ISOSPIN BREAKING CORRECTIONS TO MASSES AND HADRONIC PROCESSES ON THE LATTICE

Abstract

This dissertation is concerned with the addition of QED corrections to non-perturbative lattice QCD calculations. Such first-principles combined QCD+QED calculations are crucial for high precision tests of the Standard Model of particle physics. The thesis at hand establishes a numerical lattice QCD+QED framework, contributes to the theoretical foundation of such calculations, and provides numerical results for observables which were previously out of reach. Besides the usual QCD correction, at the percent level accuracy (reached in many decay pro cesses), it is extremely important to go beyond the isospin limit and account for the effect of isospin breaking which come both from the light-quark mass difference, ∆mud ≡ md − mu, and from the electric charge difference. After a detailed introduction explaining the subtleties related to the addition of QED corrections to lattice QCD calculations, including the definition of non-perturbative renormalization procedures of the full QCD+QED theory, isospin-breaking effects to both hadron masses and meson decay am plitudes are discussed. Numerical results are provided for the mass differences of charged and neutral pions, kaons, and D mesons. For radiative electromagnetic corrections to hadronic decays the presence of infrared divergences in intermediate stages of the calculation adds significant com plications compared to the infrared-finite case of the hadronic spectrum. In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to the emission of real photons. Only in this way do the infrared divergences cancel as first understood by Bloch and Nordsieck in 1937. In this work the leading-order isospin-breaking corrections to the light-meson leptonic decay rates are evaluated for the first time on the lattice. Furthermore, a discussion of the theoretical framework required for the computation of radia tive corrections to semileptonic decay rates in lattice simulations is provided. Finally, preliminary results regarding the real-photon emission amplitudes for the leptonic decays P → `ν`γ of pseu doscalar mesons show that the corresponding form factors can be handled numerically on the lattice. This will lead to significantly improved precision in the determination of the Cabibbo Kobayashi-Maskawa matrix elements entering such processes and it would also allow accurate, model-independent predictions of the important radiative decays of heavy mesons with the emis sion of a hard photon which could be helpful in constraining various New Physics scenarios