Vector and Axial-vector form factors in radiative kaon decay and flavor SU(3) symmetry breaking

TL;DR

This paper investigates the vector and axial-vector form factors in radiative kaon decay using a nonlocal chiral effective action, examining SU(3) symmetry breaking effects and comparing results with experimental data and chiral perturbation theory.

Contribution

It provides a detailed analysis of flavor SU(3) symmetry breaking effects on kaon decay form factors within a nonlocal chiral model, including quark mass variation impacts.

Findings

Nonlocal contributions increase vector form factor by ~20%.

Axial-vector form factor decreases by nearly 30% due to nonlocal effects.

Results at zero momentum transfer agree with experimental data.

Abstract

We study the vector and axial-vector form factors of radiative kaon decay within the framework of the gauged nonlocal effective chiral action from the instanton vacuum, focusing on the effects of flavor SU(3) symmetry breaking. The general tendency of the results are rather similar to those of radiative pion decays: The nonlocal contributions make the results of the vector form factor increased by about $20\,\%$, whereas they reduce those of the axial-vector form factor by almost $30\,\%$. Suppressing the prefactors consisting of the kaon mass and the pion decay constant, we scrutinize how the kaon form factors undergo changes as the mass of the strange current quark is varied. Those related to the vector and second axial-vector form factors tend to decrease monotonically as the strange quark mass increases, whereas that for the axial-vector form factor decreases. When $K\to e\nu\gamma$ decay is considered, both the results of the vector and axial-vector form factors at the zero momentum transfer are in good agreement with the experimental data. The results are also compared with those from chiral perturbation theory to $p^6$ order.