Pion spectral properties above the chiral crossover of QCD

Abstract

Spectral functions encode a wealth of information about the dynamics of any given system, and the determination of their non-perturbative characteristics is a long-standing problem in quantum field theory. Whilst numerical simulations of lattice QCD provide ample data for various Euclidean correlation functions, the inversion required to extract spectral functions is an ill-posed problem. In this work, we pursue previously established constraints imposed by field locality at finite temperature T, namely that spectral functions possess a non-perturbative representation which generalises the well-known Källén-Lehmann spectral form to T > 0. Using this representation, we analyse lattice QCD data of the spatial pseudo-scalar correlator in the temperature range 220–960 MeV, and obtain an analytic expression for the corresponding spectral function, with parameters fixed by the data. From the structure of this spectral function we find evidence for the existence of a distinct pion state above the chiral pseudo-critical temperature Tpc, and contributions from its first excitation, which gradually melt as the temperature increases. As a non-trivial test, we find that the extracted spectral function reproduces the corresponding temporal lattice correlator data for T = 220 MeV.

Chiral spin symmetry and the QCD phase diagram

“…Note added: After completion of our manuscript an analysis of the pseudo-scalar spectral function at temperatures above the chiral crossover appeared [91]. It shows resonance-like peaks for the pion and its first excitation which only gradually disappear, consistent with the non-perturbative dynamics of the chiral-spin-symmetric band, as desribed here.…”

Non-perturbative insights into the spectral properties of QCD at finite temperature

“…and this domination will be especially pronounced at large distances. In QCD, hadronic correlators generally receive contributions from multiple states, and in this case the previous arguments can be suitably extended [13]. The ultimate conclusion is that the lowest energy states will have the most influence on C(x 3 ) at large distances, and the damping factors associated with these states can be directly extracted from the large-x 3 behaviour of C(x 3 ).…”

“…( 5) it was shown in Ref. [13] that the spatial correlator of a scalar operator can be written in the following general manner…”

“…Here we provide an overview of the study performed in Ref. [13] which focussed on the analysis of QCD spatial pseudo-scalar meson correlators, defined by…”

“…In these proceedings we provide an overview of a novel approach developed in Ref. [13] for extracting spectral function information from spatial correlators. We will outline the theoretical foundations upon which this approach is based, and its application to lattice QCD data of the spatial pseudo-scalar meson correlator at different temperatures above the chiral pseudo-critical temperature T pc .…”