The HTL Lagrangian at NLO: the photon case

Understand

We calculate the two loop hard correction to the photon self-energy in an electron-positron plasma (EPP) for arbitrary soft momenta.

• This provides the only missing ingredient to obtain the Hard Thermal Loop (HTL) effective Lagrangian at next-to-leading order (NLO), and the full photon propagator at the same order.
• This result can be easily extended to obtain the soft photon propagator in a quark gluon plasma.
• We use the Keldysh representation of the real time formalism in the massless fermion limit, and dimensional regularization (DR) to regulate any ultraviolet (UV), infrared (IR) or collinear divergences that appear in the intermediate steps of the calculation.