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.
Categories: hep-ph hep-ex nucl-ex nucl-th