NLO quark self-energy and dispersion relation using the hard thermal loop resummation

Using the hard-thermal-loop (HTL) resummation in real-time formalism, we study next-to-leading order (NLO) quark self-energy and corresponding NLO dispersion laws. In NLO, have replaced all propagators vertices with HTL-effective ones usual diagram. Additionally, a four-point vertex diagram also contributes to self-energy. We calculate separately. those, express terms of three- functions. Feynman parametrization, integrals containing HTL effective functions solid angles. After completing angle integrals, numerically momentum plot them as function ratio energy. self-energy, correction