Particle Physics Calculations Reveal No New Exotic Meson States Near Threshold

Scientists investigate the interactions of mesons to understand the strong force that binds atomic nuclei together. David J. Wilson (DAMTP, University of Cambridge), Jozef J. Dudek (Department of Physics, College of William and Mary), Robert G. Edwards (Thomas Jefferson National Accelerator Facility) and Christopher E. Thomas et al. present a lattice QCD study of near-threshold scattering in the and channels. Their calculations, performed with a specific quark mass configuration, reveal only weakly interacting meson pairs and crucially, find no evidence for bound states or resonances between the deeply-bound state and the scattering threshold. This research is significant because it challenges previous findings suggesting the existence of such states, refining our understanding of how hadrons interact and potentially impacting models of nuclear physics.

Eta-c eta and D D meson interactions via lattice QCD

Scientists have meticulously examined near-threshold scattering of D D mesons using lattice quantum chromodynamics to ascertain the presence of bound states or resonances. Employing a framework where charm annihilation is prohibited and considering isospin symmetry, the research focused on the coupled-channel scattering of ηcη and D D mesons.
Calculations were performed across a range of light-quark masses to map the S-matrix and reveal the interactions between these meson pairs. The study demonstrates only weak interactions between the mesons, contrasting with previous investigations that suggested more complex behaviour. This work presents a detailed analysis of finite-volume spectra, utilising three light-quark masses corresponding to pion masses of approximately 239, 283 and 330 MeV.

The lattice configurations employed anisotropic lattices with 2+1 flavours of dynamical quarks, and the lattice scale was determined by matching the computed Ω baryon mass to its physical value. By extending previous calculations, researchers aimed to investigate potential dependencies of the D D scattering process on light-quark mass, addressing discrepancies found in earlier studies.

Notably, the analysis reveals no significant shifts in energy levels near the D D threshold, and the resulting scattering amplitudes exhibit no singularities indicative of bound states or resonances. This finding directly challenges earlier lattice QCD calculations which proposed the existence of a bound state below the D D threshold, alongside narrow and broad resonances at higher energies.

The results suggest that the observed spectrum is consistent with a quark model description, lacking the additional states previously reported. The research provides first-principles predictions from QCD, offering a clean theoretical framework for understanding hadron-hadron scattering. By utilising lattice QCD, the study circumvents complexities arising from experimental analyses involving progenitor particles and distorted energy dependencies, offering a more direct assessment of the underlying dynamics. These findings have implications for interpreting experimental observations of open-charm hadrons at facilities such as LHCb, Belle-II, and BES-III, and contribute to a more comprehensive understanding of the excited hadron spectrum.

Finite-volume spectra and coupled-channel scattering for resonance identification

Lattice QCD calculations underpin this work, focusing on near-threshold scattering in and to ascertain the presence of resonances or bound states. Employing a computational approach where charm-annihilation is forbidden, and with two degenerate light-quark flavors alongside a heavier strange quark, the study leverages isospin as a conserved quantum number.

The only other kinematically accessible channel is therefore considered alongside. Calculations proceeded by determining the -matrix for coupled-channel scattering, varying light-quark mass to observe any emergent phenomena. Finite spatial volume introduces a discrete spectrum, which is then used to define the scattering amplitudes. The study systematically varied the light-quark mass, performing calculations at pion masses of approximately 239, 283, and 330 MeV to explore the sensitivity of observables to these parameters.

A key innovation lies in the extension of previous work, reported in references, to lighter quark masses. This was undertaken to investigate whether discrepancies with earlier lattice QCD calculations, which proposed the existence of bound states and resonances, were attributable to light-quark mass dependence.

The team found only weakly interacting meson pairs, contrasting with other studies and revealing no evidence for bound-state or resonance singularities between the deeply-bound χc0(1P) state and the Ds Ds threshold. This rigorous analysis provides a clean theoretical prediction for comparison with experimental observations of open-charm hadron pairs.

Lattice QCD determination of light and charmed hadron masses and anisotropies

Researchers utilising lattice QCD have investigated near-threshold scattering in the coupled-channel system, focusing on isospin and the absence of charm annihilation. Analyses were performed with two degenerate light-quark flavours and a heavier strange quark, revealing only weakly interacting meson pairs.

The study employed anisotropic lattices with parameters detailed in Table I, including configurations ranging from 243 to 323 gauge configurations, vector sizes from 128 to 553, and time source numbers from 64 to 256. Anisotropies were calculated for the π, D, and ηc mesons, with ξπ values of 3.453, 3.457, and 3.456 MeV respectively, as detailed in Table III. A systematic uncertainty of δEsyst = 0.00050 was added to energy levels on the 283 MeV lattices to account for slight differences in meson masses.

Finite-volume spectra were extracted across three irreps, revealing a low-lying state in A+1 dominated by S-wave scattering, interpreted as the stable χc0(1P). The lowest state in E+, also seen in A1, corresponds to the stable χc2(1P). Above these, states with dominant overlap onto either ηcη-like or D D-like operators were observed, closely aligning with non-interacting energies.

The pattern of operator overlaps suggests limited coupling between ηcη and D D scattering channels. Specifically, the D D-like states exhibited no systematic deviations from non-interacting energies, indicating weak D D scattering and the absence of bound-states or resonances near the D D threshold. The study did not find evidence for any resonance singularity in the energy region between the deeply-bound state and the threshold, contrasting with some previous investigations.

Absence of bound states and resonances in coupled-channel meson scattering

Researchers investigated the interactions between mesons to determine the existence of bound states or resonances using lattice quantum chromodynamics. Calculations were performed with light and strange quarks, focusing on the coupled-channel scattering of particles and varying the light quark mass to observe any resulting changes.

The analysis, conducted across a range of energies between 9 MeV and 391 MeV, revealed only weak interactions between the meson pairs studied. This work demonstrates a lack of evidence for bound states or resonance singularities within the examined energy region, contrasting with some previous studies.

Specifically, the findings do not support claims of a bound state below the D D threshold or a broad resonance decaying to D D, nor do they indicate a nearly stable state at the Ds Ds threshold. The authors acknowledge that differences in lattice spacing and discretisation effects between their calculations and those of prior work may contribute to these discrepancies, with the earlier study potentially being affected by significant discretisation errors.

Furthermore, the current results suggest that any scalar resonance observed experimentally could plausibly evolve into a narrow resonance as the light quark mass increases, aligning with predictions from quark models. Future research could explore the amplitudes in the Ds Ds energy region to further investigate the stability of states containing no valence light quarks.