Abstract
We calculate the jet quenching parameter in medium with chemical potential from AdS/CFT correspondence. Our result is summarized in a plot. Moreover, we extract the explicit form of the jet quenching parameter of medium with small chemical potential for phases of dual SYM corresponding to large and small black holes. For the former phase, the jet quenching is increased as the charge density increases, however, for the latter it is the opposite though the background is thermodynamically unstable.
Highlights
The recent experiments in Relativistic Heavy Ion Collider (RHIC) produce the strongly interacting ‘quark gluon plasma’, which can be described by hydrodynamical expansion of radial and elliptical flow [1]
In the past few years, a lot of works have been done to calculate the hydrodynamical quantities, and one of the most important progress is the discovery of the universal bound of the viscosity to entropy density ratio [5, 6, 7, 8, 9], which is checked in the case of no-zero chemical potential in [10, 11, 13, 14]
We find that the phases of the gauge theory dual to large and small black holes have opposite charge dependence, especially, the result for the latter is out of expectation as the jet quenching decreases as the charge increases
Summary
The recent experiments in Relativistic Heavy Ion Collider (RHIC) produce the strongly interacting ‘quark gluon plasma’, which can be described by hydrodynamical expansion of radial and elliptical flow [1]. To study the RHIC phenomenology requires the theoretical tool to calculate the dynamical process such as the diffusion constants, viscosity or jet quenching parameter in this strongly interacting plasma Since these physical quantities characterizes the dynamical process, it is hard to calculate them in lattice QCD which is formulated in Euclidean phase and more suitable in describing the thermal equilibrium process. Though there is no definitely conserved baryon number symmetry in SYM theory as in QCD, the R-symmetry plays the similar role In this short note, we will use the AdS/CFT duality and follow the method of [19] to calculate the jet quenching parameter in a medium with nonzero chemical potential which is conjugated to the R-charge density. The explicit form of the jet quenching parameter in some limiting cases is derived
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