Production rates of $D_{s}^{+}D_{s}^{-}$ and $D\bar{D}$ molecules in $B$ decays

TL;DR

This paper calculates the production rates of certain meson molecules in B decays, showing they are within experimental detection range, and explores their possible nature as bound or virtual states related to recent discoveries.

Contribution

It employs an effective Lagrangian approach to estimate production rates of $D_{s}^{+}D_{s}^{-}$ and $ar{D}D$ molecular states in B decays, providing theoretical support for their experimental observation.

Findings

Production yields are around 10^{-4}, consistent with experimental data.

Bound or virtual states can be detected in B decays if they exist.

The production rate of X(3960) as a D_s^+D_s^- resonance is comparable, slightly smaller than that of bound states.

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\bar{s}}$ and $ X_{q\bar{q}}$) below the $D_{s}^{+}D_{s}^{-}$ and $\bar{D}D$ mass thresholds has been re-examined 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 $B^{+}\to X_{s\bar{s}} K^{+}$ and $B^{+}\to X_{q\bar{q}} K^{+}$ are of the order of $10^{-4}$, in agreement with the relevant experimental data, which indicates that, if the $D_{s}^{+}D_{s}^{-}$ and $\bar{D}D$ bound states indeed exist, they can be detected in $B$ decays. Moreover, we calculate the production rate of $B^{+}\to X(3960) K^{+}$ assuming that $X(3960)$ is a resonant state of $D_{s}^{+}D_{s}^{-}$ and find that it is also of the order of $10^{-4}$ but a bit smaller than that as a $D_s^+D_s^-$ bound state.