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

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 ${\rho }_T(\omega =\mathrm{\mid }\vec{k}\mathrm{\mid },\vec{k})$. 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 $T\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}L$ correlator on $N_f=2+1$ flavour HISQ configurations with $m_l=m_s\mathrm{/}5$ 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.