Bound States of the Heavy Flavor Vector Mesons and Y(4008) and $Z^{+}_1(4050)$

TL;DR

This paper investigates the possible bound states of heavy flavor vector mesons using a one boson exchange model, predicting certain molecular states and analyzing their likelihood and experimental signatures.

Contribution

It provides a detailed dynamical study of $D^{*}ar{D}^{*}$ and $B^{*}ar{B}^{*}$ systems, predicting specific molecular states and their quantum numbers, which is a novel application of the one boson exchange model to these systems.

Findings

Certain $B^{*}ar{B}^{*}$ molecules with specific quantum numbers are predicted to exist.

$D^{*}ar{D}^{*}$ bound states with the same quantum numbers are likely.

Y(4008) is unlikely to be a $D^{*}ar{D}^{*}$ molecule due to its large width.

Abstract

The $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ systems are studied dynamically in the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and $\omega$ exchanges are taken into account. Ten allowed states with low spin parity are considered. We suggest that the $1^{--}$, $2^{++}$, $0^{++}$ and $0^{-+}$ $B^{*}\bar{B}^{*}$ molecules should exist, and the $D^{*}\bar{D}^{*}$ bound states with the same quantum numbers very likely exist as well. However, the CP exotic ($1^{-+}$, $2^{+-}$) $B^{*}\bar{B}^{*}$ and $D^{*}\bar{D}^{*}$ states may not be bound by the one boson exchange potential. We find that the I=0 configuration is more deeply bound than the I=1 configuration, hence $Z^{+}_1(4050)$ may not be a $D^{*}\bar{D}^{*}$ molecule. Although Y(4008) is close to the $D^{*}\bar{D}^{*}$ threshold, the interpretation of Y(4008) as a $D^{*}\bar{D}^{*}$ molecule is not favored by its huge width. $1^{--}$ $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ states can be produced copiously in $e^{+}e^{-}$ annihilation, detailed scanning of the $e^{+}e^{-}$ annihilation data near the $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ threshold is an important check to our predictions.