The Self-energy of Nucleon for the Pole term of the Axial-vector Current and the Neutron $\beta$-decay

TL;DR

This paper investigates how the pion propagator influences neutron beta decay, aiming to reconcile theoretical models with experimental data by including the pole term and vertex corrections.

Contribution

It introduces a method to incorporate the pole term and vertex corrections to improve agreement between theoretical predictions and experimental results for neutron beta decay.

Findings

The pion propagator significantly affects the axial-vector to vector ratio.

Vertex corrections can reconcile model predictions with experimental data.

The approach suggests improvements in theoretical modeling of nucleon decay processes.

Abstract

The effect of the pion propagator on the $\beta$-decay of neutron is investigated to account for the ratio of the axial-vector to the vector part $g_A/g_V$ by including the pole term. A suggestion is made that the sign and the size of the vertex correction is appropriate to improve the discrepancy between the result of the model hamiltonian and the experiment.