  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
L\"uscher 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.
