Isospin-breaking corrections to light pseudoscalar leptonic decays rates
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Date
13/02/2023Author
Yong, Andrew Zhen Ning
Metadata
Abstract
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.