Heavy flavor puzzle from data measured at the BNL Relativistic Heavy Ion Collider: Analysis of the underlying effects

Suppressions of light- and heavy-flavor observables are considered to be excellent probes of QCD matter created in ultrarelativistic heavy ion collisions. Suppression predictions of quark and gluon jets appear to suggest a clear hierarchy according to which neutral pions should be more suppressed than $D$ mesons, which in turn should be more suppressed than single electrons. However, joint comparison of neutral pion (light probe) and nonphotonic single-electron (heavy probe) suppression data at the BNL Relativistic Heavy Ion Collider (RHIC) unexpectedly showed similar jet suppression for these two probes, which presents the well-known heavy-flavor puzzle at RHIC. We here analyze which effects are responsible for this unexpected result by using the dynamical energy-loss formalism. We find that the main effect is a surprising reversal in the suppression hierarchy between neutral pions and $D$ mesons, which is due to the deformation of the suppression patterns of light partons by fragmentation functions. Furthermore, we find that, due to the decay functions, the single-electron suppression approaches the $D$-meson suppression. Consequently, we propose that these two effects, taken together, provide a clear intuitive explanation of this longstanding puzzle.

Figure 1

Parton suppression and contribution to pions and single electrons. Momentum dependence of the jet suppression is shown in the left panel, for charm quarks (dashed curve), bottom quarks (dot-dashed curve), light quarks (full curve), and gluons (dotted curve). Electric to magnetic mass ratio is fixed to ${\mu }_M/{\mu }_E=0.4$. The central panel of the figure shows the gluon to light quark contribution ratio in the initial distributions of charged hadrons. The right panel of the figure shows the charm to bottom quark ratio in the initial distributions of nonphotonic single electrons. The suppression predictions and the parton contributions are computed according to the numerical procedure described in Ref. [6] and outlined in the numerical framework section.

Figure 2

The heavy-flavor puzzle at RHIC. The figure shows together the experimentally measured 0%–10% central 200 GeV RHIC $R_{AA}$ data for neutral pions (open red squares from STAR [7] and open blue squares from PHENIX [8]) and nonphotonic single electrons (full red circles from STAR [9] and full blue circles from PHENIX [10]). Shaded areas represent systematic error bars, while lines represent statistic error bars.

Figure 3

Comparison of pion and $D$-meson suppression predictions. The figure shows the comparison of neutral-pion suppression predictions (light-gray band) with $D$-meson (dark-gray band) suppression predictions, as a function of momentum. Gray regions correspond to $0.4<{\mu }_M/{\mu }_E<0.6$, where the upper (lower) boundary on each band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$.

Figure 4

Comparison of the light-flavor suppression predictions. The left panel shows the comparison of neutral-pion suppression predictions (full curve) with light-quark (the dashed curve) and gluon (the dot-dashed curve) suppression predictions, as a function of momentum. On the right panel, the dashed curve shows what would be the neutral-pion suppression if only light quarks contributed to pions. The dot-dashed curve shows what would be the neutral-pion suppression if only gluons contributed to pions, while the full curve shows the actual neutral-pion suppression predictions. In each panel, the electric to magnetic mass ratio is fixed at ${\mu }_M/{\mu }_E=0.4$.

Figure 5

Comparison of single-electron with $D$- and $B$-meson suppression predictions. The left panel shows the comparison of nonphotonic single-electron suppression predictions (dark-gray band with full curve boundaries) with $D$-meson (light-gray band with dashed curve boundaries) and $B$-meson (light-gray band with dot-dashed curve boundaries) suppression predictions, as a function of momentum. The right panel shows the comparison of nonphotonic single-electron suppression predictions (dark-gray band with full curve boundaries) with single-electron suppression from $D$ mesons (light-gray band with dashed curve boundaries) and single-electron suppression from $B$ mesons (light-gray band with dot-dashed curve boundaries), as a function of momentum. Gray regions correspond to $0.4<{\mu }_M/{\mu }_E<0.6$, where the upper (lower) boundary on each band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$.

Figure 6

Comparison of neutral-pion and single-electron suppression predictions with experimental data. The left panel shows the comparison of neutral-pion suppression predictions (light-gray band) with nonphotonic single-electron suppression predictions (dark-gray band). The central panel compares theoretical predictions for neutral pions (light-gray band) with available pion $R_{AA}$ data at 0%–10% central 200 GeV RHIC (open red squares from STAR [7] and open blue squares from PHENIX [8]). The right panel compares theoretical predictions for single electrons (dark-gray band) with the available RHIC single electron $R_{AA}$ data (full red circles from STAR [9] and full blue circles from PHENIX [10]). Gray regions correspond to $0.4<{\mu }_M/{\mu }_E<0.6$, where the upper (lower) boundary on each band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$.