Dissociation driven quarkonium spin alignment in Pb--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

TL;DR

The paper investigates how medium vorticity in a rotating quark–gluon plasma can drive spin alignment of quarkonia produced in Pb–Pb collisions at 5.02 TeV. It develops a framework with a medium-modified complex potential and spin–vorticity coupling, solved alongside second-order viscous hydrodynamics to compute state-dependent decay widths arising from collisional damping and gluonic dissociation. By solving a rotating-frame Schrödinger equation and integrating over the evolving medium, it predicts state-, p_T-, and centrality-dependent behavior of the spin-density matrix element ρ_{00} for J/ψ, ψ(2S), Υ(1S), and Υ(2S). The results show a clear state dependence: 1S states favor ρ_{00} > 1/3 while 2S states favor ρ_{00} < 1/3, highlighting the competition between thermal dissociation and rotational effects and establishing spin-dependent dissociation as a contributing mechanism to quarkonium spin alignment.

Abstract

The observation of spin alignment of quarkonia in ultra-relativistic heavy-ion collisions provides deep insight into the possible formation of the quark-gluon plasma (QGP). The present study investigates the spin alignment of quarkonia induced by dissociation mechanisms arising from medium effects imposed on quarkonia. We implement an effective Hamiltonian with a medium-modified color-singlet potential to incorporate the coupling of quarkonium spin with medium vorticity. This coupling gives rise to spin-dependent dissociation, which we identify as a plausible mechanism contributing to quarkonium spin alignment. Within the ambit of second-order relativistic viscous hydrodynamics, we calculate the spin-dependent decay widths of charmonium ($J/ψ$, $ψ$(2S)) and bottomonium ($Υ$(1S), $Υ$(2S)) in a rotating thermal medium, including collisional damping and gluonic dissociation effects. We evaluate the observable $ρ_{00}$ for Pb--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV as a function of transverse momentum of the quarkonia, charged particle multiplicity, and medium rotation. The results demonstrate that medium vorticity modifies the quarkonia net decay width and, as a consequence, quarkonia spin alignment gets modified. These findings suggest new directions for understanding spin transport and the microscopic dynamics of vortical QGP.

Figures (7)

• Figure 1: (Color online) The effective temperature ($T_{\rm eff}$) as a function of $p_{\rm T}$ for $J/\psi$, $\psi$(2S), $\Upsilon$(1S), and $\Upsilon$(2S) states calculated at medium temperature $T$ = 0.400 GeV.
• Figure 2: The total decay width $\Gamma_{\rm D}$ as a function of transverse momentum ($p_{\rm T}$) for $J/\psi$ (upper left), $\psi$(2S) (upper right), $\Upsilon (1S)$ (lower left), and $\Upsilon$(2S) (lower right) in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. Results are presented for three different temperatures, such as $T$ = 0.400 GeV (red dotted dashed line), $T$ = 0.300 GeV (blue dashed line), and $T$ = 0.175 GeV (green solid line), with the circulation parameter $C = 0$ fm.
• Figure 3: The total decay width $\Gamma_{\rm D}$ as a function of transverse momentum ($p_{\rm T}$) for $J/\psi$ (upper), and $\psi$(2S) (lower) in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV for three different spin projections $m_{j}=$ 1 (red dotted dashed line), $m_{j}=$ 1 (blue dashed line), $m_{j}=$ 1 (green solid line) states with the circulation parameter $C = 1$ fm. The upper (lower) left and right panels present the $J/\psi$ ($\psi$(2S)) decay width for two different temperatures: $T$ = 0.400 GeV and 0.175 GeV, respectively.
• Figure 4: The total decay width $\Gamma_{\rm D}$ as a function of transverse momentum ($p_{\rm T}$) for $\Upsilon (1S)$ (upper), and $\Upsilon$(2S) (lower) in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV for three different spin projections $m_{j}=$ 1 (red dotted dashed line), $m_{j}=$ 1 (blue dashed line), $m_{j}=$ 1 (green solid line) states with the circulation parameter $C = 1$ fm. The upper (lower) left and right panels present the $\Upsilon (1S)$ ($\Upsilon$(2S)) decay width for two different temperatures: $T$ = 0.400 GeV and 0.175 GeV, respectively.
• Figure 5: (Color online) The spin alignment observable $\rho_{00}$ as a function of charged particle multiplicity ($<dN_{\rm ch}/d\eta>$) for $J/\psi$ (upper left), $\psi$(2S) (upper right), $\Upsilon (1S)$ (lower left), and $\Upsilon$(2S) (lower right) in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV integrated in the transverse momentum range 1$< p_{\rm T} <$ 30 GeV/c for different values of the circulation parameter, $C$.