Heavy flavour Langevin diffusion with the chromo-electromagnetic field fluctuations in the quark-gluon plasma

The chromo-electromagnetic field is produced due to the motion of partons in a quark-gluon plasma created by relativistic heavy-ion collisions. The fluctuations in the produced chromo-electromagnetic field are important, since they cause heavy quarks to gain energy in the low velocity limit. We study the effect of such fluctuations on heavy quark diffusion in quark-gluon plasma within the framework of Langevin dynamics under the background matter described by the ($3+1$)-dimensional relativistic viscous hydrodynamics. Theoretical calculations of the nuclear modification factor ($R_{AA}$) of heavy mesons ($D$ and $B$ mesons), with the effect of these fluctuations, are compared with experimental measurements in $Au-Au$ collisions at $\sqrt{s_{NN}} = 200$ GeV by the STAR experiment at the BNL Relativistic Heavy Ion Collider (RHIC) and $Pb-Pb$ collisions at $\sqrt{s_{NN}} = 2.76$ and $5.02$ TeV by the ALICE and CMS experiments at the CERN Large Hadron Collider (LHC). We find a significant effect of these fluctuations in describing the the measured $R_{AA}$ of $D$ and $B$ mesons in both RHIC and LHC energies.