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 $220-960\text{MeV}$, 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 $T_{\text{pc}}$, 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 $T=220\text{MeV}$.

19 pages, 3 figures; v3: references updated, matches published version

References in corpus (16)

• Charmonium properties in hot quenched lattice QCD
• Heavy Quarkonium in Extreme Conditions
• Meson screening masses from lattice QCD with two light and the strange quark
• Towards quantitative precision in the chiral crossover: masses and fluctuation scales
• Symmetries of spatial meson correlators in high temperature QCD
• In-medium modifications of open and hidden strange-charm mesons from spatial correlation functions
• Flow equations for spectral functions at finite external momenta
• A relation between screening masses and real-time rates
• Dynamics of the $O(4)$ critical point in QCD
• Chiral dynamics in the low-temperature phase of QCD
• Decay constants of the pion and its excitations on the lattice
• Quasi-static probes of the QCD plasma
• Spectral representation of the shear viscosity for local scalar QFTs at finite temperature
• A comparison of spectral reconstruction methods applied to non-zero temperature NRQCD meson correlation functions
• Euclidean thermal correlation functions in local QFT
• Real-time observables from Euclidean thermal correlation functions

Cited by in corpus (14)

• Chiral spin symmetry and the QCD phase diagram
• Chiral spin symmetry and hot/dense QCD
• Pseudo-scalar meson spectral properties in the chiral crossover region of QCD
• Symmetries of meson correlators in high temperature QCD with physical $(u/d,s,c)$ domain-wall quarks
• On the (in)consistency of perturbation theory at finite temperature
• Non-perturbative insights into the spectral properties of QCD at finite temperature
• Goldstone bosons at non-zero temperature
• Quark models: What can they teach us?
• Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD
• Goldstone bosons across thermal phase transitions
• Symmetries in high-temperature lattice QCD with (u, d, s, c, b) optimal domain-wall quarks
• Confined but chirally and chiral spin symmetric hot matter
• Implementation of Cluster expansion for hot QCD matter
• Non-perturbative constraints on perturbation theory at finite temperature