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 \(\rho_T(\omega=|\vec k|, \vec k)\). 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.