Holographic spin alignment for vector mesons

We develop a general framework for studying the spin alignment rho 00 for flavorless vector mesons by using the gauge/gravity duality. Focusing on the dilepton production through vector meson decay, we derive the relation between production rates at each spin channel and meson's spectral function in a thermal medium, which can be evaluated by holographic models for a strongly coupled system. As examples, we study rho 00 for J/psi and phi mesons, induced by the relative motion to a thermal background, within the soft-wall model. Spectral functions for J/psi at T - 150 MeV have significant resonance peaks, indicating that c - c <overline> can exist as quasistable J/psi mesons. However, no significant peaks for the phi meson are observed at the same temperature, implying that phi mesons are melting down at this temperature and spectral functions are interpreted as probabilities of unstable s - s <overline> pairs. These pairs are related to free-streaming phi mesons by an instantaneous freeze-out assumption, which is performed by sandwiching the in-medium spectral function between the meson's free-streaming propagators. Then only states with invariant masses closing to the meson's vacuum mass survive during the freeze-out stage and contribute to final results. We show that rho 00 in the helicity frame for J/psi and phi mesons have positive and negative deviations from 1/3 at T = 150 MeV, respectively, which consequently leads to different properties for their global spin alignments.