Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

TL;DR

This paper derives and verifies Ward identities linking pseudoscalar susceptibilities and quark condensates in three-flavor QCD, incorporating finite temperature effects and explaining lattice screening mass behavior near chiral restoration.

Contribution

It provides the first derivation and verification of Ward identities in the full three-flavor QCD including the $ ext{U}_A(1)$ anomaly and finite temperature effects, with new results on quark condensates and susceptibilities.

Findings

Derived Ward identities relating susceptibilities and condensates.

Verified identities using ChPT in $SU(3)$ and $U(3)$ frameworks.

Established scaling relations for pseudoscalar masses near chiral restoration.

Abstract

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the $\eta$-$\eta'$ sector and the $U_A(1)$ anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard $SU(3)$ framework for the octet case and combining the use of the $U(3)$ framework and the large-$N_c$ expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of $U(3)$ quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses, which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.