Medium-Induced Gluon Radiation off Massive Quarks Fills the Dead Cone

TL;DR

Problem: quantify how a massive quark's passage through dense QCD matter modifies medium-induced gluon radiation and energy loss. Approach: develop a path-integral formalism and analyze both opacity expansion and dipole (multiple soft scattering) limits to obtain the double-differential spectrum as a function of ω and k⊥, for finite m/E, L and density. Findings: medium-induced radiation generally fills the dead cone but the high-ω tail is depleted for massive quarks, resulting in reduced average energy loss; finite-energy kinematics can complicate the trend, and complete charm suppression is not ruled out but not required by the data. Implications: mass-dependent jet quenching should influence open charm and D-meson to pion ratios in RHIC/LHC, motivating more precise measurements and finite-energy treatments for robust phenomenology.

Abstract

We calculate the transverse momentum dependence of the medium-induced gluon energy distribution radiated off massive quarks in spatially extended QCD matter. In the absence of a medium, the distribution shows a characteristic mass-dependent depletion of the gluon radiation for angles smaller than m/E, the so-called dead cone effect. Medium-modifications of this spectrum are calculated as a function of quark mass, initial quark energy, in-medium pathlength and density. Generically, medium-induced gluon radiation is found to fill the dead cone, but it is reduced at large gluon energies compared to the radiation off light quarks. We quantify the resulting mass-dependence for momentum-averaged quantities (gluon energy distribution and average parton energy loss), compare it to simple approximation schemes and discuss its observable consequences for nucleus-nucleus collisions at RHIC and LHC. In particular, our analysis does not favor the complete disappearance of energy loss effects from leading open charm spectra at RHIC.

Figures (9)

• Figure 1: The medium-induced gluon energy distribution as a function of the transverse momentum $\bar{\kappa}^2 = {\bf k}_\perp^2/\mu^2$ and for different values of $\bar{\gamma} = \bar{\omega}_c/\omega$. Different curves correspond to the full medium-induced gluon distribution (\ref{['3.14']}) for a mass to energy ratio 0.03 of the heavy quark (solid line), the massless limit (\ref{['3.17']}) of this spectrum (dotted line), and its dead cone approximation (\ref{['3.18']}) (dashed line).
• Figure 2: Same as Fig. \ref{['fig1']} but for the larger mass to energy ratios $\frac{m}{E} = 0.1$ and $\frac{m}{E} = 0.3$.
• Figure 3: The medium-induced gluon energy distribution (\ref{['3.15']}) calculated from the full expression (\ref{['3.14']}) for a massive quark (solid line), from the massless limit (\ref{['3.17']}) (dotted line), from the dead-cone approximation (\ref{['3.18']}) (dashed line) and from the average dead cone factor (\ref{['3.19']}) multiplied by the massless spectrum (dash-dotted line).
• Figure 4: The average medium-induced parton energy loss (\ref{['3.16']}) for massive quarks, normalized to the massless limit, for different values of the density parameter $\bar{R} = \bar{\omega}_c\, L$. Curves are calculated for the full medium-induced radiation (\ref{['3.14']}) off massive quarks (solid lines), the dead cone approximation (\ref{['3.18']}) (dashed lines) and the corresponding expression with averaged dead cone (\ref{['3.19']}) (dash-dotted lines).
• Figure 5: For finite quark energy $E$, the normalized average energy loss (rhs) depends significantly on the kinematic boundary up to which the gluon energy distribution (lhs) is integrated. This entails significant uncertainties, which are discussed in the text. Parameter values are taken from Ref. Djordjevic:2003zk.