We calculate the $\phi$-meson propagator at finite temperature at the one--loop order. The real and imaginary parts are studied separately in full kinematic ranges. From this activity we investigate how temperature affects such things as decay widths and dispersion relations. { }From here we estimate the thermal rate of lepton pair radiation in a hadron gas proceeding through $K^{ +}K^{ -}\to \phi \to \ell^{ +}\ell^{ -}$ and $\pi\rho\to \phi \to \ell^{ +}\ell^{ -}$. We find several interesting things. From the dispersion relations we learn the effective mass calculated this way increases with temperature as does the partial width, but only slightly. At $T=200$ MeV, the mass increases by $\sim$ 4 MeV and the partial width increases by 34\%. Polarizations are indistinguishable for practical purposes.
Categories: nucl-th hep-ph