  We calculate two- and three-body decays of the (lightest) vector glueball
into (pseudo)scalar, (axial-)vector, as well as pseudovector and excited vector
mesons\textbf{ }in the framework of a model of QCD. While absolute values of
widths cannot be predicted because the corresponding coupling constants are
unknown, some interesting branching ratios can be evaluated\textbf{ }by setting
the mass of the yet hypothetical vector glueball to $3.8$ GeV as predicted by
quenched Lattice QCD\textbf{.} We find that the decay mode $\omega\pi\pi$
should be one of the largest (both through the decay chain
$\mathcal{O}\rightarrow b_{1}\pi\rightarrow$ $\omega\pi\pi$ and through the
direct coupling $\mathcal{O}\rightarrow\omega\pi\pi$)$.$ Similarly, the (direct
and indirect) decay into $\pi KK^{\ast}(892)$ is sizable. Moreover, the decays
into $\rho\pi$ and $K^{\ast}(892)K$ are, although subleading, possible and
could play a role in explaining the $\rho\pi$ puzzle of the charmonium state
$\psi(2S)$ thank to a (small) mixing with the vector glueball. The vector
glueball can be directly formed at the ongoing BESIII experiment as well as at
the future PANDA experiment at the FAIR facility. If the width is sufficiently
small ($\lesssim100$ MeV) it should not escape future detection. It should be
stressed that the employed model is based on some inputs and simplifying
assumptions: the value of glueball mass (at present, the quenched lattice value
is used), the lack of mixing of the glueball with other quarkonium states, and
the use of few interaction terms. It then represents a first step toward the
identification of the main decay channels of the vector glueball, but shall be
improved when corresponding experimental candidates and/or new lattice results
will be available.
