$DK$ $I=0,$ $D\bar{K}$ $I=0,1$ scattering and the $D_{s0}^{\ast }(2317)$ from lattice QCD

Abstract

Elastic scattering amplitudes for $I=0$ $DK$ and $I=0,1$ $D\bar{K}$ are computed in $S$, $P$ and $D$ partial waves using lattice QCD with light-quark masses corresponding to $m_{\pi }=239$ MeV and $m_{\pi }=391$ MeV. The $S$-waves contain interesting features including a near-threshold $J^P=0^{+}$ bound state in $I=0$ $DK$, corresponding to the $D_{s0}^{\ast }(2317)$, with an effect that is clearly visible above threshold, and suggestions of a $0^{+}$ virtual bound state in $I=0$ $D\bar{K}$. The $S$-wave $I=1$ $D\bar{K}$ amplitude is found to be weakly repulsive. The computed finite-volume spectra also contain a deeply-bound $D^{\ast }$ vector resonance, but negligibly small $P$-wave $DK$ interactions are observed in the energy region considered; the $P$ and $D$-wave $D\bar{K}$ amplitudes are also small. There is some evidence of $1^{+}$ and $2^{+}$ resonances in $I=0$ $DK$ at higher energies.

53 pages, 22 figures, small changes to match published version

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