Heavy Hadron Spectroscopy from Lattice QCD - Gayer, Luke Richard (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2024)
In this thesis, heavy hadron spectroscopy was studied through the formalism of lattice quantum chromodynamics. A summary of relevant theory is provided, followed by an overview of the current state-of-the-art spectroscopy methods that were employed in this work. Finite volume spectra were computed using the variational method with distillation. The finite-volume spectra computed were used to constrain infinite-volume scattering amplitudes using L?scher?s method. The scattering amplitude of the isospin-1/2 D-pi S-wave was computed. By analytically continuing this amplitude to complex energies, a resonance pole was found. This pole was identified as the D_0^? meson. Extrapolating to physical pion mass suggests that the current reported experimental mass of the D_0^? is too high. Also covered in this thesis is a calculation of the excited and exotic spectra of the B, B_s and B_c mesons. The presence of hybrid mesons was investigated, with candidate states for a hybrid supermultiplet proposed in each meson sector. The mixing of states occurring due to symmetry breaking on the lattice was also studied. The B and B_s mesons were found to be strongly mixed, while the mixing in B_c was much weaker. The analysis of the B meson was extended further, with an exploratory study of isospin-3/2 B-pi scattering performed. The scattering amplitude for the S-wave was computed, and was found to be the form of a weakly repulsive interaction. This thesis concludes with an overview of its findings.
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Keywords: Lattice QCD; Hadron Spectroscopy; heavy-light mesons; Scattering