Extracting the jet transport coefficient from jet quenching in high-energy heavy-ion collisions

Within five different approaches to parton propagation and energy loss in dense matter, a phenomenological study of experimental data on suppression of large-$p_T$ single inclusive hadrons in heavy-ion collisions at both the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) was carried out. The evolution of bulk medium used in the study for parton propagation was given by 2 + 1 dimensional or 3 + 1 dimensional hydrodynamic models which are also constrained by experimental data on bulk hadron spectra. Values for the jet transport parameter $\widehat{q}$ at the center of the most central heavy-ion collisions are extracted or calculated within each model, with parameters for the medium properties that are constrained by experimental data on the hadron suppression factor $R_{AA}$. For a quark with initial energy of 10 GeV we find that $\widehat{q}\approx 1.2\pm 0.3$ GeV${}^2$/fm at an initial time ${\tau }_0=0.6$ fm/$c$ in Au + Au collisions at $\sqrt{s}=200$ GeV/n and $\widehat{q}\approx 1.9\pm 0.7$ GeV${}^2$/fm in Pb + Pb collisions at $\sqrt{s}=2.76$ TeV/n. Compared to earlier studies, these represent significant convergence on values of the extracted jet transport parameter due to new constraints provided by recent experiment data from the LHC.

Figure 1

cujet2.0 [76] results for the nuclear modification factor at midrapidity for neutral pion spectra in 0–5% central Au + Au collisions at $\sqrt{s}=200$ GeV/n (upper panel) and for charged hadrons in Pb + Pb collisions at $\sqrt{s}=2.76$ TeV/n (lower panel) with a range of values of frozen strong coupling constant ${\alpha }_{\max }$, as compared to PHENIX data [77, 78] at RHIC and ALICE [27] and CMS data [26] at LHC.

Figure 2

The ${\chi }^2$/d.o.f. as a function of the model parameter ${\alpha }_{\max }$ from fitting to the PHENIX data [77, 78] (combined 2008 and 2012 data set) at RHIC and combined ALICE [27] and CMS [26] data at LHC by the cujet2.0 [76] model calculation of the nuclear suppression factor $R_{AA}\left(p_T\right)$ as shown in Fig. 1.

Figure 3

ht-bw results for the nuclear modification factor at mid-rapidity for neutral pion spectra in $0-5\%$ central Au + Au collisions at $\sqrt{s}=200$ GeV/n (upper panel) and charged hadron spectra in 0–5% central Pb + Pb collisions at $\sqrt{s}=2.76$ TeV/n (lower panel) with a range of values of initial quark jet transport parameter ${\widehat{q}}_0$ at ${\tau }_0=0.6$ fm/$c$ in the center of the most central collisions, as compared to PHENIX data [77, 78] at RHIC and ALICE [27] and CMS data [26] at LHC.

Figure 4

The ${\chi }^2$/d.o.f. as function of the initial quark jet transport parameter ${\widehat{q}}_0$ from fitting to the PHENIX data [77, 78] (combined 2008 and 2012 data set) at RHIC for $p_T>5$ GeV/$c$ and combined ALICE [27] and CMS [26] data at LHC for $p_T>15$ GeV/$c$ by the ht-bw model calculation of the nuclear suppression factor $R_{AA}\left(p_T\right)$ as shown in Fig. 3.

Figure 5

ht-m results for the nuclear modification factor at mid-rapidity for neutral pion spectra in 0–5% central Au + Au collisions at $\sqrt{s}=200$ GeV/n (upper panel) and charged hadron spectra in 0–5% central Pb + Pb collisions at $\sqrt{s}=2.76$ TeV/n (lower panel) with a range of values of initial gluon jet transport parameter ${\widehat{q}}_0$ (at ${\tau }_0=0.6$ fm/$c$) in the center of the most central collisions, as compared to PHENIX data [77, 78] at RHIC and ALICE [27] and CMS data [26] at LHC.

Figure 6

The ${\chi }^2$/d.o.f. as function of the initial gluon jet transport parameter ${\widehat{q}}_0$ from fitting to the PHENIX data [77, 78] (combined 2008 and 2012 data set) at RHIC and combined ALICE [27] and CMS [26] data at LHC by the ht-m model calculation of the nuclear suppression factor $R_{AA}\left(p_T\right)$ as shown in Fig. 5.

Figure 7

The nuclear modification factors for the central Au + Au collisions at RHIC (upper panel) (from Ref. [55]) and Pb-Pb collisions at the LHC (lower panel) from the martini model as compared to PHENIX data [77, 78] at RHIC and combined ALICE [27] and CMS [26] data at LHC. The bulk medium space-time profile is given by 3 + 1 dimensional simulations by Nonaka and Bass [65] for Au + Au collisions at RHIC and by the music 3 + 1D ideal hydrodynamics calculation [66] for Pb + Pb at LHC.

Figure 8

The nuclear modification factors $R_{AA}$ from mcgill-amy model as a function of $p_T$ for neutral pions in 0–5% Au + Au collisions at RHIC (upper panel) and charged hadrons in 0–5% central Pb + Pb collisions at LHC (lower panel). Experimental data are taken from PHENIX experiment [77, 78] at RHIC and CMS [26] and ALICE experiment [27] at LHC. For difference curves from the top to the bottom, the values of ${\alpha }_s$ are from 0.23 to 0.31 at RHIC and from 0.19 to 0.27 at the LHC with an increment of 0.1.

Figure 9

The ${\chi }^2$/d.o.f. as a function of ${\alpha }_s$ from fitting to the PHENIX data [77, 78] (combined 2008 and 2012 data set) at RHIC (solid) and combined ALICE [27] and CMS [26] data at LHC (dashed) by the mcgill-amy model calculation of the nuclear suppression factor $R_{AA}\left(p_T\right)$ as shown in Fig. 8.

Figure 10

The assumed temperature dependence of the scaled jet transport parameter $\widehat{q}/T^3$ in different jet quenching models for an initial quark jet with energy $E=10$ GeV. Values of $\widehat{q}$ at the center of the most central $A+A$ collisions at an initial time ${\tau }_0=0.6$ fm/$c$ in ht-bw and ht-m models are extracted from fitting to experimental data on hadron suppression factor $R_{AA}$ at both RHIC and LHC. In glv-cujet, martini, and mcgill-amy models, it is calculated within the corresponding model with parameters constrained by experimental data at RHIC and LHC. Errors from the fits are indicated by filled boxes at three separate temperatures at RHIC and LHC, respectively. The arrows indicate the range of temperatures at the center of the most central $A+A$ collisions. The triangle indicates the value of ${\widehat{q}}_N/T_{\mathrm{eff}}^3$ in cold nuclei from DIS experiments.

Figure 11

Values of scaled jet transport parameter $\widehat{q}/T^3$ for an initial quark jet with energy $E=10$ GeV at the center of the most central $A+A$ collisions at an initial time ${\tau }_0=0.6$ fm/$c$ constrained by experimental data on hadron suppression factor $R_{AA}$ at both RHIC and LHC. The dashed boxes indicate expected values in $A+A$ collisions at $\sqrt{s}=0.063$, 0.130, and 5.5 TeV/n, assuming the initial entropy is proportional to the final measured charged hadron rapidity density [85]. The triangle indicates the value of ${\widehat{q}}_N/T_{\mathrm{eff}}^3$ in cold nuclei from DIS experiments. Values of ${\widehat{q}}_{\mathrm{SYM}}^{\mathrm{NLO}}/T^3$ from NLO SYM theory are indicated by two arrows on the right axis.