{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/298909"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/298909","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"The scattering of spinning hadrons from lattice QCD","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.","abstract_html":"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 JP=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 JP=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 JPC=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.","abstract_has_math":true,"creators":["Woss, Antoni James"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Thomas, Christopher"],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-30","date_published":"2019-11-30","updated_at":"2026-07-22T22:24:31Z","subjects":["Quantum chromodynamics","lattice","lattice gauge theories","hadron spectroscopy"],"languages":["en"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/68b58faa-225f-44d7-8840-cd09d4589235/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000273778812"],"render_values":[{"text":"0000-0002-7377-8812","href":"https://orcid.org/0000-0002-7377-8812","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.45966","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Thomas, Christopher"]},{"key":"dc:creator","label":"Author","values":["Woss, Antoni James"]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000273778812"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2019-11-30"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/298909"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Quantum chromodynamics","lattice","lattice gauge theories","hadron spectroscopy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/68b58faa-225f-44d7-8840-cd09d4589235/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.45966"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/8f1f58be-a4ff-4291-86f5-af8e102b9408/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["4358bf5f0f802071e701fda49fceadb5","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["The scattering of spinning hadrons from lattice QCD"]}]}],"canonical_facts":{"dc:contributor.advisor":["Thomas, Christopher"],"dc:creator":["Woss, Antoni James"],"dc:creator.authoridentifier":["0000000273778812"],"dc:date.issued":["2019-11-30"],"dc:description.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."],"dc:format.checksum.md5":["4358bf5f0f802071e701fda49fceadb5","87eda9de84448d1f82354d60eee3eb5f"],"dc:identifier.doi":["10.17863/CAM.45966"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/8f1f58be-a4ff-4291-86f5-af8e102b9408/download"],"dc:language":["en"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/298909"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/68b58faa-225f-44d7-8840-cd09d4589235/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["Quantum chromodynamics","lattice","lattice gauge theories","hadron spectroscopy"],"dc:title":["The scattering of spinning hadrons from lattice QCD"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:31Z"}