Effect of the chromo-electromagnetic field fluctuations on heavy quark propagation in a deconfined hadronic medium at energies available at the CERN Large Hadron Collider

We consider the effect of the chromo-electromagnetic field fluctuations in addition to the collisional as well as the radiative energy losses suffered by heavy quarks while propagating through the hot and dense deconfined medium of quarks and gluons created in relativistic heavy ion collisions. The chromo-electromagnetic field fluctuations play an important role as they lead to an energy gain of heavy quarks of all momenta and are significant at low momentum. We include the effect of these fluctuations, for the first time, while computing the nuclear modification factor ($R_{AA}$) of heavy mesons, viz., $D$ mesons and $B$ mesons, and compare with the experimental measurements in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ and $5.02$ TeV by the CMS and ALICE experiments at the CERN Large Hadron Collider. Our results are found to be in very good agreement with the measurements.

Figure 1

The energy loss of a charm quark inside the QGP medium as a function of its momentum, obtained using PP [19], AJMS [31], and fluctuation [30] methods.

Figure 2

The energy loss of a bottom quark inside the QGP medium as a function of its momentum, obtained using PP [19], AJMS [31], and fluctuation [30] methods.

Figure 3

Fractional energy loss of a charm quark inside the QGP due to fluctuations, collisions (PP), and radiation (AJMS) as a function of its momentum. The path length considered here is $L=5$ fm.

Figure 4

Fractional energy loss of a bottom quark inside the QGP due to fluctuations, collisions (PP), and radiation (AJMS) as a function of its momentum. The path length considered here is $L=5$ fm.

Figure 5

The nuclear modification factor $R_{AA}$ of $D^0$ mesons with collisional (PP) and radiative (AJMS) energy loss along with the effect of fluctuations as a function of transverse momentum $p_T$ for $\left(0\text{–}10\right)\%$ centrality in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The experimental data are taken from measurements by the ALICE [50] and CMS experiments [51].

Figure 6

The nuclear modification factor $R_{AA}$ of $D^0$ mesons with collisional (PP) and radiative (AJMS) energy loss along with the effect of fluctuations as a function of transverse momentum $p_T$ for $\left(0\text{–}100\right)\%$ centrality in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The experimental data are taken from measurements by the CMS experiment [51].

Figure 7

The nuclear modification factor $R_{AA}$ of $D^0$ mesons with collisional (PP) and radiative (AJMS) energy loss along with the effect of field fluctuations as a function of transverse momentum $p_T$ for $\left(0\text{–}100\right)\%$ centrality in Pb-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. The experimental data are taken from measurements by the CMS experiment [52].

Figure 8

The nuclear modification factor $R_{AA}$ of $B^{+}$ mesons with collisional (PP) and radiative (AJMS) energy loss along with the effect of field fluctuations as a function of transverse momentum $p_T$ for $\left(0\text{–}100\right)\%$ centrality in Pb-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. The experimental data are taken from measurements by the CMS experiment [53].