Energy Loss of a Heavy Quark Produced in a Finite Size Medium

Abstract

We study the medium-induced energy loss $-\Delta E_0(L_p)$ suffered by a heavy quark produced at initial time in a quark-gluon plasma, and escaping the plasma after travelling the distance $L_p$. The heavy quark is treated classically, and within the same framework $-\Delta E_0(L_p)$ consistently includes: the loss from standard collisional processes, initial bremsstrahlung due to the sudden acceleration of the quark, and transition radiation. The radiative loss {\it induced by rescatterings} $-\Delta E_{rad}(L_p)$ is not included in our study. For a ultrarelativistic heavy quark with momentum $p\text{gsim}10\mathrm{GeV}$, and for a finite plasma with $L_p\text{lsim}5\mathrm{fm}$, the loss $-\Delta E_0(L_p)$ is strongly suppressed compared to the stationary collisional contribution $-\Delta E_{coll}(L_p)\propto L_p$. Our results support that $-\Delta E_{rad}$ is the dominant contribution to the heavy quark energy loss (at least for $L_p\text{lsim}5\mathrm{fm}$), as indeed assumed in most of jet-quenching analyses. However they might raise some question concerning the RHIC data on large $p_{\perp }$ electron spectra.

Comments: 18 pages, 3 figures. New version clarified and simplified. A critical discussion added in section 2, and previous sections 3 and 4 have been merged together. Main results are unchanged