Mass tomography at different momentum ranges in quark-gluon plasma

We here show that at lower momentum (i.e., $p_{\perp }\sim 10\mathrm{GeV}$) single particle suppression for different types of probes exhibit a clear mass hierarchy, which is a direct consequence of the differences in the energy loss, rather than the differences in the initial distributions. On the other hand, we predict that the mass hierarchy is not expected at high momentum (i.e., $p_{\perp }\sim 100\mathrm{GeV}$); i.e., while we surprisingly predict that suppression for charged hadrons will be somewhat smaller than the suppression for heavy mesons, we find that this difference will be a consequence of fragmentation functions, not the finite mass effects. That is, apart from the fragmentation functions, the probes of different masses exhibit nearly the same suppression in the high momentum region. We also argue that the same insensitivity on the probe types also appears for jets. In particular, the experimental data in the momentum regions where they exist for both types of probes, show similar suppressions of charged hadrons and inclusive jet data. Interestingly, we also find that our state-of-the-art suppression predictions for high momentum single particles are also in agreement with the jet suppression data, where the reasons behind this agreement yet remain to be understood. Finally, the available jet data also show (though with large error bars) an overlap between b jets (heavy) and inclusive jets (light) probes. Consequently, our results suggest that single particles in the momentum region below 50 GeV present an excellent tool for mass tomography, while high momentum single particles and (possibly) jets are somewhat insensitive to the details of the interaction with quark-gluon plasma.

Figure 1

$R_{AA}$ vs $N_{\mathrm{part}}$ for single particles at the 2.76 TeV Pb+Pb collisions at the LHC experiments. (a) Theoretical predictions for $R_{AA}$ vs $N_{\mathrm{part}}$ are compared with CMS experimental data for D mesons [38] (red triangles) and nonprompt $J/\mathrm{\Psi }$ [39] (orange circles) in, respectively, $8<p_{\perp }<16\mathrm{GeV}$ and $6.5<p_{\perp }<30\mathrm{GeV}$ momentum regions. Gray bands with dashed, and dot-dashed boundaries, respectively, correspond to predictions for D mesons and nonprompt $J/\mathrm{\Psi }$ in corresponding momentum regions. (b) Theoretical predictions for $h^{\pm }$, and D and B mesons $R_{AA}$ vs $N_{\mathrm{part}}$ in $60<p_{\perp }<95\mathrm{GeV}$ momentum region are, respectively, provided as white bands with full, dashed, and dot-dashed boundaries. The $h^{\pm }$ predictions are compared with ATLAS (green squares) [40] $h^{\pm }$ experimental data in the same momentum region. On each panel, the upper (lower) boundary of each gray (or white) band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$.

Figure 2

Suppression contributions at lower momentum. (a) Theoretical predictions for $R_{AA}$ vs $N_{\mathrm{part}}$ are compared for D mesons (dashed curve, $8<p_{\perp }<16\mathrm{GeV}$ momentum region) and nonprompt $J/\mathrm{\Psi }$ (dot-dashed curve, $6.5<p_{\perp }<30\mathrm{GeV}$ momentum region). Gray curve shows the analogous nonprompt $J/\mathrm{\Psi }$ predictions, if the originating bottom quark would have the same energy loss as charm quark in QGP. (b) Theoretical predictions for $R_{AA}$ vs $N_{\mathrm{part}}$ are compared for D and B mesons in $8<p_{\perp }<16\mathrm{GeV}$ momentum region. Comparing (a) and (b) shows the effect of decay functions to the contributions analyzed in (a). (c) Theoretical predictions for $R_{AA}$ vs $p_{\perp }$ are compared for D and B mesons. In (b) and (c), the curve legend is the same as in (a) with distinction that now B replaces $J/\mathrm{\Psi }$. In each panel, the full arrow points to the contribution of the different initial distributions to the difference in the suppression between the D meson and nonprompt $J/\mathrm{\Psi }$ (or B meson), while the dashed arrow points to the contribution of the different energy losses to the difference between D-meson and the nonprompt $J/\mathrm{\Psi }$ (or B-meson) suppression. Magnetic-to-electric mass ratio is set to ${\mu }_M/{\mu }_E=0.4$.

Figure 3

$R_{AA}$ vs $p_{\perp }$ for single particles at the 5.02-TeV Pb+Pb 0%–10% central collisions at the LHC. (a) Theoretical predictions for $h^{\pm }$, and D and B mesons $R_{AA}$ vs $p_{\perp }$ are, respectively, given as white bands with full, dashed, and dot-dashed boundaries. The upper (lower) boundary of each band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$. (b) Theoretical predictions for bare quark $R_{AA}$ vs $p_{\perp }$ are shown for $u$ (dotted curve), $c$ (dashed curve), and $b$ (dot-dashed curve). ${\mu }_M/{\mu }_E$ ratio is set to 0.4. (c) Theoretical predictions for $R_{AA}$ vs $p_{\perp }$ are compared for $u$ (dotted curve) with $h^{\pm }$ (full curve). ${\mu }_M/{\mu }_E$ ratio is set to 0.4.

Figure 4

Comparison of $R_{AA}$ predictions for charge hadrons at 2.76 and 5.02 TeV. Charged hadron suppression predictions, as a function of transverse momentum, are shown. $R_{AA}$ predictions at 5.02 TeV (2.76 TeV) 0%–10% central Pb+Pb collisions at the LHC are presented as white bands with full (dashed) boundaries. The upper (lower) boundary of each band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$.

Figure 5

Comparison of single particle and jet suppression data at the LHC experiments. (a) $R_{AA}$ vs $p_{\perp }$ experimental data are compared for inclusive jets from ATLAS [14] (blue squares) and CMS [13] (blue circles) and charged hadrons [40] from ATLAS (green squares) and CMS [46] (green circles). ATLAS jet data correspond to 0%–10% centrality, while the other data correspond to 0%–5% centrality. (b) $R_{AA}$ vs $N_{\mathrm{part}}$ ATLAS experimental data are compared for inclusive jets [14] (blue squares, $63<p_{\perp }<80\mathrm{GeV})$ and charged hadrons [40] (green squares, $65<p_{\perp }<90\mathrm{GeV})$.

Figure 6

Single particle suppression predictions vs jet data. (a) Theoretical $R_{AA}$ vs $p_{\perp }$ predictions for single particles are compared with 0%–10% centrality ATLAS experimental data for inclusive jets [14] (blue squares). (b) $R_{AA}$ vs $p_{\perp }$ single particle predictions are compared with CMS experimental data for inclusive jets [13] (blue circles, 0%–5% centrality) and b jets [12] (orange triangles, 0%–10% centrality). On each panel, white bands with dashed, dot-dashed, and full boundaries, respectively, correspond to charm, bottom, and light flavor predictions, and the upper (lower) boundary of each band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$.

Figure 7

Single particle suppression predictions vs jet data. Single particle predictions for $R_{AA}$ vs $N_{\mathrm{part}}$ are compared with ATLAS data for inclusive jets [14] (blue squares, $80<p_{\perp }<100\mathrm{GeV}$ momentum region) and CMS data for b jets [12] (orange triangles, $80<p_{\perp }<90\mathrm{GeV}$ momentum region). White bands with dashed, dot-dashed, and full boundaries, respectively, correspond to charm, bottom, and light flavor predictions for $80<p_{\perp }<100\mathrm{GeV}$. The upper (lower) boundary of each band corresponds to ${\mu }_M/{\mu }_E=0.6$ $\left({\mu }_M/{\mu }_E=0.4\right)$.