Production rates of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> molecules in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math> decays

Abstract

Motivated by the recent discovery of a charmonium $X(3960)$ in $B$ decays by the LHCb Collaboration, the likely existence of two bound/virtual states (denoted by ${X}_{s\overline{s}}$ and ${X}_{q\overline{q}}$) below the ${D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$ and $\overline{D}D$ mass thresholds has been reexamined recently. In this work, we employ the effective Lagrangian approach to calculate their production rates in $B$ decays utilizing triangle diagrams. Our results show that the production yields of ${B}^{+}\ensuremath{\rightarrow}{X}_{s\overline{s}}{K}^{+}$ and ${B}^{+}\ensuremath{\rightarrow}{X}_{q\overline{q}}{K}^{+}$ are of the order of ${10}^{\ensuremath{-}4}$, in agreement with the relevant experimental data, which indicates that, if the ${D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$ and $\overline{D}D$ bound states indeed exist, they can be detected in $B$ decays. Moreover, we calculate the production rate of ${B}^{+}\ensuremath{\rightarrow}X(3960){K}^{+}$ assuming that $X(3960)$ is a resonant state of ${D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$ and find that it is also of the order of ${10}^{\ensuremath{-}4}$ but a bit smaller than that as a ${D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$ bound state.

Topics & Concepts