Lepton Flavour Violation and K → π ν anti-ν Decays in the Standard Model (Effective Field Theory)
Abstract
A major goal of modern physics is the detection of physics beyond the Standard Model. Promising areas to search for such signals are processes that are either forbidden or highly suppressed within the Standard Model, including Lepton Flavour Violation (LFV) and rare K decays. While LFV is forbidden in the renormalisable Standard Model, the rare K decays K+ → π+νν and KL → π0νν are not, and so precision theoretical predictions are required to distinguish any signal of new physics from the Standard Model background. We discuss the contribution of the dimension-five lepton number violating Weinberg operator to the running of dimension-six LFV operators in the Standard Model Effective Field Theory. We also consider contributions from a hypothetical second Higgs doublet, which gives rise to Wilson coefficients that cannot all be constrained by small neutrino masses. We then consider bounds on the magnitudes of these Wilson coefficients, by using phenomenological bounds on the low-energy effective theory. Finally, we discuss the calculation of the rare decays K+ → π+νν and KL → π0νν to Next-to-Next-to-Leading Order in QCD. These decays are theoretically very clean, providing a promising arena for the detection of new physics. We discuss in detail the matching of box diagrams in the full Standard Model to diagrams of the effective theory below the weak scale, to O(α2 s). This involves the evaluation of three-loop integrals, and we provide the Wilson coefficients obtained from the matching.