DK I = 0, D I = 0, 1 scattering and the from lattice QCD

DK I = 0, D I = 0, 1 scattering and the from lattice QCD

Published in JHEP 02 (2021) 100 [arXiv:2008.06432]

Much of observable strongly interacting matter can be understood in terms of the quark model whereby hadrons are composed of a quark and an antiquark or three quarks. In recent years significant deviations have been observed from quark model expectations, including unexpected experimental results for hadrons composed predominantly of a charm quark and a strange antiquark. In particular, the  was found much lower in mass than was expected.

Quantum chromodynamics (QCD) is the theory of strongly interacting matter, and in this work, we applied state-of-the-art numerical lattice QCD methods to help understand the enigmatic , and other closely-related systems. We found a bound state in DK scattering in S­­-wave (i.e. with no relative angular momentum) that resembles the experimental state and is strongly influenced by the nearby DK kinematic threshold. One useful feature of lattice QCD is the ability to vary the quark masses, and this can help us better understand why a state has a certain mass and what its composition is. We used two different light-quark masses – the D and K mesons both contain a light quark and so are strongly dependent on this – and found that the state becomes less bound as the light-quark masses are reduced from a heavy value to a value closer to that found in experiment.

The figure shows the computed DK scattering amplitudes for the lighter light-quarks (left) and the heavier light-quarks (right). The more rapid rise in the S-wave amplitude at DK threshold in the left plot is due to the bound state being closer to threshold and so having a stronger influence. The observed strong coupling of this state to S-wave DK is suggestive of a large molecular DK component – this is not included in the quark model and may account for a significant portion of difference between the observed mass and the expected mass. This study also laid vital groundwork for a more recent preprint [arXiv:2102.04973] investigating the closely related  resonance in S-wave D  scattering.

We also investigated manifestly exotic D  scattering, mapping out the scattering amplitudes for the first time – any states in this channel cannot be composed of solely a quark and an antiquark, and require (at least) two quarks and two antiquarks. While this is difficult to produce experimentally, in the calculation we found attraction in isospin-0 D  and evidence for a virtual bound state (attraction but not strong enough to form a bound state). Further calculations to investigate if an exotic bound state is present in analogous systems with different quark masses will be very interesting.

This work was made possible in part through the DiRAC Data Intensive Service hosted at the University of Cambridge.

Figure: DK scattering amplitudes (related to the scattering cross section) computed using lattice QCD shown in red (S-wave) and green (P-wave) at two light-quark masses. The rapid rise in the S-wave amplitudes is found to be due to a bound state that is closer to threshold at the lighter light-quark mass corresponding to a pion mass mp = 239 MeV (left) compared with the heavier light-quark mass corresponding to mp = 391 MeV (right).