The scattering of spinning hadrons from lattice QCD

Hadron spectroscopy is predominantly the study of resonances that decay via the strong interaction into a multitude of stable hadrons, such as the pion. The vast majority of resonances decay via an intermediate hadron with non-zero intrinsic spin. In this thesis, I will present the results of scattering calculations featuring mesons with non-zero intrinsic spin. Before doing so, I will first give a brief introduction to QCD and review the framework necessary to perform lattice QCD calculations in Chapters 1 and 2. In Chapter 3, I present the first lattice calculation of \rho π scattering in isospin-2. Here, \rhoπ features in dynamically-coupled ³{S}₁ and ³{D}₁ partial-waves with J^P=1⁺. No resonance enhancement is anticipated in the flavour exotic isospin-2 channel and as such it provides an ideal testing ground for this first calculation. I work at heavier than physical quark masses at the \text{SU}(3)_\text{F} point where the up, down and strange quarks are mass degenerate. Finite-volume spectra are calculated and, utilising the relationship between the discrete energy spectrum and the infinite-volume scattering amplitudes, partial-wave amplitudes with $J \le 3$ and the degree of dynamical mixing between the coupled ³{S}₁ and ³{D}₁ channels are determined. In Chapter 4, I investigate \rhoπ in isospin-1 where the a₁ axial-vector resonance is expected to feature. Here, I present a discussion on $G$-parity and Bose-symmetry at the \text{SU}(3)_\text{F} point. Working at heavier than physical quark masses, the resulting finite volume spectrum suggests that the a₁ is a bound-state and that the ³{S}₁- and ³{D}₁-wave, \rhoπ scattering amplitudes are similar to those in isospin-2. I present the first calculation of coupled πω and π\phi scattering in Chapter 5 where resonant enhancement is seen experimentally in the J^P=1⁺ channel. Working at a somewhat lighter pion mass than in previous chapters, the finite-volume spectra are determined and the scattering amplitudes are calculated. Analytically continuing the amplitudes into the complex energy plane, a resonance pole is found, interpreted as the analogue of the b₁ axial-vector, which couples dominantly to ³{S}₁-wave πω, with a much-suppressed coupling to ³{D}₁-wave πω, and a negligible coupling to π\phi. In Chapter 6, the exotic J^PC=1^-+ channel is studied. These quantum numbers are not allowed in the quark model but can be obtained, for example, through a gluonic excitation coupled to a quark-antiquark pair. In this exploratory calculation, performed at the \text{SU}(3)_\text{F} point, the finite-volume spectra and coupled-channel scattering amplitudes are presented. A single resonance pole is found, interpreted as the exotic π₁, and couplings to meson-meson channels, including for example π\eta\{¹{P}₁\}, π\eta'\{¹{P}₁\} and \rhoπ\{³{P}₁\}, are calculated for the first time in lattice QCD. In order to minimally present the contents of a unitary $n$-channel scattering matrix, I introduce, in Chapter 7, an $n$-channel generalisation of the traditional two-channel Stapp parameterisation.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2019

Author dc:creator

• Woss, Antoni James

Advisor dc:contributor.advisor

• Thomas, Christopher

• Quantum chromodynamics
• lattice
• lattice gauge theories
• hadron spectroscopy

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/68b58faa-225f-44d7-8840-cd09d4589235/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

en

Author Identifier

0000-0002-7377-8812

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/298909