Title:

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 nonzero intrinsic spin. In this thesis, I will present the results of scattering calculations featuring mesons with nonzero 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 isospin2. Here, $\rho\pi$ features in dynamicallycoupled $^3{S}_1$ and $^3{D}_1$ partialwaves with $J^P=1^+$. No resonance enhancement is anticipated in the flavour exotic isospin2 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. Finitevolume spectra are calculated and, utilising the relationship between the discrete energy spectrum and the infinitevolume scattering amplitudes, partialwave 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 isospin1 where the $a_1$ axialvector resonance is expected to feature. Here, I present a discussion on $G$parity and Bosesymmetry 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 boundstate and that the $^3{S}_1$ and $^3{D}_1$wave, $\rho\pi$ scattering amplitudes are similar to those in isospin2. 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 finitevolume 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 $b_1$ axialvector, which couples dominantly to $^3{S}_1$wave $\pi\omega$, with a muchsuppressed 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 quarkantiquark pair. In this exploratory calculation, performed at the $\text{SU}(3)_\text{F}$ point, the finitevolume spectra and coupledchannel scattering amplitudes are presented. A single resonance pole is found, interpreted as the exotic $\pi_1$, and couplings to mesonmeson 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 twochannel Stapp parameterisation.
