Predictions of heavy-flavor suppression at 5.1 TeV Pb + Pb collisions at the CERN Large Hadron Collider

High momentum hadron suppression is considered to be an excellent probe of jet-medium interactions in QCD matter created in ultrarelativistic heavy ion collisions. We previously showed that our dynamical energy loss formalism can accurately explain suppression measurements at 200 GeV Au + Au collisions at the Relativistic Heavy Ion Collider (RHIC) and 2.76 TeV Pb + Pb collisions at the CERN Large Hadron Collider (LHC). With the upcoming LHC measurements at notably higher collision energies, there is a question of what differences, with respect to the current (2.76 TeV) measurements, can be expected. In this paper we concentrate on heavy flavor suppression at the upcoming 5.1 TeV Pb + Pb collisions energy at the LHC. Naively, one would expect a notably $\left(\sim 30\%\right)$ larger suppression at 5.1 TeV collision energy, due to estimated (significant) energy loss increase when transitioning from 2.76 to 5.1 TeV. Surprisingly, more detailed calculations predict nearly the same suppression results at these two energies. We show that this unexpected result is due to an interplay of the following two effects, which essentially cancel each other: (i) flattening of the initial charm and bottom momentum distributions with increasing collision energies, and (ii) significantly slower than naively expected increase in the energy loss. Therefore, the obtained theoretical predictions, which suggest nearly the same heavy flavor suppression at 2.76 and 5.1 TeV, provide a clear (qualitative and quantitative) test of our energy loss formalism.

Figure 1

Comparison of $R_{AA}$ predictions for heavy flavor at 2.76 and 5.1 TeV. $D$ mesons and nonprompt $J/\psi$ suppression predictions, as a function of transverse momentum, are shown in panels (a) and (b), respectively. Full (dashed) curves correspond to $R_{AA}$ predictions at 5.1 TeV (2.76 TeV) Pb + Pb collisions at the LHC. In each panel, the gray bands correspond to the finite magnetic mass case (i.e., $0.4<{\mu }_M/{\mu }_E<0.6$ [37, 38, 39, 40]), where the lower and the upper boundaries correspond, respectively, to ${\mu }_M/{\mu }_E=0.4$ and ${\mu }_M/{\mu }_E=0.6$.

Figure 2

Comparison of initial momentum distributions for charm and bottom at 2.76 and 5.1 TeV. Charm and bottom initial momentum distributions, as a function of transverse momentum, are shown in panels (a) and (b), respectively. In each panel, the full (dashed) curve corresponds to the momentum distribution at 5.1 TeV (2.76 TeV) Pb + Pb collisions at the LHC.

Figure 3

Relative increase in $R_{AA}$ between 2.76 and 5.1 TeV. Panel (a) shows momentum dependence of the relative increase in $R_{AA}$ between 2.76 and 5.1 TeV Pb + Pb collisions at the LHC due to differences in the initial momentum distributions; to calculate the relative increase in $R_{AA}$ due to different initial momentum distributions, the energy loss is kept fixed and calculated for the 2.76 TeV case, while the distributions are varied between 2.76 and 5.1 TeV. Panel (b) shows momentum dependence of the relative increase in $R_{AA}$ between 2.76 and 5.1 TeV collisions at the LHC due to differences in the energy loss; to calculate the relative increase in $R_{AA}$ due to different energy losses, the initial momentum distribution is kept fixed and calculated for the 2.76 TeV case, while the energy loss is varied between 2.76 and 5.1 TeV. In each panel, curves that correspond to charm and bottom are marked by c and b, respectively, and the magnetic mass is fixed to ${\mu }_M/{\mu }_E=0.4$.

Figure 4

Relative energy loss increase between 2.76 and 5.1 TeV. All the panels show the momentum dependence of the relative energy loss increase between 5.1 and 2.76 TeV Pb + Pb collisions at the LHC. Panels (a), (b), and (c) correspond, respectively, to the radiative, collisional, and total energy loss cases. In each panel curves that correspond to charm (bottom) are marked by letter c (b) and the magnetic mass is fixed to ${\mu }_M/{\mu }_E=0.4$. Dashed gray horizontal lines represent the energy loss increase if it would have linear, quadratic, or cubic temperature dependence.

Figure 5

Analysis of the heavy flavor suppression between 2.76 and 5.1 TeV. The full curves correspond to $R_{AA}\mathrm{s}$ with both the energy losses and the initial momentum distributions calculated at 5.1 TeV collision energy. The dashed curves correspond to $R_{AA}\mathrm{s}$ with both the energy losses and the initial momentum distributions calculated at 2.76 TeV collision energy. The dotted curves correspond to $R_{AA}\mathrm{s}$ where the energy losses are calculated at 2.76 TeV collision energy, while the distributions are calculated at 5.1 TeV collision energy. The upper (lower) panels correspond to the charm (bottom) quark. The left panels [(a) and (d)] show how the flatter distributions at 5.1 TeV lower the heavy flavor suppression compared to the 2.76 TeV case. The central panels [(b) and (e)] show how increase in the energy loss at 5.1 TeV increases the suppression compared to the 2.76 TeV case. The right panels [(c) and (f)] show how the above two effects cancel, so as to reproduce almost the same suppression at 2.76 and 5.1 TeV Pb + Pb collision energy. In each panel, lower (upper) set of curves corresponds to the magnetic-to-electric mass ratio of ${\mu }_M/{\mu }_E=0.4\left({\mu }_M/{\mu }_E=0.6\right)$.