Spin alignment of quarkonia: a possible probe of deconfined QCD matter in Pb+Pb collisions at $$\sqrt{s_\textrm{NN}} = 5.02$$ TeV

Abstract In this study, we investigate the influence of deconfined QCD matter on quarkonium spin alignment in ultra-relativistic heavy-ion collisions. We estimate the spin alignment of charmonium ( $$J/\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> , and $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> (2 S)) and bottomonium ( $$\Upsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Υ</mml:mi> </mml:math> (1 S), and $$\Upsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Υ</mml:mi> </mml:math> (2 S)) states for Pb+Pb collisions at $$\sqrt{s_\textrm{NN}} = 5.02$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mtext>NN</mml:mtext> </mml:msub> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>5.02</mml:mn> </mml:mrow> </mml:math> TeV as a function of transverse momentum by calculating the energy eigenvalues in a thermal rotating medium. We solve the Schrödinger equation with a medium-modified color-singlet potential, considering the coupling of spin with vorticity and magnetic field. Furthermore, we evaluate the effect of medium temperature, vorticity, magnetic field, and momentum-space anisotropy on the elements of the spin density matrix. Our findings reveal that vorticity increases the spin alignment, while the magnetic fields and anisotropy modify the observables in a state-dependent manner. These findings deepen our understanding of quarkonium spin alignment in an anisotropic magneto-vortical thermal medium, shedding light on spin transport phenomena in heavy-ion collisions.