Photon production rate from Transverse-Longitudinal ($T-L$) mesonic correlator on the lattice

TL;DR

This study calculates the photon production rate from the quark-gluon plasma using lattice QCD by analyzing the transverse-longitudinal mesonic correlator with multiple spectral function models and the Backus-Gilbert method.

Contribution

It introduces a combined approach using polynomial, hydro-inspired models, and Backus-Gilbert method to estimate the photon production rate from lattice QCD data.

Findings

Consistent estimates of photon production rate from different spectral function models.

Demonstrated the IR dominance in the Euclidean correlator contributions.

Provided insights into the IR behavior of the transverse-longitudinal correlator.

Abstract

Thermal photons from the QGP provide important information about the interaction among plasma constituents. The photon production rate from a thermally equilibrated system is proportional to the transverse spectral function $\rho_T(\omega=|\vec k|, \vec k)$. One can also calculate the photon production rate from the difference between $\rho_T(\omega,\vec k)$ (transverse) and $\rho_L(\omega,\vec k)$ (longitudinal) projections, as $\rho_L$ vanishes on the photon point. Because the UV part of $\rho_T-\rho_L$ is suppressed, the corresponding Euclidean correlator receives most of its contribution from the IR part. We calculate the $T\!-\!L$ correlator on $N_f=2+1$ flavour HISQ configurations with $m_l=m_s/5$ at temperature of about $1.15\,T_{pc}$ (220 MeV). We have used two ans\"{a}tze for the spectral function: 1) A polynomial connected to the UV region consistent with OPE expansion and 2) a hydro-inspired spectral function. We have also applied the Backus-Gilbert method to estimate the spectral function. All these different approaches are combined to estimate the photon production rate.