches the next-to-leading-order (NLO) QCD matrix elements with the parton shower (PS) effect. The transport approach describes dijets’ in-medium evolution, which considers both elastic and inelastic partonic interactions in the quark-gluon plasma (QGP). First, we present the theoretical results of the dijet xJ in Xe+Xe collisions at sNN=5.44 TeV compared with recently reported ATLAS measurements. Specifically, we discuss medium modification’s flavor and mass dependence on the dijet xJ. We studied the respective medium-modification patterns and fraction changes of the gg, qg, qq, as well as the q1g2 and g1q2 components in the dijet samples for both p+p and Xe+Xe collisions. We also investigated the mass effect of the xJ modifications by comparing the Δ xJ of the inclusive, cc¯ and bb¯ dijets in the Xe+Xe collisions. Finally, we present the calculated results of dijets nuclear modification factor for Xe+Xe at sNN=5.44 TeV and Pb+Pb at sNN=5.02 TeV compared with recent ATLAS data.

2

Theoretical framework

In this study, we generated next-to-leading-order (NLO) matrix elements for QCD jet processes [72] in the framework of POWHEG-BOX-V2 [73-75] and then simulated the parton shower (PS) with PYTHIA 8.309 [76] to produce p+p events. CT18NLO parton distribution functions (PDF) [77] were chosen for computation. The jets were reconstructed using the anti-kT clustering algorithm and the radius parameter R = 0.4, as implemented in the FastJet package [78]. Then, the two highest pT jets out of the set of jets in an event are selected as the dijet candidates. The leading jet transverse momentum pT,1 and subleading jet transverse momentum pT,2 must be greater than 100 GeV/c and 32 GeV/c, respectively. The two jets are required to be nearly back-to-back in azimuth with Δϕ|ϕ1ϕ2|7π/8 and to be in the rapidity region |y| < 2.1. If all these conditions are satisfied, the desired dijet candidate is accepted.

We calculated the normalized xJ distributions in p+p collisions and compared them with the ATLAS data [55] as shown in Fig. 1. We observe that the xJ distributions calculated by POWHEG+PYTHIA8 provide decent descriptions at small value of xJ for all six different pT,1 intervals compared to the ATLAS data, except for a slight overestimation of xJ distributions compared to the ATLAS data near 1. At each pT interval, the xJ distribution peaks near xJ1, where the leading and subleading jets are almost balanced. However, higher-order perturbative QCD corrections and splitting processes during the parton shower in a vacuum produce a considerable fraction of dijets with an imbalanced transverse momentum in the smaller xJ region.

Fig. 1
(Color online) Normalized xJ distributions of dijets in p+p collisions at s=5.02 TeV for six pT,1 intervals: [100, 112], [112, 126], [126, 141], [141, 158], [158, 171] and [171, 200] GeV/c are compared with the ATLAS data [55]
pic

The in-medium evolution of both light- and heavy-flavor diets was simulated using the SHELL model [34, 79], which considers the elastic and inelastic partonic energy loss within the hot/dense QGP medium. The initial spatial distribution of hard scatterings was sampled using a Monte Carlo Glauber model [80]. Since the propagation of massive partons in the QCD medium can be viewed as “Brownian motion," the transport of heavy quarks can be well described by the modified Langevin equations, Δx(t)=p(t)EΔt, (1) Δp(t)=ηDpΔt+ξ(t)Δtpg(t). (2) These two equations describe heavy quarks’ position and momentum updates traversing the QGP medium. ηD is the drag coefficient that controls the energy-dissipation strength of heavy quarks in the medium. The stochastic term ξ(t) denotes random kicks as heavy quarks scattered by a thermal particle, which obeys a Gaussian distribution. The diffusion coefficient κ can be related to ηD using the fluctuation-dissipation theorem κ=2ηDET. The first two terms on the right-hand side of Eqs. 2 represents the collisional energy loss of heavy quarks. In contrast, the last term, -pg is the momentum correction caused by medium-induced gluon radiation. In our framework, the higher-twist [66, 81-83] formalism was employed to simulate the medium-induced gluon radiation of the jet partons, in which the gluon radiation spectra of an energetic parton in the QGP can be obtained as dNgdxdk2dt=2αsP(x)q^πk4sin2(tti2τf)(k2k2+x2M2)4, (3) where x and k denote the energy fraction and transverse momentum of the radiated gluon, respectively. P(x) is the QCD splitting function for the splitting processes gg+g and q(Q)q(Q)+g [84], τf=2Ex(1x)/(k2+x2M2) is the formation time of the daughter gluon. q^ denotes the general jet transport parameter in QGP [85]. The last term in Eq. 3 represents the suppression factor resulting from the “dead-cone” effect of heavy quarks [65, 86], which reduces the probability of gluon radiation within a small cone (θMQ/E). The collisional energy loss is generally dominant for low-energy heavy quarks due to the “dead-cone” effect. In contrast, radiative energy loss is usually expected to become significant at pTQ>5mQ [87].

For massless partons, the collisional energy loss is estimated by pQCD calculations within the Hard-Thermal Loop approximation [88, 89], whereas the same higher-twist formalism estimates their radiative contribution as for massive partons. The hydrodynamic time-space evolution of the QGP medium is described using CLVisc programs [90, 91], which provide the temperature and velocity of the expanding hot/dense nuclear matter. The SHELL model has been successfully applied in the study of heavy-flavor jets in high-energy nuclear collisions, which gives satisfactory descriptions on a series of experiment measurements, such as pT imbalance [34], radial profiles [79, 92-94] and fragmentation functions [95] of heavy-flavor jets, correlations of Z0+ HF hadron/jet [96, 97].

3

Numerical Results and Discussions

In Fig. 2a, we firstly show the dijet xJ distributions in Xe+Xe collisions at sNN=5.44 TeV calculated by the SHELL model as a comparison to the ATLAS data for four centrality bins (0%-10%, 10%-20%, 20%-40% and 40%-80%) and two pT,1 intervals ([100, 126] GeV/c and [158, 199] GeV/c). The centrality bins corresponding to the values of b are listed in Table 1, which are calculated using the GIauber model [80]. We use the average impact parameter b in our calculations for simplicity. We found that the calculations using the SHELL model provide a satisfactory description of the recently reported ATLAS data for almost all four centrality bins and two pT,1 intervals, except for the data at 158 < pT,1 < 199 GeV/c in the central 0%-10% collisions, which shift the xJ distribution towards larger xJ values compared with the ATLAS data. Furthermore, our theoretical results show a more balanced xJ distribution for higher pT dijets (158 < pT,1 < 199 GeV/c) than for lower ones, which is consistent with the trend observed in the ATLAS measurements. To determine the collision centrality and jet pT dependence of the medium modification on the dijet xJ distributions, we compared the dijet xJ distributions in the Xe+Xe collisions with their p+p baseline for two pT intervals, as shown in the bottom panels of Fig. 2b. The xJ distributions were observed to shift towards smaller xJ values in the Xe+Xe collisions compared with their p+p baseline, especially for the most central collisions. The phenomenon in which the dijet transverse momentum becomes more imbalanced in A+A collisions owing to the asymmetric energy loss suffered by the leading and subleading jets as the dijet traverses the QGP [25, 54] has been observed in previous measurements of Pb+Pb collisions at 2.76 TeV [53] and 5.02 TeV [55]. In central collisions, such an asymmetric energy loss between the leading and subleading jets can be more significant because of the larger medium size and higher temperature than in the peripheral case. In addition, we observe a slightly weaker xJ modification for higher pT dijets than for lower ones, which is consistent with expectations.

Fig. 2
(Color online) (a) Calculated normalized dijet xJ distributions in Xe+Xe collisions at sNN=5.44 TeV are compared with the ATLAS data for four centrality bins (0%-10%, 10%-20%, 20%-40% and 40%-80%) and two pT,1 intervals (green: [100, 126] GeV/c, red: [158, 199] GeV/c). (b) Comparison of the normalized dijets xJ distributions between the Xe+Xe and p+p collisions at sNN=5.44 TeV for two pT,1 intervals (left: [100, 126] GeV/c, right: [158, 199] GeV/c) and the ratios of XeXe/pp are shown in the bottom panels
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Table 1
Relations between centrality bins and the values of impact parameter b for sNN=5.02 TeV Pb+Pb and sNN=5.44 TeV Xe+Xe collisions calculated by Glauber model
  Pb+Pb Xe+Xe
  bmin (fm) bmax (fm) b(fm) bmin (fm) bmax (fm) b(fm)
0%-10% 0 4.98 3.52 0 4.28 3.02
10%-20% 4.98 7.05 6.10 4.28 6.05 5.24
20%-40% 7.05 9.98 8.64 6.05 8.56 7.41
40%-80% 9.98 14.11 12.22 8.56 12.12 10.49
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The flavor dependence of the medium modification of dijet pT balance is also an interesting topic in heavy ion collisions. Because of the different color factors, the gluon-initiated jets are expected to lose more energy than the quark-initiated one as traversing the hot and dense nuclear matter, and the “dead-cone” effect also leads to smaller energy loss of heavy quarks than that of the light one [2, 18, 65-68]. An optimal step toward this goal is determining the flavor of the selected jets in nucleus-nucleus collisions using an infrared and collinear (IRC) safe jet algorithm. In recent years, four IRC-safe jet-algorithm-based approaches have been developed to identify the flavor of the underlying hard partons for the final-state reconstructed jets, called “flavor-kT” [98], “flavor anti-kT” [99], “flavor-dressing” [100] and “Interleaved Flavor Neutralisation (IFN)” [101]. In this study, we employ the IFN algorithm to identify the flavor of the reconstructed jets at the parton level for gluon jets, light-quark jets, and heavy-flavor jets in both p+p and nucleus-nucleus collisions. Because the flavor information of the jets is accessible at each stage of the clustering sequence, the IFN algorithm provides consistent flavor identification for both the full jets and their substructures. It should be noted that identifying gluon and quark jets in experiments remains challenging, although such identification can be achieved through Monte Carlo simulations based on the complete flavor information of the jet particles. Note that the IFN algorithm is applicable to all jets at the parton level but is currently only accessible for heavy-flavor jets at the hadron level. As the first theoretical exploration, in the present work, we identified the jet flavor at the parton level; hence, flavor identification of both inclusive dijets and heavy-flavor dijets could be efficiently implemented.

Using the IFN algorithm, inclusive dijet events can be classified into three categories: gluon-gluon (gg), quark-gluon (qg), and quark-quark (qq). In particular, by distinguishing the flavor of the leading jet, qg dijets can be further divided into q1g2 and g1q2, denoting the quark-jet-leading and gluon-jet-leading quark-gluon dijets, respectively. In the left column of Fig. 3, we show the normalized xJ distributions of gg, qg, qq, and inclusive dijets in both p+p and 0%-10% Xe+Xe collisions at sNN=5.44 TeV, and the ratio of XeXe/pp is plotted in the bottom panel. We find that gg dijets have a more imbalanced initial distribution than qq. Quarks and gluons experience different parton shower processes in a vacuum because of their different color factors and splitting functions [76, 102]. In the bottom panel, the qg dijets exhibit a slightly stronger suppression near xJ~1 and enhancement near xJ~0 than the others. The different color charges carried by the leading and subleading jets of qg dijets lead to enhanced asymmetric energy loss in Xe+Xe collisions relative to the qq and gg jets. However, qg dijets contain two types of subsets, q1g2 and g1q2, which may exhibit different modification patterns. In the right column of Fig. 3, we observe a stronger enhancement at small xJ and stronger suppression at xJ~1 on the xJ distribution of q1g2 dijets than that of g1q2. Compared to the g1q2 dijets, the leading jet of q1g2 dijets lost less energy, whereas the subleading jet lost more energy. In other words, the flavor configuration of q1g2 dijets results in a more significant asymmetric energy loss than g1q2 when traversing the QGP medium.

Fig. 3
(Color online) Calculated normalized xJ distributions in p+p (top) and 0%-10% Xe+Xe (middle) collisions as well as their ratios (bottom) for inclusive, gluon-gluon, quark-gluon, and quark-quark dijets (left column); quark-jet-leading and gluon-jet-leading of quark-gluon dijets (right column). The xJ distributions of quark-gluon dijets (dashed green line) in the right column are identical to those in the left column
pic

We also estimated the component fractions of the dijet sample in p+p and 0%-10% Xe+Xe collisions at sNN=5.44 TeV shown in Fig. 4, which would be helpful in understanding the role of jet flavor in jet-medium interactions. The left column shows the fractions of gg, qg, and qq in the inclusive dijets in the p+p (top) and Xe+Xe (middle) collisions, as well as their differences (bottom). First, we find that qg has the most prominent initial fraction (∼50%) in p+p collisions, and the fraction increases at a small xJ but decreases at xJ~1 in Xe+Xe collisions. Second, the fraction of gg is overall reduced. At the same time, that of qq is enhanced because, generally, the gg dijets lose more energy, making it more difficult to survive the jet selection relative to qq. Because qg is the most significant fraction in the dijet sample, the enhanced fractions of qg at small xJ in Xe+Xe contribute to the increased pT imbalance of the inclusive dijets. Furthermore, it is essential to address the fractional changes in the q1g2 and g1q2 subsets in the A+A collisions. In the right column of Fig. 4, it is observed that the fractions of q1g2 and g1q2 exhibit opposite behavior in the Xe+Xe collisions compared to their initial values. The fraction of q1g2 is significantly enhanced at small xJ after traversing the QGP, whereas that of g1q2 decreases in this region.

Fig. 4
(Color online) Calculated fraction of subset dijets in inclusive dijets as the function of xJ in p+p (top) and 0%-10% Xe+Xe (middle) collisions as well as their differences (bottom) for gluon-gluon, quark-gluon, and quark-quark dijets (left column); quark-jet-leading and gluon-jet-leading quark-gluon dijets (right column). The fraction distributions of the quark-gluon dijets in the right column (dashed green line) are the same as those in the left column
pic

To quantify the overall shift in the xJ distribution in Xe+Xe collisions relative to p+p, we calculated the average values (xJ) of dijet xJ distributions and their differences (ΔxJ) between the p+p and A+A collisions, defined as follows: xJ011NpairdNpairdxJxJdxJ, (4) ΔxJ=xJppxJAA. (5) To address the mass dependence of the medium modification of dijet xJ in the left column of Fig. 5, we show the xJ of the inclusive, cc¯ and bb¯ dijets in p+p and Xe+Xe collisions as a function of centrality as well as their differences ΔxJ. We find that ΔxJ decreases monotonously from central to peripheral collisions, as in Fig. 2b. It is also observed that the ΔxJ of these three kinds of dijets obey the hierarchy ΔxJincl.>ΔxJcc¯>ΔxJbb¯ in Xe+Xe collisions for the same centrality bin. This indicates that massive dijets suffer less asymmetric energy loss in A+A collisions than massless light flavors. Future measurements focusing on these comparisons will help test the mass effect of the jet energy loss. In the right column of Fig. 5, ΔxJ of q1g2 and g1q2 dijets in Xe+Xe are also plotted; the former has significantly larger values than the latter for each centrality bin.

Fig. 5
(Color online) Averaged xJ of the inclusive, cc¯, bb¯ dijets (left) and q1g2, g1q2, qg dijets (right) in p+p (top) and Xe+Xe (middle) collisions as a function of the collision centrality, as well as their differences ΔxJ (bottom)
pic

To quantitatively characterize the relative dijet yield suppression between the Xe+Xe and Pb+Pb collisions, the nuclear modification factors for the leading jets, ρXe,Pb(pT,1), are defined as follows (similarly, ρXe,Pb(pT,2) can be defined for subleading jets): RAA(pT,1)=1TAAdσAApair/dpT,1dσpppair/dpT,1, (6) ρXe,Pb(pT,1)=RXeXe(pT,1)RPbPb(pT,1). (7) In Fig. 6, we show the calculated ρXe,Pb(pT,1) (left) and ρXe,Pb(pT,2) (right) of dijets for three centrality bins: 0%-10%, 10%-20% and 20%-40%. Note that we used a cut xJ>0.32 in the calculation to be consistent with the ATLAS treatment in the measurements. We observe that the values of ρXe, Pb are generally greater than one for both the leading and subleading jets for all centrality bins. This indicates a weaker yield suppression of dijets in Xe+Xe collisions than in Pb+Pb for the same centrality bin, and this phenomenon is still evident even in peripheral collisions. These findings were consistent with those of previous phenomenological studies [62-64]. Because the nucleus of xenon has a smaller radius than that of lead, the system size and mean temperature of the QGP medium formed in Xe+Xe collisions are expected to be smaller than those in Pb+Pb collisions within the same centrality interval [103]. Hence, dijets traverse a longer path length medium and experience more effective energy loss during Pb+Pb collisions.

Fig. 6
(Color online) Calculated ratios of Xe+Xe and Pb+Pb pair nuclear modification factors, ρXe,Pb, evaluated as a function of pT,1 (left) and pT,2 (right) in the same centrality intervals, and compared to the ATLAS data
pic
4

Conclusion

In this paper, we present the first investigation of the medium modifications of dijet pT balance (xJ) in Xe+Xe collisions at sNN=5.44 TeV. The initial xJ distributions of dijets were calculated using the POWHEG+PYTHIA8 prescription, which matched the NLO QCD matrix elements with the parton shower effect. The in-medium evolution of dijets in nucleus-nucleus collisions is described by the SHELL model, which considers both elastic and inelastic partonic interactions in the quark-gluon plasma (QGP). Our theoretical results for the dijet xJ in Xe+Xe collisions exhibit a more imbalanced distribution than in p+p collisions, consistent with the recently reported ATLAS data. The dijet becomes increasingly imbalanced from peripheral to central Xe+Xe collisions, consistent with previous measurements of Pb+Pb collisions at the LHC. Furthermore, using an infrared-and-collinear-safe flavor jet algorithm, we explored the flavor dependence of the medium modification of dijet pT balance in nucleus-nucleus collisions. We studied the respective medium-modification patterns and fraction changes of the gg, qg, and qq components in the dijet sample for both p+p and Xe+Xe collisions. We demonstrate that the qg component plays a key role in the increased imbalance in the dijet xJ. In particular, we found that the q1g2 dijets experience a more significant asymmetric energy loss than the g1q2 dijets when traversing a QGP. By comparing the ΔxJ of inclusive, cc¯ and bb¯ dijets in Xe+Xe collisions, we observe ΔxJincl.>ΔxJcc¯>ΔxJbb¯ consistent with the mass hierarchy of partonic energy loss. In addition, the nuclear modification factors ρXe, Pb of dijets in Xe+Xe at sNN=5.44 TeV and Pb+Pb at sNN=5.02 TeV are consistent with the ATLAS data, indicating that the yield suppression of dijets in Pb+Pb is more pronounced than that in Xe+Xe because of the larger radius of the lead nucleus.

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Footnote

The authors declare that they have no competing interests.