We search for a $B$ decay mode where one can find a peak for a $D\overline{D}$ bound state predicted in effective theories and in lattice QCD calculations, which has also been claimed from some reactions that show an accumulated strength in $D\overline{D}$ production at threshold. We find a good candidate in the $B^{+}\to K^{+}\eta \eta$ reaction, by looking at the $\eta \eta$ mass distribution. The reaction proceeds via a first step in which one has the $B^{+}\to D_s^{*+}{\overline{D}}^0$ reaction followed by $D_s^{*+}$ decay to $D^0{K}^{+}$ and a posterior fusion of $D^0{\overline{D}}^0$ to $\eta \eta$, implemented through a triangle diagram that allows the $D^0{\overline{D}}^0$ to be virtual and to produce the bound state. The choice of $\eta \eta$ to see the peak is based on results of calculations that find the $\eta \eta$ among the light pseudoscalar channels with stronger coupling to the $D\overline{D}$ bound state. We find a neat peak around the predicted mass of that state in the $\eta \eta$ mass distribution, with an integrated branching ratio for $B^{+}\to K^{+}$ ($D\overline{D}$, bound); ($D\overline{D}$, bound) $\to \eta \eta$ of the order of $1.5\times {10}^{-4}$, a large number for hadronic $B$ decays, which should motivate its experimental search.

• Received 25 July 2023
• Accepted 8 August 2023

DOI:https://doi.org/10.1103/PhysRevD.108.054004

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Published by the American Physical Society