In-Medium Modification of $\phi$ Meson Mass over Temperature and Momentum

We analyze the in-medium modification of the $\phi$ meson mass below the pseudo-critical temperature $T_{\text{c}}$ at vanishing baryon chemical potential using QCD sum rules. The sum rules are applied separately to the transverse and longitudinal polarization modes of the $\phi$ meson defined relative to the spatial momentum in the medium rest frame. We map out the temperature and momentum dependence of the mass in each mode and quantify the resulting transverse–longitudinal mass splitting. The splitting develops with increasing temperature and momentum.