Guelpers, Vera

Portelli, Antonin

Zwicky, Roman

Del Debbio, Luigi

Yong, Andrew Zhen Ning

2023-02-13T12:51:25Z

2023-02-13T12:51:25Z

2023-02-13

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.

https://hdl.handle.net/1842/39838

http://dx.doi.org/10.7488/era/3086

en

The University of Edinburgh

Boyle, Peter A. et al. “Isospin-breaking corrections to light leptonic decays in lattice QCD+QED at the physical point.” Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022) (2022): n. pag.

A. Z. N. Yong et al., \Near Physical Point Lattice Calculation of Isospin- Breaking Corrections to K`2= `2," PoS, vol. LATTICE2021, p. 110, 2022.

P. Boyle et al., \Isospin-breaking corrections to light leptonic decays in lattice QCD+QED at the physical point," in 39th International Symposium on Lattice Field Theory, 12 2022.

Isospin-breaking Corrections

Light Pseudoscalar Leptonic Decays

Cabibbo-Kobayashi-Maskawa matrix

(CKM)

transmutation of quarks

flavor-changing weak decays

flavor physics

non-perturbative

Lattice Quantum Chromodynamics

Monte-Carlo simulations

isospin-symmetric limit

Isospin-breaking corrections to light pseudoscalar leptonic decays rates

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy