Kaon decays and other hadronic processes in lattice QCD

Abstract

This thesis deals with the study of properties and interactions of light mesons. Specifically, we focus on hadronic decay and scattering processes, which are dominated by effects of the strong interaction in the low-energy regime. A peculiarity of the strong interaction is that perturbative expansions fail at hadronic energy scales. Thus, genuine nonperturbative tools are essential to obtain first-principles predictions. Here we use Lattice Field Theory, and Effective Field Theories. The mathematical formulation of Quantum Chromodynamics (QCD) and the methods to resolve its dynamics will be addressed in Chapter 1. The research of this dissertation is divided in two parts. Chapter 2 describes our study of the 't Hooft limit of QCD using lattice simulations, while in Chapter 3 we consider processes that involve multiparticle states. The 't Hooft limit provides a simplification of nonabelian gauge theories that leads to nonperturbative predictions. We will analyze the scaling with the number of colours of various observables, such as meson masses, decay constants and weak matrix elements. A question we address is the origin of the long-standing puzzle of the $\Delta I=1/2$ rule, that is, the large hierarchy in the isospin amplitudes of the $K\to \pi \pi$ weak decay. Regarding multiparticle processes, we will discuss generalizations of the Lüscher formalism to explore three-particle processes from lattice simulations. The focus will be on our contributions, such as our implementation of the finite-volume formalism that includes higher partial waves, and the first application of the formalism to a full lattice QCD spectrum. We will also comment on the extension of the approach to generic three-pion systems. A summary in Spanish will be given in Chapter 4. The final part of the thesis (Part II) includes the peer-reviewed publications in their original published form.

arXiv commentPhD thesis. Based on arXiv:1901.07095, arXiv:1907.11511, arXiv:1909.02973, arXiv:2003.10293, arXiv:2003.10974, and arXiv:2101.10246

References in corpus (18)

• Weak Decays Beyond Leading Logarithms
• Renormalization of the Three-Body System with Short-Range Interactions
• Scattering processes and resonances from lattice QCD
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• Three-body spectrum in a finite volume: the role of cubic symmetry
• Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Three-particle systems with resonant subprocesses in a finite volume
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Spectrum of three-body bound states in a finite volume
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• Perturbative results for two and three particle threshold energies in finite volume
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Universal three-body recombination via resonant d-wave interactions