Semiclassical treatment of bottomonium suppression and regeneration in $p+{\rm Pb}$ collisions

TL;DR

Bottomonium production in $p+{ m Pb}$ collisions at the LHC is shaped by both cold nuclear matter (CNM) effects and a short-lived hot QCD medium. The authors develop a three-stage framework combining EPPS21 nPDFs, coherent energy loss, and a 3+1D anisotropic hydrodynamics background to evolve bottomonia via a semiclassical kinetic-rate equation, considering two dissociation-rate schemes: TAMU-P with a perturbative in-medium $U$-potential and TAMU-NP based on nonperturbative $T$-matrix constrained by lattice QCD. They also incorporate regeneration through equilibrium limits and instantaneous coalescence, finding large regeneration in the TAMU-NP scenario, especially for excited states, which helps reconcile suppression data with observations, and they provide predictions for $\chi_b$ suppression in $p+{ m Pb}$ at $8.16$ TeV. The study highlights the importance of regeneration in small systems and sets the stage for future charmonium investigations, offering a coherent picture of bottomonium behavior across collision energies and rapidities. Potentially, these insights inform our understanding of QGP properties and heavy-quark dynamics in both small and large collision systems.

Abstract

We study bottomonium suppression in $p+ {\rm Pb}$ relative to $p+p$ collisions at center-of-mass energies of $\sqrt{s_{NN}}= 5.02$ and 8.16~TeV. Specifically, we combine cold nuclear matter effects (nuclear modifications of the parton densities, energy loss and momentum broadening) with those from hot nuclear matter (suppression and regeneration) by implementing the formation of a quark-gluon plasma in hydrodynamic simulations. Bottomonium transport in the quark-gluon plasma is evaluated semiclassically, employing two different reaction rates. The first includes quasi-free inelastic scattering and gluo-dissociation employing a perturbative coupling to the medium. The second is based on in-medium $T$-matrix calculations where the input potential is constrained by lattice quantum chromodynamics to extract the bottomonium masses and dissociation rates. These semiclassical results are compared to previous calculations in an open quantum systems approach and to the experimental data. Predictions for $χ_b$ suppression at $\sqrt{s_{NN}} = 8.16$~TeV are also presented.

Figures (15)

• Figure 1: The nuclear suppression factor in $\sqrt{s_{NN}} = 8.16$ TeV $p+{\rm Pb}$ collisions due to CNM effects. The nPDF effects are shown in the pink band, including the EPPS21 uncertainties, while the effect of energy loss and transverse momentum broadening is given by the black dashed curve. The total effect, including both nPDF effects and energy loss plus broadening, is given by the gray band. The results for $b \overline b$ production are shown as a function of rapidity on the far left while the following three panels show the results as a function of $p_T$ at backward rapidity (center left), midrapidity (center right) and forward rapidity (far right).
• Figure 2: Bottom-quark mass (upper panels) and bottomonium binding energies (lower panels) as a function of temperature for the $U$-potential scenario (left) and WLCs (right) constrained by lattice QCD data. In the right panel, solid lines represent the binding energies of S-wave states, the 1S (blue), 2S (orange), 3S (green), and 4S (red) states, while the dashed lines represent the binding energies of P-wave states, the 1P (blue), 2P (orange), and 3P (red) states. Only the 1S, 2S, 1P, and 3S states are included in the $U$-potential scenario.
• Figure 3: Perturbative rates based on a in-medium $U$-potential for bottomonium binding, as functions of temperature at $p=0$. The solid lines represent the inelastic scattering rates while the dashed lines represent the gluo-dissociation rates for the 1S (blue), 1P (orange), 2S (green), and 3S (red) states.
• Figure 4: Perturbative bottomonium rates (inelastic scattering and gluon dissociation) assuming an in-medium $U$-potential, as functions of momentum for various temperatures. Each panel corresponds to a specific bottomonium state. The colors represent different temperatures, ranging from $T=170$ MeV (blue) to $T=700$ MeV (gray), as indicated in the legend.
• Figure 5: Nonperturbative bottomonium dissociation rates as a function of momentum over a range of temperatures. Each panel corresponds to a specific bottomonium state except the bottom right panel which shows twice the quark rates. The colors represent different temperatures, ranging from $T=170$ MeV (blue) to $T=700$ MeV (gray), as indicated in the legends. At high temperatures, the rates merge with the sum of the $b$ and $\overline b$ rates, shown in the bottom right panel.