The $N-\Delta$ Weak Axial-Vector Amplitude $C_{5}^a(0)$

TL;DR

This paper calculates the weak $N-\Delta$ axial-vector transition amplitude $C_{5}^a(0)$ using a broken symmetry algebraic approach to QCD, providing results consistent with experimental data.

Contribution

It introduces a novel algebraic method based on broken symmetry in QCD to compute the $N-\Delta$ axial-vector form factor $C_{5}^A(0)$.

Findings

Calculated $C_{5}^A(0)$ in good agreement with experiment.

Demonstrated the effectiveness of broken symmetry algebraic approach.

Provided insights into $N^{*}$ production processes.

Abstract

The weak $N-\Delta$ axial-vector transition amplitude $<\Delta| A_{\pi ^{+}}^\mu |N>$ - important in $N^{*}$ production processes in general and in isobar models describing $\nu_\mu N\to \mu \Delta$ processes in particular - is examined using a broken symmetry algebraic approach to QCD which involves the realization of chiral current algebras. We calculate a value for the form factor $C_{5}^{A}(0)$ in good agreement with experiment.