Hadron Scattering Amplitudes from Lattice QCD

Abstract

In this thesis we compute hadron scattering amplitudes within the framework of lattice quantum chromodynamics. Finite-volume spectra are computed using distillation and the variational method. These spectra constrain infinite-volume scattering amplitudes through the L?scher formalism. By analytically continuing these amplitudes to complex energies, pole singularities are identified in the complex plane and related to unstable particles.

One focus lies on open-charm meson-meson scattering. We compute the resonant elastic $I=1/2$ $D\pi$ $S$-wave amplitude. The complex pole found in this amplitude is identified with the scalar $D_0^\ast(2300)$ state. We also compute coupled $I=1/2$ $D^\ast \pi$, $D^\ast \eta$ and $D_s^\ast \bar{K}$ amplitudes and identify axial-vector resonances that we relate to the physical $D_1(2430)$ and $D_1(2420)$ as well as a tensor resonance which is identified with the $D_2^\ast(2460)$. Additionally indications of a pole at higher energies are found in the $S$-wave amplitude.

A second focus is on the development of algorithmic improvements to the distillation method. Using sparse tensor contractions in conjunction with stochastic methods the performance of computing Wick contractions is improved. This algorithm is tested in a calculation of $I=3/2$ $N\pi$ correlation functions.