Isospin-breaking corrections to light pseudoscalar leptonic decays rates
Yong, Andrew Zhen Ning
The Cabibbo-Kobayashi-Maskawa (CKM) matrix is a 3x3 unitary matrix in the Standard Model of particle physics. It characterises the transmutation of quarks in flavor-changing weak decays. In flavor physics, a precise determination of its matrix elements represents a crucial test of the limits of the Standard Model. One of the major theoretical challenges in this enterprise is the inclusion of low energy hadronic quantities. In this non-perturbative regime, Lattice Quantum Chromodynamics remains the ab initio approach for fi rst principle calculations of the hadronic observables required. Traditionally, the Euclidean n-point correlation functions from these Monte-Carlo simulations are calculated in the isospin-symmetric limit, where α = 0 and mᵤ - mₔ = 0. In recent years, however, lattice calculations of fπ and fₖ, which are necessary for the determination of Vᵤₔ and Vᵤₛ from leptonic decays, respectively, have reached an impressive precision of σ(1%) or better. To make further progress, lattice simulations can no longer neglect percent-level isospin-breaking effects. In this thesis, isospin-breaking corrections to the inclusive rate K⁺=π⁺ → μ⁺vμ[γ] and an update to Vᵤₛ=Vᵤₔ are presented. A distinct feature of this work is the amplitude correction arising from a virtual photon coupling the initial pseudoscalar to the fi nal state charged lepton. The non-perturbative, electro-quenched result comes from the RBC-UKQCD 2 + 1 flavor Domain Wall fermion simulations with near-physical quark masses. The QED interactions are introduced via a perturbative expansion of the action in α and the photon propagators are implemented in the Feynman gauge and QEDₗ formulation. The isospin-breaking corrections obtained from the lattice are then corrected for nite volume effects and combined with the analytic real photon emission term to remove the IR divergence. For this latter term, all possible photon energies are integrated over. The phenomenological quantity Vᵤₛ=Vᵤₔ determined in this thesis is discussed in light of the latest published results.