Generalized two-point tree-level amplitude $jf \to j^{\, \prime} f^{\, \prime}$ in a magnetized medium

TL;DR

This paper calculates two-point tree-level amplitudes for fermion-current interactions in a magnetic field and plasma, analyzing special cases like strong fields and forward scattering, with applications to neutrino processes.

Contribution

It provides a general framework for calculating these amplitudes for various interaction vertices and magnetic field strengths, including resonance effects in neutrino photoproduction.

Findings

Derived explicit amplitude formulas for different interaction types.

Analyzed special cases such as strong magnetic fields and forward scattering.

Calculated neutrino emissivity including resonance effects.

Abstract

The tree-level two-point amplitudes for the transitions $jf \to j^{\, \prime} f^{\, \prime}$, where $f$ is a fermion and $j$ is a generalized current, in a constant uniform magnetic field of an arbitrary strength and in charged fermion plasma, for the $jff$ interaction vertices of the scalar, pseudoscalar, vector and axial-vector types have been calculated. The generalized current $j$ could mean the field operator of a boson, or a current consisting of fermions, e.g. the neutrino current. The particular cases of a very strong magnetic field, and of the coherent scattering off the real fermions without change of their states (the "forward" scattering) have been analysed. The contribution of the neutrino photoproduction process, $\gamma e\to e \nu \bar \nu$, to the neutrino emissivity has been calculated with taking account of a possible resonance on the virtual electron.