Observations on the radiative corrections to pion beta-decay

TL;DR

This paper investigates the radiative corrections to pion beta-decay within different theoretical frameworks, highlighting small differences due to short-distance effects and comparing various approaches including current algebra and chiral perturbation theory.

Contribution

It demonstrates the subtle differences in radiative corrections between current algebra and pion field calculations, and clarifies their relation to chiral perturbation theory and the Standard Model.

Findings

Small difference in corrections when using current algebra versus pion fields.

Difference arises from short-distance effects related to current algebra.

No difference when comparing current algebra with chiral perturbation theory.

Abstract

We find that, in the local V-A theory, the radiative corrections to pion beta-decay involving the weak vector current, when evaluated in the current algebra (CA) formulation in which quarks are the fundamental underlying fields, show a small difference with the more elementary calculations based directly on the pion fields. We show that this difference arises from a specific short-distance effect that depends on the algebra satisfied by the weak and electromagnetic currents. On the other hand, we present a simple theoretical argument that concludes that this difference does not occur when the CA formulation is compared with the chiral perturbation theory (chiPT) approach. Comparisons with previous studies, and with a more recent calculation based on chiPT, are included. We also briefly review the important differences between the results in the local V-A theory and the Standard Model.