A New Theory Framework for the Electroweak Radiative Corrections in $K_{l3}$ Decays

TL;DR

This paper introduces a novel theoretical framework combining current algebra and effective field theory to improve calculations of electroweak radiative corrections in $K_{l3}$ decays, aiding precise determination of $V_{us}$.

Contribution

It presents a unified approach to compute radiative corrections in $K_{l3}$ decays, emphasizing the $K_{l3}^{0}$ channel's reduced dependence on uncertain low-energy constants.

Findings

The framework describes dominant radiative corrections with a single tensor $T^{}$.

The $K_{l3}^{0}$ channel is less affected by poorly-constrained constants.

Potential for more accurate extraction of $V_{us}$.

Abstract

We propose a new theory framework to study the electroweak radiative corrections in $K_{l3}$ decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important $\mathcal{O}(G_F\alpha)$ radiative corrections are described by a single tensor $T^{\mu\nu}$ involving the time-ordered product between the charged weak current and the electromagnetic current, and all remaining pieces are calculable order-by-order in Chiral Perturbation Theory. We further point out a special advantage in the $K_{l3}^{0}$ channel that it suffers the least impact from the poorly-constrained low-energy constants. This finding may serve as a basis for a more precise extraction of the matrix element $V_{us}$ in the future.