Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD
Luke Gayer, Nicolas Lang, Sinéad M. Ryan, David Tims, Christopher E. Thomas, David J. Wilson
Abstract
A bstract 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 $$ {D}_0^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> 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 $$ {D}_{s0}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> , and $$ {D}_0^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> 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 $$ {D}_0^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> , in contrast to the currently reported experimental result.