Nuclear axial current operators to fourth order in chiral effective field theory

TL;DR

This paper derives nuclear axial charge, current, and pseudoscalar operators up to fourth order in chiral effective field theory, ensuring renormalizability and consistency with nuclear forces and the continuity equation.

Contribution

It provides a complete, renormalized derivation of nuclear axial operators to fourth order in chiral EFT using the unitary transformation method, clarifying ambiguities.

Findings

Operators are explicitly derived up to fourth order.

Renormalization and ambiguity elimination are demonstrated.

Continuity equation validity is verified.

Abstract

We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.