<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3960</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> seen in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>−</mml:mo></mml:msubsup></mml:math> as the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3930</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> state seen in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>D</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>
M. Bayar, A. Feijoo, E. Oset
Abstract
We perform a calculation of the interaction of the $D\overline{D}$, ${D}_{s}{\overline{D}}_{s}$ coupled channels and find two bound states, one coupling to $D\overline{D}$ and another one at higher energies coupling mostly to ${D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$. We identify this latter state with the ${X}_{0}(3930)$ seen in the ${D}^{+}{D}^{\ensuremath{-}}$ mass distribution in the ${B}^{+}\ensuremath{\rightarrow}{D}^{+}{D}^{\ensuremath{-}}{K}^{+}$ decay, and also show that it produces an enhancement of the ${D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$ mass distribution close to threshold which is compatible with the recent LHCb observation in the ${B}^{+}\ensuremath{\rightarrow}{D}_{s}^{+}{D}_{s}^{\ensuremath{-}}{K}^{+}$ decay which has been identified as a new state, ${X}_{0}(3960)$.