arXiv subjects

Christopher E. Thomas

Publications and source records attributed to Christopher E. Thomas.

At least 19 recordsLinked to original sources

arXiv2026

Exotic $T^_{csJ}$ and $T^_{c\bar{s}J}$ states and coupled-channel scattering at the $SU(3)$ flavour symmetric point from lattice QCD

Motivated by recent experimental observations of the flavour-exotic $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, we present the first lattice QCD study of coupled-channel scattering of a charm meson with a light meson in the flavour-exotic sectors at the $SU(3)_f$ flavour symmetric point. Utilising five volumes with $m_π\approx 700$ MeV and employing large bases of meson-meson operators, finite-volume spectra are extracted and used to constrain infinite-volume scattering amplitudes with $J^P = \{0, 1, 2, 3, 4\}^+$ via the Lüscher formalism. In the flavour $\mathbf{6}$ sector, each $S$-wave channel considered is found to be attractive with the scattering amplitudes having an associated pole singularity on an unphysical sheet below threshold, giving six flavour-exotic poles in the energy region constrained. In $J^P = 0^+$ there is a virtual bound state and a resonance. The latter is identified with the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, appearing as one state in the $SU(3)_f$ flavour symmetric limit, and suggests the existence of an isospin-$\frac{1}{2}$ partner. In $J^P =1^+$ there are three poles, one of which is identified as a $J^P =1^+$ partner of the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, and $J^P =2^+$ contains one pole which is identified as their $J^P =2^+$ partner. Only mild interactions and no poles are seen in the $J^P = \{3, 4\}^+$ scattering amplitudes. In the flavour $\overline{\mathbf{15}}$ sector, weak interactions are observed in $J^P = \{0, 1, 2, 3, 4\}^+$ with no well-determined poles in the energy region constrained.

hep-lat↗

arXiv2026

$D\bar{D}$ interactions are weak near threshold in QCD

We study near-threshold $D\bar{D}$ scattering in $S$ and $D$-wave to determine whether or not resonances or bound states are present. Working in the approximation where charm-annihilation is forbidden, with two degenerate light-quark flavors and a heavier strange quark, isospin is a good quantum number, and the only other other channel that is kinematically open is $\eta_c\eta$. Using lattice QCD we compute, as a function of varying light-quark mass, the $S$-matrix for coupled-channel $\eta_c\eta - D\bar{D}$ scattering and find only weakly interacting meson pairs. In contrast to several other studies, we find no evidence for any bound-state or resonance singularity in the energy region between the deeply-bound $\chi_{c0}(1P)$ state and the $D_s\bar{D}_s$ threshold.

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arXiv2026

Coupled-channel scattering of $DD, DD^$ and $D^ D^*$ in isospin-$1$ from lattice QCD

The first coupled-channel determination of two-body $D$ and $D^*$ scattering amplitudes in isospin-$1$ from lattice quantum chromodynamics is presented. Using three lattice volumes at $m_π\approx 391~\mathrm{MeV}$, finite-volume energies relevant for the channels of interest are determined. Through the Lüscher formalism, these energies are used to constrain amplitudes of coupled $J^P=0^+$ $DD - DD^*$, $J^P=1^+$ $DD^*- D^*D^*$ and $J^P=2^+$ $DD - DD^* - D^* D^*$ scattering. All channels feature weakly repulsive interactions in $S$ wave, except for a weak $D^* D^*$ attraction in $J^P=0^+$. No amplitude singularities corresponding to physical states are found. Some of these amplitudes will be a necessary component of future lattice QCD analyses of $DDπ$ and $DD^*$ scattering taking into account three-body and left-hand cut effects.

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arXiv2025

Isotensor $πππ$ scattering with a $ρ$ resonant subsystem from QCD

This work presents a lattice quantum chromodynamics (QCD) determination of $πππ$ scattering amplitudes for the isospin-2 channel with angular momentum and parity $J^{P} = 1^+$. The calculation is performed using unphysically heavy light-quark masses, corresponding to a pion mass of $m_π \approx 400$~MeV, for which the $ρ$ meson manifests as a narrow resonance. The analysis employs a previously developed formalism that non-perturbatively relates the finite-volume spectra of two- and three-pion systems to their infinite-volume scattering amplitudes. We combine earlier lattice QCD results for $ππ$ systems with isospins 1 and 2 with new determinations of the isospin-2 three-pion finite-volume spectrum, obtained for three cubic, periodic lattice volumes with box length ranging from $\approx 4/m_π$ to $6/m_π$. These combined data constrain the low-lying partial waves of the infinite-volume three-pion K matrix, from which we solve a set of coupled integral equations to extract the corresponding scattering amplitudes.

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arXiv2025

Near-threshold states in coupled $DD^{\ast}-D^{\ast}D^{\ast}$ scattering from lattice QCD

The first determination of doubly-charmed isospin-0 coupled-channel $DD^\ast-D^\ast D^\ast$ scattering amplitudes from lattice QCD is presented. The finite-volume spectrum is computed for three lattice volumes with a light-quark mass corresponding to $m_π\approx 391$ MeV and is used to extract the scattering amplitudes in $J^P = 1^+$ via the Lüscher quantization condition. By analytically continuing the scattering amplitudes to complex energies, a $T_{cc}$ pole corresponding to a virtual bound state is found below $DD^\ast$ threshold. We also find a second pole, $T_{cc}^\prime$, corresponding to a resonance pole below the kinematically closed $D^\ast D^\ast$ channel, to which it has a strong coupling. A non-zero coupling is robustly found between the $S$-wave $D D^\ast$ and $D^\ast D^\ast$ channels producing a clear cusp in the $D D^\ast$ amplitude at the $D^\ast D^\ast$ threshold energy. This suggests that the experimental $T_{cc}^\prime$ should be observable in $D D^\ast$ and $D^\ast D^\ast$ final states at ongoing experiments.

hep-lat↗

arXiv2024

$DK/Dπ$ scattering and an exotic virtual bound state at the $SU(3)$ flavour symmetric point from lattice QCD

Elastic $S-$wave scattering of a charm meson with a light pseudoscalar meson in $J^P =0^+$ is investigated in the flavour $\bar{\mathbf{3}}$, $\mathbf{6}$ and $\overline{\mathbf{15}}$ sectors at the $SU(3)_f$ flavour point using lattice QCD, working on three volumes with $m_π \approx 700$ MeV. Large bases of interpolating operators are employed to extract finite-volume spectra, which are subsequently used with the Lüscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, the $S-$wave amplitude in the flavour $\bar{\mathbf{3}}$ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the $J^P = 0^+$ $D_{s0}^*(2317)$. In the exotic flavour $\mathbf{6}$ sector a virtual bound state is found at $\sqrt{s_{\rm{pole}}} = 2510 - 2610$ MeV, roughly $40-140$ MeV below threshold, whereas the $\overline{\mathbf{15}}$ channel shows weak repulsion.

hep-lat↗

arXiv2024

Radiative Transitions in Charmonium from Lattice QCD

The coupling of various charmonium mesons to a photon is studied using lattice QCD, giving access to radiative form factors and transitions, and probing the mesons' structure. Methods are developed which allow the robust determination of amplitudes, including those involving an excited state as well as multiple form factors, for a range of kinematics. These are applied in dynamical lattice QCD calculations using the distillation technique to compute the underlying three-point correlation functions. Form factors and amplitudes involving the low-lying charmonia, $η_c$, $J/ψ$, $χ_{c0}$ and $η_c'$, are calculated, demonstrating the methods and providing the first dynamical lattice QCD results for some quantities.

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arXiv2023

Charmonium $χ_{c0}$ and $χ_{c2}$ resonances in coupled-channel scattering from lattice QCD

In order to explore the spectrum of hidden-charm scalar and tensor resonances, we study meson-meson scattering with $J^{PC}=0^{++}, 2^{++}$ in the charmonium energy region using lattice QCD. Employing a light-quark mass corresponding to $m_π\approx 391$ MeV, we determine coupled-channel scattering amplitudes up to around 4100 MeV considering all kinematically relevant channels consisting of a pair of open-charm mesons or a charmonium meson with a light meson. A single isolated scalar resonance near 4000 MeV is found with large couplings to $D\bar{D}$, $D_s \bar{D}_s$ and the kinematically closed $D^* \bar{D}^*$ channel. A single tensor resonance at a similar mass couples strongly to $D\bar{D}$, $D\bar{D}^*$ and $D^* \bar{D}^*$. We compare the extracted resonances to contemporary experimental candidate states, previous lattice results and theoretical modeling. In contrast to several other studies, we do not find any significant feature in the scalar amplitudes between the ground state $χ_{c0}(1P)$ and the resonance found around 4000 MeV.

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arXiv2023

Scalar and tensor charmonium resonances in coupled-channel scattering from QCD

We determine $J^{PC}=0^{++}$ and $2^{++}$ hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at $m_π\approx 391$ MeV, more than 200 finite-volume energy levels are computed and these are used in extensions of the Lüscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single $χ_{c0}$ and a single $χ_{c2}$ resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically-closed $D^* \bar{D}^*$ channels in $S$-wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state $χ_{c0}$, no other scalar bound-states or near-$D\bar{D}$ threshold resonances are found, in contrast to several theoretical and experimental studies.

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arXiv2022

Hadron Spectroscopy with Lattice QCD

The status and prospects for investigations of exotic and conventional hadrons with lattice QCD are discussed. The majority of hadrons decay strongly via one or multiple decay-channels, including most of the experimentally discovered exotic hadrons. Despite this difficult challenge, the properties of several hadronic resonances have been determined within lattice QCD. To further discern the spectroscopic properties of various hadrons and to help resolve their nature we present our suggestions for future analytic and lattice studies.

hep-lat↗

arXiv2021

Isospin-1/2 $Dπ$ scattering and the lightest $D_0^\ast$ resonance from lattice QCD

Isospin-1/2 $Dπ$ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately $(3.6\; \mathrm{fm})^3$ and with a light quark mass corresponding to $m_π\approx239$ MeV. The spectrum of the elastic $Dπ$ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic $Dπ$ scattering. By analytically continuing a range of scattering amplitudes, a $D_0^\ast$ resonance pole is consistently found strongly coupled to the $S$-wave $Dπ$ channel, with a mass $m\approx 2200$ MeV and a width $Γ\approx400$ MeV. Combined with earlier work investigating the $D_{s0}^\ast$, and $D_0^\ast$ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $D_0^\ast$ is consistently found well below that of the $D_{s0}^\ast$, in contrast to the currently reported experimental result.

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arXiv2021

Decays of an exotic $1^{-+}$ hybrid meson resonance in QCD

We present the first determination of the hadronic decays of the lightest exotic $J^{PC}=1^{-+}$ resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange quark masses approximately match the physical strange-quark mass giving $m_π\sim 700$ MeV, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open pseudoscalar--pseudoscalar, vector--pseudoscalar and vector--vector decay channels, but large couplings to at least one kinematically-closed axial-vector--pseudoscalar channel. Attempting a simple extrapolation of the couplings to physical light-quark mass suggests a broad $π_1$ resonance decaying dominantly through the $b_1 π$ mode with much smaller decays into $f_1 π$, $ρπ$, $η' π$ and $ηπ$. A large total width is potentially in agreement with the experimental $π_1(1564)$ candidate state, observed in $ηπ$, $η' π$, which we suggest may be heavily suppressed decay channels.

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arXiv2021

The energy-dependent $π^+ π^+ π^+$ scattering amplitude from QCD

Focusing on three-pion states with maximal isospin ($π^+π^+π^+$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.

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arXiv2021

$DK$ $I=0,$ $D\bar{K}$ $I=0,1$ scattering and the $D_{s0}^\ast(2317)$ from lattice QCD

Elastic scattering amplitudes for $I=0$ $DK$ and $I=0,1$ $D\bar{K}$ are computed in $S$, $P$ and $D$ partial waves using lattice QCD with light-quark masses corresponding to $m_π= 239$ MeV and $m_π= 391$ MeV. The $S$-waves contain interesting features including a near-threshold $J^P=0^+$ bound state in $I=0$ $DK$, corresponding to the $D_{s0}^\ast(2317)$, with an effect that is clearly visible above threshold, and suggestions of a $0^+$ virtual bound state in $I=0$ $D\bar{K}$. The $S$-wave $I=1$ $D\bar{K}$ amplitude is found to be weakly repulsive. The computed finite-volume spectra also contain a deeply-bound $D^\ast$ vector resonance, but negligibly small $P$-wave $DK$ interactions are observed in the energy region considered; the $P$ and $D$-wave $D\bar{K}$ amplitudes are also small. There is some evidence of $1^+$ and $2^+$ resonances in $I=0$ $DK$ at higher energies.

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arXiv2020

The $XYZ$ states: experimental and theoretical status and perspectives

The quark model was formulated in 1964 to classify mesons as bound states made of a quark-antiquark pair, and baryons as bound states made of three quarks. For a long time all known mesons and baryons could be classified within this scheme. Quantum Chromodynamics (QCD), however, in principle also allows the existence of more complex structures, generically called exotic hadrons or simply exotics. These include four-quark hadrons (tetraquarks and hadronic molecules), five-quark hadrons (pentaquarks) and states with active gluonic degrees of freedom (hybrids), and even states of pure glue (glueballs). Exotic hadrons have been systematically searched for in numerous experiments for many years. Remarkably, in the past fifteen years, many new hadrons that do not exhibit the expected properties of ordinary (not exotic) hadrons have been discovered in the quarkonium spectrum. These hadrons are collectively known as $XYZ$ states. Some of them, like the charged states, are undoubtedly exotic. Parallel to the experimental progress, the last decades have also witnessed an enormous theoretical effort to reach a theoretical understanding of the $XYZ$ states. Theoretical approaches include not only phenomenological extensions of the quark model to exotics, but also modern non-relativistic effective field theories and lattice QCD calculations. The present work aims at reviewing the rapid progress in the field of exotic $XYZ$ hadrons over the past few years both in experiments and theory. It concludes with a summary on future prospects and challenges.

hep-ex↗

arXiv2019

The $b_1$ resonance in coupled $πω$, $πϕ$ scattering from lattice QCD

We present the first lattice QCD calculation of coupled $πω$ and $πϕ$ scattering, incorporating coupled $S$ and $D$-wave $πω$ in $J^P=1^+$. Finite-volume spectra in three volumes are determined via a variational analysis of matrices of two-point correlation functions, computed using large bases of operators resembling single-meson, two-meson and three-meson structures, with the light-quark mass corresponding to a pion mass of $m_π\approx 391$ MeV. Utilizing the relationship between the discrete spectrum of finite-volume energies and infinite-volume scattering amplitudes, we find a narrow axial-vector resonance ($J^{PC}=1^{+-}$), the analogue of the $b_1$ meson, with mass $m_{R}\approx1380$ MeV and width $Γ_{R}\approx 91$ MeV. The resonance is found to couple dominantly to $S$-wave $πω$, with a much-suppressed coupling to $D$-wave $πω$, and a negligible coupling to $πϕ$ consistent with the `OZI rule'. No resonant behavior is observed in $πϕ$, indicating the absence of a putative low-mass $Z_s$ analogue of the $Z_c$ claimed in $πJ/ψ$. In order to minimally present the contents of a unitary three-channel scattering matrix, we introduce an $n$-channel generalization of the traditional two-channel Stapp parameterization.

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arXiv2019

The quark-mass dependence of elastic $πK$ scattering from QCD

We present a determination of the isospin-1/2 elastic $πK$ scattering amplitudes in S and P partial waves using lattice Quantum Chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV. Below the first inelastic threshold, the P-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound-state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the S-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $κ$/$K_0^\star(700)$-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely-determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.

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arXiv2018

Dynamically-coupled partial-waves in $ρπ$ isospin-2 scattering from lattice QCD

We present the first determination of $ρπ$ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 $ρπ$, we calculate partial-wave amplitudes with $J \le 3$ and determine the degree of dynamical mixing between the coupled $S$ and $D$-wave channels with $J^P=1^+$. The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that $m_π\sim 700$ MeV, ensuring that the $ρ$ is stable against strong decay. This work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.

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