Charm and anti-charm quarks combine to form “charmonium” mesons that produce a dense spectrum of states around 3 times more massive than the proton. Experiments such as LHCb at CERN have found several new unexpected resonances (short-lived states) in this energy region and work is underway to understand their origin by identifying the underlying degrees of freedom.

Quantum Chromodynamics (QCD) is the theory of the strong interactions, but the quarks and gluons of QCD interact with such strength that making predictions from the fundamental equations is challenging. A first principles, systematically-improvable approach is lattice QCD where the equations are solved numerically in a finite, discretised spacetime using large computational facilities such as DiRAC.

In this work [arXiv:2309.14070,arXiv:2309.14071], we computed the scattering amplitudes of many hadron-hadron combinations containing a pair of charm and a pair of light quarks to improve our understanding of these systems. Working with unphysically-heavy light quarks corresponding to a pion mass of 391 MeV, we find resonant enhancements in scalar (spin J=0, parity P=+ and charge-conjugation C=+) and tensor (J=2, P=+, C=+) quantum numbers in the scattering of specific hadron-hadron pairs, along with strong couplings between some of the channels. The upper part of the figure shows the scalar scattering amplitudes where sharp features can be seen in the D-anti-D meson channels just below 4000 MeV. These features can be traced back to a pole singularity corresponding to an unstable resonance. The mass and width of the resonance are shown in the lower part of the figure along with its couplings to some channels — several couplings are found to be large and significant. This and similar results for tensor quantum numbers show that these isolated resonances have an impact on multiple final states.

Significant progress has been made experimentally in recent years, but the picture in these systems is not yet fully resolved. Our work suggests that some of the experimental observations may have a common underlying dynamical origin. Thus simplification and consolidation of some of the observations may be possible through use of coupled-channel scattering amplitudes to connect features observed in different final states.