$B^+$ decay to $K^+\eta\eta$ with ($\eta\eta$) from the $D\bar{D}(3720)$ bound state

TL;DR

This paper predicts a detectable peak in the $ ext{B}^+ o ext{K}^+ ext{eta eta}$ decay channel indicating a $Dar{D}$ bound state, supported by theoretical calculations and a proposed experimental signature.

Contribution

It introduces a novel decay mechanism involving a triangle diagram to identify the $Dar{D}$ bound state in $B^+$ decays, with specific predictions for experimental observation.

Findings

A clear peak around the predicted bound state mass in $ ext{eta eta}$ mass distribution.

Estimated branching ratio of about $1.5 imes 10^{-4}$ for the decay process.

The proposed decay channel is experimentally accessible and significant for future searches.

Abstract

We search for a $B$ decay mode where one can find a peak for a $D \bar{D}$ 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 $D \bar{D}$ 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 $B^+\to D_s^{*+} \bar{D}^0$ reaction followed by $D_s^{*+}$ decay to $D^0 K^+$ and a posterior fusion of $D^0 \bar{D}^0$ to $\eta \eta$, implemented trough a triangle diagram that allows the $D^0 \bar{D}^0$ to be virtual and 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 $D \bar{D}$ 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 $B^+\to K^+$ ($D\bar{D}$, bound) ; ($D\bar{D}$, 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.