$$B^0 \rightarrow D^0 \bar{D}^0 K^0$$ B 0 → D 0 D ¯ 0 K 0 , $$B^+ \rightarrow D^0 \bar{D}^0 K^+$$ B + → D 0 D ¯ 0 K + , and the scalar $$D \bar{D}$$ D D ¯ bound state

L R Dai,Ju-Jun Xie,E Oset

doi:10.1140/epjc/s10052-016-3946-7

Abstract

We study the $B^0$ decay to $D^0 \bar D^0 K^0$ based on the chiral unitary model that generates the X(3720) resonance, and make predictions for the $D^0 \bar D^0$ invariant mass distribution. From the shape of the distribution, the existence of the resonance below threshold could be induced. We also predict the rate of production of the X(3720) resonance to the $D^0 \bar D^0$ mass distribution with no free parameters.

Highlights

IntroductionThe chiral Lagrangians can be obtained from a more general framework, which includes vector mesons, the local hidden gauge approach [14,15,16,17]
The chiral Lagrangians can be obtained from a more general framework, which includes vector mesons, the local hidden gauge approach [14,15,16,17]. In this picture the chiral Lagrangians are obtained by exchanging vector mesons between the pseudoscalar mesons. This picture is most welcome because it allows us to extend the dynamics of the chiral Lagrangians to the heavy quark sector, and the interaction of D D, for instance, would be given by the exchange of light vector mesons
Heavy vector mesons could be exchanged, but their large mass makes the contributions of these terms subdominant, and the dominant terms, where the heavy quarks act as spectators [18,19], automatically satisfy the rules of heavy quark spin symmetry (HQSS) [20,21]

Summary

Introduction

The chiral Lagrangians can be obtained from a more general framework, which includes vector mesons, the local hidden gauge approach [14,15,16,17]. The study of B and D weak decays looking at resonances in the final state, or threshold behavior of invariant mass distributions, has shown that these reactions have a potential to tell us about the existence of “hidden” resonances and their nature In this sense, in [27] a natural explanation was given, in terms of the f0(500), f0(980) as dynamically generated resonances [5,11], for the experimental facts that in the Bs0 → J/ψπ +π − reaction the f0(980) was clearly observed and no trace of the f0(500) was seen [28], while in the case of the B0 decay, the f0(500) was seen and only a minor fraction of the f0(980) was observed [29]. Our study indicates that the B0 → D0 D 0 K 0 reactions is better suited than the B+ → D0 D 0 K + one to give information on that state

Formalism

Complementary test of the molecular nature of the resonances

Results

Further considerations

Conclusions