Next-To-Leading Order Scalars Dispersion Relations in HTL Scalar QED

Abstract

We investigate the next-to-leading order (NLO) contributions to scalar dispersion relations in hot scalar quantum electrodynamics (SQED) within the framework of hard-thermal-loop (HTL) resummed perturbation theory. Using the real-time formalism, we derive analytic expressions for the effective propagators and compute the complete NLO retarded scalar self-energy for slow-moving scalars with soft momentum. The results provide compact expressions for both the real and imaginary parts of the scalar self-energy, corresponding respectively to corrections to the energy and damping rates. Contributions from both longitudinal and transverse photon modes are evaluated.