Empirical determination of the energy loss of heavy quarks in nuclear collisions at RHIC and LHC energies

Heavy quarks produced in the heavy ion collisions loose energy while propagting in the hot partonic matter which finally fragment to heavy ($D$ or $B$) mesons. The energy loss suffered by the heavy quarks is imprinted in the nuclear modification factor as a function of transverse momenta ($p_T$) of these heavy mesons. An alternate measure of in-medium energy loss comes through the effective shift in transverse momentum spectra of hadrons recorded in nucleus-nucleus collisions when it is compared to the same in proton-proton collisions. We start by parametrizing invariant momentum yields of heavy mesons in p+p collisions. The fit function from p+p collisions and measured nuclear modification factor in heavy ion collisions are then utilised to obtain the shift in the transeverse mass $\Delta m_T$ of heavy mesons produced at the RHIC and LHC experiments.The energy loss $\Delta m_T$ so obtained is found to scale with the transverse mass ($m_T$) of heavy mesons through a power law at different energies and centralities of collisions. We have also calculated using theoretical formalism, the total energy loss suffered by a charm quark in quark-gluon plasma produced in Pb~+~Pb collisions at the LHC energies. The evolution of the plasma is described by (2+1) dimensional longitudinal boost-invariant ideal hydrodynamics. It is found that the total energy loss of charm quarks scales with the transverse mass of charm quarks through a similar power law which supports our empirical analysis of energy loss.