Holographic description of heavy-flavored baryonic matter decay involving glueball

Abstract

We holographically investigate the decay of heavy-flavoured baryonic hadron involving glueball by using the Witten-Sakai-Sugimoto model. Since baryon in this model is recognized as the D4-brane wrapped on $S^{4}$ and the glueball field is identified as the bulk gravitational fluctuations, the interaction of the bulk graviton and the baryon brane could be naturally interpreted as glueball-baryon interaction through the holography which is nothing but the close-open string interaction in string theory. In order to take account into the heavy flavour, an extra pair of heavy-flavoured branes separated from the other flavour branes with a heavy-light open string is embedded into the bulk. Due to the finite separation of the flavour branes, the heavy-light string creates massive multiplets which could be identified as the heavy-light meson fields in this model. As the baryon brane on the other hand could be equivalently described by the instanton configuration on the flavour brane, we solve the equations of motion for the heavy-light fields with the Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton solution for the $N_{f}=2$ flavoured gauge fields. Then with the solutions, we evaluate the soliton mass by deriving the flavoured onshell action in strongly coupling limit and heavy quark limit. After the collectivization and quantization, the quantum mechanical system for glueball and heavy-flavoured baryon is obtained in which the effective Hamiltonian is time-dependent. Finally we use the standard technique for the time-dependent quantum mechanical system to analyze the decay of heavy-flavoured baryon involving glueball and we find one of the decay process might correspond to the decay of baryonic B-meson involving the glueball candidate $f_{0}\left(1710\right)$. This work is a holographic approach to study the decay of heavy-flavoured hadron in nuclear physics.