Polarization dependence of the $\phi$ meson from finite-temperature QCD sum rules

We study the $\phi$ meson at finite temperature and finite momentum using QCD sum rules. The presence of medium breaks the Lorentz invariance, and induces distinct in-medium modifications of the transverse and longitudinal modes at finite momentum. We find that, with increasing momentum, the masses of both modes increase and a clear transverse–longitudinal splitting develops. The splitting is found to grow with temperature and to be mainly generated by the dimension-four spin-dependent thermal condensates.