The Effect of Hadronic Matter on Parton Energy Loss

TL;DR

This work extends the Jetscape framework by introducing reduced parton distributions near the QCD transition and including nuclear shadowing to extend parton energy loss into the hadronic phase. By coupling MATTER and LBT with a hadronic-phase extension (T_0=135 MeV) and a simple dispersion modification (multiplicative factor $1+a/T$), the authors obtain a more realistic description of both $R_{AA}$ and high-$p_T$ $v_2$ for jets and leading hadrons across centralities and collision energies. The approach yields a non-monotonic $igl( ext{$ ext{hat}{q}$}/T^3igr)$ behavior with temperature, aligns with lattice trends at intermediate temperatures, and improves agreement with data in peripheral events. The findings suggest a significant role for hadronic-phase interactions and shadowing in jet quenching and motivate future Bayesian calibration and inclusion of recombination and hadronic energy loss mechanisms to further sharpen the description.

Abstract

Modified thermal distributions (dispersion relations) are introduced within both the MATTER and LBT event generators used to describe jet modification in a heavy-ion collision, within the JETSCAPE framework. Hard partons, propagating through dense matter, scatter off the partonic substructure of the medium, leading to stimulated emission, accompanied by recoiling medium partons. We introduce a simple modification, a multiplicative $(1 + a/T)$ correction to the dispersion relation of quarks and gluons (equivalent to an effective fugacity). This leads to calculated transport coefficients (e.g. $\hat{q}/T^3$) showing the expected behavior of depreciating at lower temperatures, including within the hot hadronic gas. This simple modification recovers the light-like dispersion relations at high temperatures, and introduces an excess depreciation factor for parton populations at lower temperatures, allowing partonic energy loss and recoil calculations to be extended into the hadronic phase. This modified distribution, in combination with initial state cold nuclear matter effects (shadowing), is used to simultaneously describe the nuclear modification factor and elliptic anisotropy of jets and leading hadrons, over multiple centralities and collision energies.

Figures (12)

• Figure 1: Elastic scattering rates $\Gamma_{ab\rightarrow cd}$ for a gluon (top) and a quark or antiquark (bottom) as functions of projectile energy at fixed temperature $T=200\,\mathrm{MeV}$ (with $\alpha_s=0.3$). Solid curves show equilibrium rates; dark-red curves and Monte-Carlo points correspond to the modified recoil distribution of Eq. \ref{['eq:ModifiedDistribution']}.
• Figure 2: Elastic scattering rates $\Gamma_{ab\rightarrow cd}$ for a gluon (top) and a quark or antiquark (bottom) as functions of temperature at fixed projectile energy $E=100\,\mathrm{GeV}$ (with $\alpha_s=0.3$). Solid curves show total scattering rates of quark/gluon; dark-red curves and Monte-Carlo points correspond to the modified recoil distribution of Eq. \ref{['eq:ModifiedDistribution']}.
• Figure 3: Ratio of the jet transport coefficient $\hat{q}/T^3$ as a function of temperature $T$. The solid lines show the high-temperature hard-thermal-loop (HTL) limits for gluons (green) and quarks (blue) with a fixed coupling $\alpha_s = 0.3$. The dashed green and blue lines represent the corresponding gluon and quark estimates including a medium-modification factor with $a = 17~\mathrm{MeV}$, while keeping the coupling unchanged. The yellow and red dashed lines illustrate the effect of changing the coupling to $\alpha_s = 0.35$ and the modification parameter to $a = 25~\mathrm{MeV}$. The Monte Carlo performance of the model is shown by the circular blue(quark) and green(gluon) points.
• Figure 4: The jet transport parameter for an initial gluon (top) or quark (bottom) with different initial energies going through a single scattering (solid symbols) in a uniform and static QGP medium at different temperatures. Solid lines are analytic results for a single scattering within the small-angle approximation.
• Figure 5: Elastic energy loss per unit length a gluon(top) or a quark(bottom) in a uniform and static medium with a temperature $T = 200, 300$ and $400$ MeV as a function of the initial energy from simulations of a single scattering (solid symbols) as compared to analytic results (solid lines) with a small-angle approximation. The dashed lines are analytic estimates for the case without reduced distributions.