Non-perturbative diffusion of Heavy Quark moving in a hot and magnetised Quark Gluon Plasma

Abstract: Heavy Quarks (HQs) serve as excellent probes to understand various characteristics of deconfined hot QCD medium, comprising light quarks and gluons, created in the Heavy Ion Collisions (HICs). Strong magnetic fields in non-central HICs may significantly affect HQ dynamics in this medium. Exploring the impact of the magnetic field on the perturbative and non-perturbative transport coefficients of HQ is an intriguing endeavor. This necessitates the development of 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 Quarkonium potential in the hot and magnetic QCD medium is implemented as the effective gluon propagator to calculate the rate of elastic scattering between HQ and the light partons 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/non-perturbative potential (npQCD) for two cases in which 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 to intermediate momenta of charm quark. As the momentum of charm quark as well as the temperature of the medium increase pQCD starts to gain on the npQCD contribution, ultimately prevailing at higher temperatures and charm momenta.