The scattering of spinning hadrons from lattice QCD
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Authors
Advisors
Thomas, Christopher
Date
2019-11-30Awarding Institution
University of Cambridge
Author Affiliation
Department of Applied Mathematics and Theoretical Physics
Qualification
Doctor of Philosophy (PhD)
Language
English
Type
Thesis
Metadata
Show full item recordCitation
Woss, A. J. (2019). The scattering of spinning hadrons from lattice QCD (Doctoral thesis). https://doi.org/10.17863/CAM.45966
Abstract
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 $\rho \pi$ scattering in isospin-2. Here, $\rho\pi$ 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 $\rho\pi$ in isospin-1 where the $a_1$ 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 $a_1$ is a bound-state and that the $^3{S}_1$- and $^3{D}_1$-wave, $\rho\pi$ scattering amplitudes are similar to those in isospin-2.
I present the first calculation of coupled $\pi\omega$ and $\pi\phi$ 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 $b_1$ axial-vector, which couples dominantly to $^3{S}_1$-wave $\pi\omega$, with a much-suppressed coupling to $^3{D}_1$-wave $\pi\omega$, and a negligible coupling to $\pi\phi$.
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 $\pi_1$, and couplings to meson-meson channels, including for example $\pi\eta\{^1{P}_1\}$, $\pi\eta'\{^1{P}_1\}$ and $\rho\pi\{^3{P}_1\}$, 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.
Keywords
Quantum chromodynamics, lattice, lattice gauge theories, hadron spectroscopy
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.45966
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