DK I = 0, $$ D\overline{K} $$ I = 0, 1 scattering and the $$ {D}_{s0}^{\ast } $$(2317) from lattice QCD
Gavin K. C. Cheung, Christopher E. Thomas, David J. Wilson, Graham Moir, Michael Peardon, Sinéad M. Ryan
Abstract
A bstract Elastic scattering amplitudes for I = 0 DK and I = 0 , 1 $$ D\overline{K} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> are computed in S , P and D partial waves using lattice QCD with light-quark masses corresponding to m π = 239 MeV and m π = 391 MeV. The S -waves contain interesting features including a near-threshold J P = 0 + bound state in I = 0 DK , corresponding to the $$ {D}_{s0}^{\ast } $$ <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> (2317), with an effect that is clearly visible above threshold, and suggestions of a 0 + virtual bound state in I = 0 $$ D\overline{K} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . The S -wave I = 1 $$ D\overline{K} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> amplitude is found to be weakly repulsive. The computed finite-volume spectra also contain a deeply-bound D * vector resonance, but negligibly small P -wave DK interactions are observed in the energy region considered; the P and D -wave $$ D\overline{K} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> amplitudes are also small. There is some evidence of 1 + and 2 + resonances in I = 0 DK at higher energies.