Generalized Emission Functions for Photon Emission from Quark-Gluon Plasma

The Landau-Pomeranchuk-Migdal effects on photon emission from the quark gluon plasma have been studied as a function of photon mass, at a fixed temperature of the plasma. The integral equations for the transverse vector function (${\bf \tilde{f}(\tilde{p}_\perp)}$) and the longitudinal function ($\tilde{g}({\bf \tilde{p}_\perp})$) consisting of multiple scattering effects are solved by the self consistent iterations method and also by the variational method for the variable set \{$p_0,q_0,Q^2$\}, considering the bremsstrahlung and the $\bf aws$ processes. We define four new dynamical scaling variables, $x^b_T$,$x^a_T$,$x^b_L$,$x^a_L$ for bremsstrahlung and {\bf aws} processes and analyse the transverse and longitudinal components as a function of \{$p_0,q_0,Q^2$\}. We generalize the concept of photon emission function and we define four new emission functions for massive photon emission represented by $g^b_T$, $g^a_T$, $g^b_L$, $g^a_L$. These have been constructed using the exact numerical solutions of the integral equations. These four emission functions have been parameterized by suitable simple empirical fits. In terms of these empirical emission functions, the virtual photon emission from quark gluon plasma reduces to one dimensional integrals that involve folding over the empirical $g^{b,a}_{T,L}$ functions with appropriate quark distribution functions and the kinematic factors. Using this empirical emission functions, we calculated the imaginary part of the photon polarization tensor as a function of photon mass and energy.