Hadron interactions and cosmic strings from lattice simulations

This doctoral thesis focuses on the application of lattice techniques to study two separate topics: hadron interactions within quantum chromodynamics (QCD), and the emission of particles and gravitational waves (GWs) from cosmic string loops. The first part of the dissertation deals with the study of two- an three-particle interactions using lattice QCD simulations, complemented by the limit of large number of colors and chiral perturbation theory. The basics of QCD and the different techniques used to study its non perturbative regime are presented in chapter 1. Chapter 2 then introduces the topic of hadron scattering, and explains how multiparticle interactions can be studied on the lattice. Five original works are presented in chapters 3 to 7. Chapters 3 and 4 deal with the study of meson-meson interactions as a function of the number of colors and the question of whether tetraquark resonances exist in a four flavor theory. Chapters 5 and 6 are focused on the study of three-pion interactions using chiral perturbation theory at next-to-leading order. Lastly, chapter 7 presents results on the study of two and three particles in the (1+1)-dimensional O(3) non-linear sigma model. The results presented in this part of the thesis represent a step forward in the understanding of the non-perturbative regime of QCD, in particular, in relation to the existence of exotic resonances and the interactions between three mesons. They also open the door to future studies of more complex systems, such as three-particle resonances or light nuclei. The second part of the thesis is devoted to the study of the dynamics and decay into particles and GWs of cosmic string loops, using classical-field-theory lattice computations. The basics of numerical simulations in an expanding background, as well as the techniques used to study the production of GWs, are presented in chapter 8. Results on global string loops are presented in chapter 9, where we find that the emission of particles dominates that of GWs independently of the size, shape and angular momentum of the loops. In the case of local loops, presented in chapter 10, it is possible to fabricate loops for which the production of GWs is the main decay channel at cosmological scales. However, for realistic loops expected to form in the early universe, the emission of particles is predominant at all scales. The results presented in this part of the dissertation highlight the importance of a field-theory description of string loops, in contrast to the Nambu-Goto approximation, which neglects the internal structure of the strings. This work also opens the door to a new path to determine the full background of GWs emitted by a network of strings in the early universe, by combining our results for the emission of GWs from a single loop with Nambu-Goto predictions of the loop number density through the history of the universe.