Exotic charm resonances and coupled-channel scattering from lattice QCD

The standard model is the best description of particle physics to date, collectively describing the electromagnetic, weak and strong forces all under one mathematical framework. Despite its extraordinary success, large parts of the theory remain theoretically poorly understood. In particular, the strong force -- governed by a subset of the standard model called quantum chromodynamics (QCD) -- becomes a strongly-coupled quantum field theory at low energies. The strong coupling between quarks and gluons gives rise to incredibly important phenomena, most notably the confining of quarks and gluons into composite states called hadrons, of which the proton and neutron are two examples amongst many. However, this strong coupling also renders the conventional perturbative methods inapplicable, and so there is little analytical understanding of these hadrons. Here, we present work which advances our understanding of the strong force and hadron interactions using a numerical method called lattice QCD. In this method, continuous Minkowski spacetime is approximated with a finite Euclidean lattice, rendering the theory amenable to numerical simulation and thus allowing for the extraction of strongly-coupled physics in the low-energy regime of the theory. We use lattice techniques to study hadronic resonances (unstable hadrons) containing charm quarks, with a focus on exotic hadrons. These are hadrons that cannot be described by simple quark-antiquark or three-quark configurations -- a model that works well for low-energy and stable (under the strong force) hadrons. We investigate these charmed resonances through coupled-channel scattering amplitudes, determined from lattice QCD, and work with an enhanced SU(3)_f flavour symmetry where the up, down, and strange quark masses are all equal. This symmetry enables us to discern the hadronic content in these sectors, and the resulting unphysically-heavy pion mass allows us to explore the QCD spectrum over a larger energy region (using the methods outlined in this thesis). In Chapter 2, we present a brief review of QCD and scattering theory, defined in an infinite-volume continuum, and discuss how hadrons can be rigorously defined as poles in the complex-energy plane of scattering amplitudes. In Chapter 3, we introduce lattice QCD as a non-perturbative framework to study the strong force and discuss how infinite-volume continuum QCD observables can be obtained from lattice QCD calculations. In particular, we will introduce the Lüscher formalism, which provides a relationship between infinite-volume scattering amplitudes and finite-volume spectra computed from lattice QCD. After this, we present our methodology and implementation for obtaining scattering amplitudes and unstable hadrons from the Lüscher formalism in Chapter 4. In Chapter 5, we present the first project constituting this thesis, in which we investigate elastic $S$-wave scattering with J^P =0⁺ in the open-charm sector at the SU(3)_f symmetric flavour point. Working on three volumes with m_\pi \approx 700 MeV, we use large bases of interpolating operators to extract the finite-volume spectra, which are used to constrain the scattering amplitudes in each of the flavour \bar{3}, 6 and \overline{15} sectors. Upon examining the singularities of the amplitudes, the $S$-wave amplitude in the flavour \bar{3} sector is found to contain a deeply bound state, strongly coupled to elastic threshold. We identify this state with the J^P = 0⁺ D_s0^*(2317). In the exotic flavour 6 sector, a virtual bound state is found at \sqrt{s_\rm{pole}} = 2510 - 2610 MeV, roughly $40-140$ MeV below threshold. This is the first time that this charmed exotic state had been seen from a first-principles calculation of QCD. The $S$-wave amplitude in the \overline{15} sector is found to be weakly repulsive. We end the chapter with a discussion on our findings and the insights they yield regarding the hadronic content of the open-charm sector at the physical pion mass. Chapter 6 builds upon the work of Chapter 5 by venturing higher in energy and investigating the coupled-channel scattering amplitudes of the open-charm flavour-exotic sectors, again working at the symmetric flavour point. Several finite-volume spectra across five volumes are computed and used to constrain the scattering amplitudes of the J^P = \{0, 1, 2, 3, 4\}⁺ sectors via the Lüscher formalism. In the flavour 6 J^P = 0⁺ sector, a resonance is found just below inelastic threshold, predominantly coupled to the vector-vector channel, in addition to the virtual-bound state at elastic threshold which was already found in Chapter 5. We identify the resonance with the recently observed T^*_cs0(2870)⁰ and T^*_c\bar{s}0(2900), unified as a flavour 6 pole at the SU(3)_f symmetric point, suggesting the existence of an isospin-$\frac{1}{2}$ partner to these states which is currently experimentally unobserved. Additionally, resonances predominantly coupled to the vector-vector channel are found in the flavour 6 J^P=\{1, 2\}⁺ sectors, suggesting J^P = \{1, 2\}⁺ partners to the T^*_cs0(2870)⁰ and T^*_c\bar{s}0(2900). Furthermore, two more poles are found in the J^P=1⁺ sector predominantly coupled to the pseudoscalar-vector channels, whilst only mild interactions are seen in the J^P = \{3, 4\}⁺ scattering amplitudes. In the flavour \overline{15} sector, only weak attraction or weak repulsion in the energy levels are observed and no poles are robustly found on the corresponding J^P = \{0, 1, 2, 3, 4\}⁺ coupled-channel amplitudes in the energy region constrained. In Chapter 7, we present work towards determining the pattern of charmonium states. In particular, we investigate near-threshold excited \chi_cJ states, which carry the quantum numbers J^PC = J⁺⁺. We compute the spectra for several finite-volume irreducible representations and on five volumes, and from them infer qualitative features about the interactions in the hidden-charm J^PC = J⁺⁺ sectors. Our findings suggest strong interactions in the open-charm channels with possible bound states and resonances with large $c\bar{c}$ character, but only weak and decoupled interactions in the charmonia-light channels. Finally, in Chapter 8, we summarise our work and finish with an outlook, where we suggest future work which will build upon the work done for this thesis and further our understanding of QCD.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2025

Author dc:creator

• Yeo, Daniel

Advisor dc:contributor.advisor

• Thomas, christopher

• high-energy physics
• lattice gauge theory
• hadron spectroscopy
• quantum chromodynamics
• strong force
• exotic hadrons
• lattice QCD

Licence

• https://www.repository.cam.ac.uk/bitstreams/05b36b2e-15e3-443c-b569-2181eec19ddd/download
• http://purl.org/NET/rdflicense/allrightsreserved

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.130627

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/403832