Isospin-1/2 Dπ scattering and the lightest D 0 ∗ $$ {D}_0^{\ast } $$ resonance from lattice QCD

Abstract

Abstract Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to m π ≈ 239 MeV. The spectrum of the elastic Dπ 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 Dπ scattering. By analytically continuing a range of scattering amplitudes, a D 0 ∗ $$ {D}_0^{\ast } $$ resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the D s 0 ∗ $$ {D}_{s0}^{\ast } $$ , and D 0 ∗ $$ {D}_0^{\ast } $$ 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 ∗ $$ {D}_0^{\ast } $$ is consistently found well below that of the D s 0 ∗ $$ {D}_{s0}^{\ast } $$ , in contrast to the currently reported experimental result.

Keywords

• Lattice QCD
• Lattice Quantum Field Theory