Diffusion of heavy quark in strong magnetic field: perturbative vs non-perturbative

Abstract

Heavy Quark (HQ) serves as an excellent probe to understand perturbative as well as non-perturbative aspects of hot deconfined medium of light quarks and gluons. Additionally, the existence of a strong magnetic field in non-central Heavy Ion Collisions (HICs) might play a crucial role in controlling the dynamics of HQ transport in the hot QCD medium produced as a result of the HICs. It would be intriguing to explore the effect of the magnetic field on the perturbative and non-perturbative transport coefficients of HQ. This solicits a comprehensive theoretical framework accommodating the non-perturbative Quantum Chromo Dynamics(npQCD) description alongside perturbative QCD(pQCD). The present work provides such a formulation in which HQ-anti quark potential in the hot and magnetic QCD medium is implemented as an effective gluon propagator to calculate the rate of elastic scattering between HQ and the light quarks and gluons inside a medium of hot Quark Gluon Plasma(QGP) in the presence of a strong but uniform magnetic field. Diffusion coefficients of a charm quark have been computed for a short-range Yukawa potential ( pQCD) as well as a long-range confining potential (npQCD) for the scenarios where the velocity of the charm quark is parallel and perpendicular to the magnetic field respectively. Non-perturbative contribution is seen to dominate over the perturbative one in the regime of low temperatures and low momenta of charm quark. As the momentum of charm quark as well as the temperature of the medium increase pQCD starts to catch up with npQCD finally taking a complete hold at higher temperatures and charm momenta.