Isospin-1/2 $D\pi$ scattering and the lightest $D_0^{\ast }$ resonance from lattice QCD

Abstract

Isospin-1/2 $D\pi$ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately $(3.6\mathrm{fm}{)}^3$ and with a light quark mass corresponding to $m_{\pi }\approx 239$ MeV. The spectrum of the elastic $D\pi$ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic $D\pi$ scattering. By analytically continuing a range of scattering amplitudes, a $D_0^{\ast }$ resonance pole is consistently found strongly coupled to the $S$-wave $D\pi$ channel, with a mass $m\approx 2200$ MeV and a width $\Gamma \approx 400$ MeV. Combined with earlier work investigating the $D_{s0}^{\ast }$, and $D_0^{\ast }$ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $D_0^{\ast }$ is consistently found well below that of the $D_{s0}^{\ast }$, in contrast to the currently reported experimental result.

Comments: 40 pages, 15 figures. Various small changes to match the version accepted by JHEP