DK/Dπ scattering and an exotic virtual bound state at the SU(3) flavour symmetric point from lattice QCD
J. Daniel E. Yeo, Christopher E. Thomas, David J. Wilson
Abstract
A bstract Elastic S -wave scattering of a charm meson with a light pseudoscalar meson in J P = 0 + is investigated in the flavour $$ \overline{\textbf{3}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mn>3</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , 6 and $$ \overline{\textbf{15}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mn>15</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> sectors at the SU(3) f flavour point using lattice QCD, working on three volumes with m π ≈ 700 MeV. Large bases of interpolating operators are employed to extract finite-volume spectra, which are subsequently used with the Lüscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, the S -wave amplitude in the flavour $$ \overline{\textbf{3}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mn>3</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the $$ {J}^P={0}^{+}\ {D}_{s0}^{\ast }(2317) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>J</mml:mi> <mml:mi>P</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>+</mml:mo> </mml:msup> <mml:mspace/> <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:mfenced> <mml:mn>2317</mml:mn> </mml:mfenced> </mml:math> . In the exotic flavour 6 sector a virtual bound state is found at $$ \sqrt{s_{\textrm{pole}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mtext>pole</mml:mtext> </mml:msub> </mml:msqrt> </mml:math> = 2510 – 2610 MeV, roughly 40 – 140 MeV below threshold, whereas the $$ \overline{\textbf{15}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mn>15</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> channel shows weak repulsion.