<i>D</i>₁ and <i>D</i>₂ resonances in coupled-channel scattering amplitudes from lattice QCD

Abstract

Abstract Isospin-1/2 charmed axial-vector D ∗ π − D ∗ η −

$$ {D}_s^{\ast}\overline{K} $$

D s ∗

K ¯

scattering amplitudes are computed, along with interactions in several other I = 1/2 J

P channels. Using lattice QCD, we work at a light-quark mass corresponding to m

π ≈ 391 MeV, where the lowest three-hadron threshold (Dππ) lies high enough to enable a rigorous treatment of this system considering only two-hadron scattering channels. At this light-quark mass, an axial-vector D 1 bound state is observed just below D ∗ π threshold, that is strongly coupled to D ∗ π in a relative S-wave and influences a wide energy region up to the D ∗ η threshold. An axial-vector

$$ {D}_1^{\prime } $$

D 1 ′

resonance is observed in the elastic D ∗ π energy-region, which is coupled more strongly to D-wave D ∗ π. A single narrow tensor state is seen in J

P = 2+ coupled to both Dπ and D ∗ π. In the region where D ∗ η and

$$ {D}_s^{\ast}\overline{K} $$

D s ∗

K ¯

are kinematically open, the available energy levels indicate significant S-wave interactions. Upon searching this region for poles, several possibilities exist with large uncertainties. One additional state consistently arises, predominantly coupled to the S-wave D ∗ π − D ∗ η −

$$ {D}_s^{\ast}\overline{K} $$

D s ∗

K ¯

amplitudes around the upper energy limit of this analysis.