Extracting jet transport coefficient via single hadron and dihadron productions in high-energy heavy-ion collisions

We study the suppressions of high transverse momentum single hadron and dihadron productions in high-energy heavy-ion collisions based on the framework of a next-to-leading-order perturbative QCD parton model combined with the higher-twist energy loss formalism.Our model can provide a consistant description for the nuclear modification factors of single hadron and dihadron productions in central and non-central nucleus-nucleus collisions at RHIC and the LHC energies. We quantitatively extract the value of jet quenching parameter $\hat q$ via a global $\chi^2$ analysis, and obtain ${\hat{q}}/{T^3} = 4.1 \sim 4.4$ at $T = 378$~MeV at RHIC and ${\hat{q}}/{T^3} = 2.6 \sim 3.3$ at $T = 486$~MeV at the LHC, which are consistent with the results from JET Collaboration. We also provide the predictions for the nuclear modification factors of dihadron productions in Pb+Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV and in Xe+Xe collisions at $\sqrt{s_{\rm{NN}}}$ = 5.44 TeV.


I. INTRODUCTION
The strongly-interacting quark-gluon plasma (QGP) can be created in high-energy heavy-ion collisions performed at the Large Hadron Collider (LHC) and the Relativistic Heavy-Ion Collider (RHIC). Jet quenching [1][2][3] has been regarded as an extremely useful tool for studying the properties of such hot and dense nuclear matter. When hard quarks or gluons traverse the QGP matter, they interact with the medium via multiple scatterings and medium-induced gluon radiations. The elastic and inelastic interactions between jet and medium may cause the energy loss of hard jet and also change the energy distribution among jet partons. As one of the consequences of jet quenching and energy loss, the yield of high transverse momentum hadrons fragmented from the surviving hard partons is suppressed as compared to that in proton-proton collisions normalized by the number of binary nucleon-nucleon collisions. Phenomenological studies have been performed on various jet quenching observables, such as the nuclear modifications of single hadron productions [4][5][6][7], dihadron and photon-hadron correlations [8][9][10][11][12][13], as well as the observables related to fully reconstructed jets in relativistic nuclear collisions [14][15][16][17][18][19][20][21].
In recent years, jet quenching studies have entered the quantitative era in that much effort has been devoted to the quantitative extraction of the so-called jet quenching parameterq. This parameter is defined as the transverse momentum squared per unit length exchanged between the propagating hard parton and the traversed medium, q = d (∆p T ) 2 /dt, and may be directly related to the gluon density of the nuclear medium [22]. Jet transport parameterq also controls the amount of medium-induced gluon radiation and thus radiative jet energy loss [22][23][24][25][26][27]. In addition, the transverse momentum broadening effect as controlled byq may lead to significant nuclear modification on back-to-back dijet, dihadron and other jet-related angular correlations [12,13]. Among many quantitative jet quenching studies, one of the most important steps is performed by JET Collaboration in Ref. [6] which has compared five different theoretical jet quenching models with the nuclear modification data on single hadron productions in most central collisions at RHIC and the LHC and quantitatively extracted the temperature dependence of jet quenching parameterq. The values ofq temperatures available at RHIC and the LHC have been obtained as:q/T 3 = 4.6 ± 1.2 at T ≈ 370 MeV andq/T 3 = 3.7±1.4 at T ≈ 470 MeV for a 10 GeV quark jet [28]. Following this direction, Ref [29,30] has studied the centrality and collision energy dependence ofq values at both RHIC and the LHC. Also, Refs. [12] has utilized the nuclear modification data on back-to-back dihadron and hadron-jet angular correlations to extract the value ofq at RHIC. This paper follows closely the above efforts and study the nuclear modifications of both single hadron and dihadron productions at high transverse momenta using a next-to-leading-order (NLO) perturbative QCD model combined with the higher-twist energy loss formalism. In particular, we perform a global χ 2 analysis on the nuclear modification data on single hadron and dihadron productions at RHIC [31][32][33][34] and the LHC [35][36][37][38][39][40][41][42] and quantitatively extract the values of jet quenching parameterq. Our analysis yieldsq/T 3 = 4.1 ∼ 4.4 at T = 378 MeV at RHIC andq/T 3 = 2.6 ∼ 3.3 at T = 486 MeV at the LHC. These results are quantitatively consistent with JET Collaboration. We also extract theq values for Pb+Pb collisions at √ s NN = 5.02 TeV and Xe+Xe collisions at √ s NN = 5.44 TeV using the single hadron nuclear modification data, and predict the nuclear modification factors for dihadron productions for these collisions.
Our paper is organized as follows. In Sec. II, we briefly introduce our framework to study the productions of single hadrons and dihadrons at high transverse momenta in proton-proton and nucleus-nucleus collisions. In Sec. III, arXiv:1901.04155v1 [hep-ph] 14 Jan 2019 we perform a global χ 2 analysis and extract jet quenching parameterq from the nuclear modification data on single hadron and dihadron productions at RHIC and the LHC. We also provide our predictions for the nuclear modification factors of dihadron productions in central and non-central Pb+Pb collisions at √ s NN = 5.02 TeV and Xe+Xe collisions at √ s NN = 5.44 TeV at the LHC.
Sec. IV contains our summary.

II. FRAMEWORK
In high-energy proton-proton collisions, the production cross section of high transverse momentum hadrons can be factorized into a convolution of parton distribution functions (PDFs), the cross section of hard partonic scatterings, and fragmentation functions (FFs), Here, f a (x a , µ 2 ) and f b (x b , µ 2 ) are parton distribution functions which we take from CT14 [43]; D h c (z c , µ 2 ) is fragmentation function which we take from Refs. [44,45]; dσ ab→cd /dt is the tree-level 2 → 2 partonic scattering cross section. The NLO correction at O(α 3 s ) contains 2 → 2 virtual diagrams and 2 → 3 tree diagrams, and has been included in our calculation. It has been shown in Ref. [8] that NLO perturbative QCD calculation for single π 0 production in proton-proton collisions agrees well with the experimental data at RHIC.
Similarly, the production cross section for high transverse momentum dihadrons in high-energy proton-proton collisions can be written as, where the phase space is dP S = dy h1 d 2 p h1 T dy h2 d 2 p h2 T . In relativistic nucleus-nucleus collisions, one has to consider both cold nuclear matter effect in the initial state and hot nuclear matter effect in the final state. The yield of single hadron production at high transverse momentum may be obtained as [8,46], Similarly, the yield of dihadron production at high transverse momentum in nucleus-nucleus collisions may be calculated as [8,46,47] dN h1h2 In the above two equations, t A ( r) is the nuclear thickness function, normalized as d 2 rt A ( r) = A, with A the mass number of the nucleus. Here we use the Woods-Saxon form for the nuclear density distribution. f a/A (x a , µ 2 , r) is the nuclear modified PDF, which we calculate as follows [48,49]: where Z is the proton number of the nucleus. Here, S a/A (x a , µ 2 , r) is called the nuclear shadowing factor and denotes the nuclear modification to the PDF in a free proton f a/p (x a , µ 2 ). The shadowing factor S a/A (x a , µ 2 , r) is calculated using the following form [50,51], where S a/A (x a , µ 2 ) is taken from the EPPS16 [52]. D h c (z c , ∆E c ) is the medium-modified fragmentation function and is calcualted as follows [8,45,46]: where ∆E c is the energy loss of parton c, and N g is the average number of gluons radiated by parton c. In this work, we use the higher twist formalism [53][54][55] to calculate medium-induced gluon radiation and parton energy loss. For a quark with initial energy E, the total energy loss ∆E can be calculated as, where C A = 3, and l T is the transverse momentum of radiated gluon. We assume the energy loss of a gluon is simply 9/4 times that of a quark [53]. The average number of radiated gluons from the propagating hard parton is calculated as [56], The parton energy loss is controlled by jet transport parameterq [22], for which we take the following form: where T is the local temperature of the medium, T 0 is a reference temperature which is usually taken as the temperature at the center of the medium at the hydrodynamics initial time τ 0 = 0.6 fm in central nucleus-nucleus collisions, and u µ is the four flow velocity of the fluid. In our calculation, the dynamical evolution of the QGP medium is obtained using the OSU (2+1)-dimensional viscous hydrodynamics model (VISH2+1) [57][58][59][60].

III. NUMERICAL RESULTS
In this section, we present our numerical results for single hadron and dihadron nuclear modification factors in The nuclear modification factor R AA for single hadron production in heavy-ion collisions is defined as [45], where is the overlap function of two colliding nuclei and the average in the equation is taken for a given centrality class. As for dihadron production at high transverse momentum in heavy-ion collisions, the nuclear modification factor I AA can be defined either as a function of p assoc T or as a function of z T = p assoc , where D AA (z T ) = p trig T D AA (p assoc T ) is called hadrontriggered fragmentation function [61], AA /dy trig dp trig T dy assoc dp assoc T T AA dσ h1 AA /dy trig dp trig T .(13) pared with the experimental data taken from PHENIX [31,32] and STAR [34] Collaborations. In each plot, different lines represent our model calculations for R AA or I AA using different values of jet quenching parameterq 0 . The solid line in the middle denotes the result using the best value ofq 0 obtained from our global χ 2 analysis, which is shown in Fig. 2. In the figure, we also show f as a function ofq 0 using only R AA data or only I AA data. We can see that two fitting results are consistent with each other. This means that with the similar value ofq 0 , both single hadron and dihadron nuclear suppression factors can be described consistently within our jet energy loss model. Our global χ 2 analysis renders: q 0 = 1.1 ∼ 1.2 GeV 2 /fm at T 0 = 378 MeV. In terms of the scaled dimensionless jet quenching parameter, it reads,q/T 3 = 4.1 ∼ 4.4 at T = 378 MeV. These values are consistent with the results obtained by JET Collaboration [6].
To test the goodness of our approach, we use the samê q 0 value obtained above to calculate the nuclear modifi-  We also test our approach by using the sameq 0 value obtained above to calculate the nuclear modification factors R AA and I AA in the non-central (50 − 60%) Pb+Pb collision at √ s NN = 2.76 TeV. The result is shown in Fig. 6: the solid lines in the middle denote the results using the bestq 0 value (i.e.,q 0 = 1.6 GeV 2 /fm at T 0 = 486 MeV), while the other two lines (usingq 0 = 1.5 and 1.9 GeV 2 /fm) represent the uncertainty for our extractedq 0 value. We can see that with the sameq 0 value, TeV compared with ALICE [35] and CMS [36,42] data.
our jet energy loss model can also describe the experimental data on single and dihadron nuclear modification in non-central Pb+Pb collisions at √ s NN = 2.76 TeV. Another interesting result is that for both Au+Au collisions at RHIC and Pb+Pb collision at the LHC, the nuclear modification factors I AA for dihadron productions are typically larger than single hadron suppression factors R AA given the same nucleus-nucleus collision conditions. One of the main reasons for such difference is the dominance of tangential emissions in dijet (dihadron) events, as has been been pointed out in Ref. [8]. terms of the scaled jet quenching parameterq/T 3 : One can see that the scaled jet quenching parameter q/T 3 has some temperature dependence: it decreases as one increase the temperature, which may be understood as decreasing jet-medium interaction strength at higher temperature regimes. For better visualization, we also plot the above values in Fig. 9, where the results from JET Collaboration onq/T 3 for Au+Au collisions at √ s NN = 0.2 TeV and Pb+Pb collisions at √ s NN = 2.76 TeV are also shown. We can see that our extracted values for the scaled jet quenching parameter q/T 3 are consistent with the JET Collaboration results.

IV. SUMMARY
In this work, we have studied the nuclear suppressions of single hadron and dihadron productions at high transverse momentum regimes in high-energy heavy-ion collisions at RHIC and the LHC. We compute the cross section of single hadron and dihadron productions in relativistic nuclear collisions based on the NLO perturbative QCD framework. For hadron production in heavy-ion collisions, we include both initial-state cold nuclear matter effect and final-state hot nuclear matter effect. The effect of jet energy loss in hot QGP medium is taken into account using medium-modified fragmentation functions, which are calculated based on the higher-twist formalism. The numerical results from our jet energy loss model calculations show consistent descriptions of the nuclear modifications of single hadron and dihadron productions in central and non-central nucleus-nucleus collisions at RHIC and the LHC.
We have further performed a detailed χ 2 analysis by comparing our jet energy loss model calculations with the experimental data on single hadron and dihadron have used single hadron R AA data to extract theq values. These extracted values are then used to predict the nuclear modification effects in dihadron productions in these collisions. Our work provides an important contribution to our quantitative extraction of the temperature dependence of jet quenching parameter by using multiple jet quenching observables from different collision systems and energies, and is helpful to achieve a consistent understanding of jet quenching in relativistic heavy-ion collisions.