Collinear spin correlations of final-state radiation in dense QCD matter

Spin correlations are required to reproduce the correct azimuthal dependence of matrix elements for successive branchings at disparate angles in QCD jets. In this paper, we study modifications to this, $\cos (2{\psi }_{12})$, azimuthal pattern in the presence of a quark-gluon plasma. To that end, we consider a simplified setup in which a narrow and energetic QCD antenna is formed inside a medium of fixed length and radiates a collinear emission outside it. The calculation includes both light and heavy-quarks. Further, we do not include medium-induced spin-flip interactions since they are energy suppressed in our formalism. We show that the amplitude of the azimuthal modulation in the presence of a medium is always suppressed with respect to the vacuum baseline, with its magnitude depending on the medium properties and splitting kinematics. For a medium with a momentum space anisotropy, we find that the azimuthal modulation acquires a phase shift, i.e., $\cos (2{\psi }_{12})\to \cos (2{\psi }_{12}+{\phi }_{\mathrm{m}\mathrm{e}\mathrm{d}})$, where ${\phi }_{\mathrm{m}\mathrm{e}\mathrm{d}}$ is a process-dependent function that again depends on the medium properties and splitting kinematics. This work provides theory guidance for implementing spin-driven interference effects in phenomenological studies of jet quenching in heavy-ion collisions.