Energy weighted sum rules for mesons in hot and dense matter

TL;DR

This paper investigates energy weighted sum rules for pions and kaons in hot, dense nuclear matter, using spectral functions derived from chiral models and many-body interactions to test and validate theoretical approaches.

Contribution

It introduces a method to evaluate sum rules for mesons in nuclear matter and assesses their effectiveness as consistency checks for spectral function models.

Findings

Sum rules are satisfied for lower energy weights.

Spectral densities reflect quasi-particle and collective modes.

Sum rules are sensitive to spectral strength distribution.

Abstract

We study energy weighted sum rules of the pion and kaon propagator in nuclear matter at finite temperature. The sum rules are obtained from matching the Dyson form of the meson propagator with its spectral Lehmann representation at low and high energies. We calculate the sum rules for specific models of the kaon and pion self-energy. The in-medium spectral densities of the K and anti-K mesons are obtained from a chiral unitary approach in coupled channels which incorporates the S- and P-waves of the kaon-nucleon interaction. The pion self-energy is determined from the P-wave coupling to particle-hole and Delta-hole excitations, modified by short range correlations. The sum rules for the lower energy weights are fulfilled satisfactorily and reflect the contributions from the different quasi-particle and collective modes of the meson spectral function. We discuss the sensitivity of the sum rules to the distribution of spectral strength and their usefulness as quality tests of model calculations.