Evaluating chiral symmetry restoration through the use of sum rules

TL;DR

This paper investigates chiral symmetry restoration by analyzing in-medium modifications of hadronic spectral functions using sum rules, focusing on vector and axial-vector channels, and presents preliminary finite temperature results.

Contribution

It demonstrates the importance of including excited resonances in spectral functions to satisfy sum rules and explores finite temperature effects on the rho spectral function.

Findings

Inclusion of excited resonances is essential for sum rule consistency.

Preliminary results show the rho' peak flattens at finite temperature.

Flattening of the rho' may indicate chiral restoration.

Abstract

We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector and axial-vector channels. We first present an update on constructing quantitative results for pertinent vacuum spectral functions. These spectral functions serve as a basis upon which the in-medium spectral functions can be constructed. A striking feature of our analysis of the vacuum spectral functions is the need to include excited resonances, dictated by satisfying the Weinberg-type sum rules. This includes excited states in both the vector and axial-vector channels. Preliminary results for the finite temperature vector spectral function are presented. Based on a rho spectral function tested in dilepton data which develops a shoulder at low energies, we find that the rho' peak flattens off. The flattening may be a sign of chiral restoration, though a study of the finite temperature axial-vector spectral function remains to be carried out.