Abstract
We propose a new theory framework to study the electroweak radiative corrections in Kl3 decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important mathcal{O} (GFα) radiative corrections are described by a single tensor Tμν 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 Vus in the future.
Highlights
The situation described above has changed since last year, following a series of reevaluation of the electroweak radiative corrections in superallowed beta decays, from where Vud is most precisely extracted
Preliminary investigations indicate that they largely cancel each other, and cause only a slight increase in the total uncertainty: ∆CKM = −0.0016(6) [10]. This is, not yet conclusive and needs to be further scrutinized. Further discussions along this line have led to the identification of well-defined steps toward the further reduction of the |Vud| uncertainty: first, next-generation neutrino experiments at the LongBaseline Neutrino Facility (LBNF) at Fermilab are expected to provide much more precise neutrino data input to the dispersion integral [11], second, a direct lattice approach to the γW -box diagram is recently suggested [12], alternative computational methods of the box diagram are proposed in comparison to the dispersive method [13], and there are plans to study the above-mentioned new nuclear effects with ab-initio methods [6]
For the non-enhanced terms that are suppressed in the neutron and superallowed beta decays but not in Kl3, we develop a diagrammatic approach to calculate them order-byorder in Chiral Perturbation Theory (ChPT), and point out along this process that the Kl03 channel possesses a natural advantage of having minimal dependence on the poorly-constrained low-energy constants (LECs)
Summary
We start by defining the electromagnetic and charged weak current in the hadron sector that are responsible for generic semi-leptonic beta decays: Jeμm. The former, including strong isospin-breaking effects, is a part of the pure-QCD dressings to the Kπ form factor, which could be studied more systematically with other methods, such as in a dispersive representation [27,28,29,30,31] or in lattice QCD It is the inclusion of dynamical photons that greatly complicates the problem, for instance, it was not until very recently that the first direct lattice calculation of the electromagnetic effects to Kl2 and πl decay rates was available [32], and the same method applied to semi-leptonic decays is expected to be extremely challenging [33, 34]. For the electromagnetic radiative corrections to the form factor, all the ln MW enhanced terms are contained in the two-point function, so such a separation makes it easy to discuss the large MW , MZ behavior of the generic O(GF α) correction to the decay rate [38]. OMS+WI+ChPT framework possesses both conceptual and practical advantages over the pure ChPT framework, and is a better starting point
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