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

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 $1.15T_{pc}$ (220 MeV). We have used two ansätze 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.

Comments: 10 pages, 7 figures, Contribution to the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany