Abstract
We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlin’s representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the O(GFα) radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and JP=0+ nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed.
Highlights
Beta decays are defined as decay processes φi → φf ν triggered by charged weak interactions, where a strong-interacting particle φi decays into another particle φf, accompanied by the emission of a charged lepton and a neutrino ν
We describe how the contributions from the physics at the hadron scale are constrained by lattice Quantum Chromodynamics (QCD), dispersion relation or other non-perturbative methodologies to achieve a precision level of 10−4
We reviewed some recent progress in the calculation of the O(GFα) electroweak radiative corrections (EWRCs) to semileptonic beta decays of strongly-interacting systems, which are important avenues for precision tests of the Standard Model (SM)
Summary
Beta decays are defined as decay processes φi → φf ν triggered by charged weak interactions, where a strong-interacting particle φi decays into another particle φf , accompanied by the emission of a charged lepton and a neutrino ν. All the dependences on the non-perturbative QCD at the chiral symmetry breaking scale Λχ ∼ 4πFπ (where Fπ is the pion decay constant) are parameterized in terms of a few low energy constants (LECs) in the chiral Lagrangian that are not constrained by the chiral symmetry and must be estimated separately with phenomenological models [88,89] Within this theory framework, the RC to πe3 [90] and K 3 [91,92,93] were both calculated to the order O(e2 p2), with e the positron charge and p a typical small momentum scale in ChPT. These two sections set the stage for our later analysis. We provide in Appendix A a simple derivation of the relations above using the Wick’s theorem of free fields
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