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

TL;DR

This study uses lattice QCD to analyze isospin-1/2 Dπ scattering, identifying a light scalar D0* resonance with specific mass and width, and compares it with related states, providing insights into their properties.

Contribution

The paper presents the first lattice QCD calculation of Dπ scattering amplitudes and the properties of the D0* resonance, including its mass, width, and coupling, in a single volume with near-physical pion mass.

Findings

Identified a D0* resonance with mass ~2200 MeV and width ~400 MeV.

Mapped out the elastic Dπ scattering amplitude across energy levels.

Found the D0* mass below that of the D_{s0}* contrary to experimental reports.

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 $m_\pi\approx239$ MeV. The spectrum of the elastic $D\pi$ energy region is computed yielding 20 energy levels. Using the L\"uscher 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 $\Gamma\approx400$ 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.