Understanding and obtaining predictions from Quantum Chromodynamics (QCD), the theory of strongly-interacting quarks and gluons, is one of the foremost problems in particle physics.

The vast majority of ordinary strongly-interacting matter is composed of protons and neutrons, themselves composed of light up and down quarks. However, the spectrum of QCD also contains excitations involving other types of quarks such as charm and strange. The lowest mass QCD states appear to be made of either three quarks, like protons and neutrons, or a quark-antiquark combination, like pions and kaons. Other combinations could exist, such as four-quark states or states with intrinsic gluons. These are thought to be unstable resonances that decay to lighter strongly-interacting particles and this obscures their nature.

Short-lived hadron resonances containing a charm quark are readily observed at hadron physics experiments such as LHCb. They are also accessible theoretically, such as in lattice QCD, a first-principles approach to QCD where calculations are performed numerically, and so are a particularly useful comparison point.

In this work [Phys. Rev. Lett. 129, 252001 (2022); arXiv:2205.05026], we used lattice QCD to study the scattering of a pion (composed of a light quark and a light antiquark) with a spin-1 (vector) D* meson (composed of a charm and an antilight quark), employing the DiRAC Data Analytic facility in Cambridge for some of the calculations. The intrinsic spin of the D* meson can combine with orbital angular momentum in different ways to produce states with the same total angular momentum. This produces a rich, dense spectrum of states with differing properties.

Working with an unphysically-large light-quark mass to suppress multihadron channels, we computed various scattering amplitudes and from these obtained the masses, widths, couplings and thus decay modes of two axial-vector D_1 mesons and a spin-2 tensor D_2 resonance. The upper panel of the figure shows the scattering amplitudes relevant for the axial-vector mesons. These two mesons have very different character: one couples dominantly to a decay mode with no orbital angular momentum (S-wave) producing a broad feature (red band), while the other couples to a decay mode with orbital angular momentum 2 (D-wave) and produces a narrow peak (green band). There is very little coupling between the two channels (orange band).

Excited hadrons can be described by pole singularities at complex energies in the scattering amplitude. The positions of the axial-vector meson poles in the complex energy plane are plotted in the middle panel of the figure. The couplings obtained from these poles are illustrated by the histograms at the bottom of the figure and demonstrate again that each couples dominantly to one decay mode. The tensor resonance was found to decay to D pi and D* pi in approximately equal amounts.

A useful theoretical comparison point is the limit where the charm quark is made infinitely heavy. In this limit four mesons arise in two doublets: the two in one doublet decay via S-wave and the other two decay via D-wave. Even though the charm quark is only 10 or so times larger than the scale of QCD interactions, we found that our results closely follow the pattern predicted from this limit. This study is the first time that it has been possible to study this in a first-principles approach to QCD.