Multi-Meson Dynamics in Chiral Perturbation Theory

Abstract: This thesis concerns scattering of light mesons in the case where the number of external particles exceeds four (that is, three or more particles in the initial or final state), calculated using chiral perturbation theory.This is both of theoretical interest in the study of scattering amplitudes, and relevant for systems of three or more pions simulated using lattice quantum chromodynamics.The introduction derives chiral perturbation theory from a background of quantum chromodynamics, which itself is motivated from general principles for the benefit of non-expert readers.Both theories are connected to the phenomenology of mesons and other hadrons, and related frameworks (including lattice quantum chromodynamics) are surveyed.The various computational techniques employed in the papers are summarized, related, and slightly expanded upon.Paper I derives a generalized diagrammatic method for computing tree-level scattering amplitudes with a large number of external particles and including higher-order vertices, which serve as counterterms to loop diagrams.The treatment of flavor and kinematics is formalized, and some novel scattering amplitudes are computed explicitly.Paper II applies the principles of analyticity, unitarity and crossing symmetry to the general two-to-two meson scattering amplitude in order to derive bounds on the otherwise free parameters that govern chiral perturbation theory.Previous results are generalized, both methodologically and in incorporating also the next-to-next-to-leading order of the amplitude.A mathematical framework is derived for organizing, improving and visualizing these bounds.Paper III describes the calculation of the next-to-leading-order amplitude with six external particles, using a family of variants of chiral perturbation theory and mesons of nonzero but equal mass.Some concepts from paper I are used and improved.Paper IV applies the amplitude considered in paper III to derive the three-pion K-matrix, which parametrizes finite-volume effects and pion mass dependence in three-pion systems in lattice quantum chromodynamics.This is done for the maximum-isospin channel, for which lattice results are available.A significant discrepancy is resolved between these results and the K-matrix obtained using only the leading-order amplitude.Paper V generalizes the results of paper IV to all isospin channels, in anticipation of future lattice results and in preparation for further theoretical developments.