Dissociation-driven quarkonium spin alignment in Pb–Pb collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>NN</mml:mi> </mml:mrow> </mml:msub> </mml:msq

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.