  We study the spectroscopy of the states which defy conventional $c\bar{c}$
charmonium and $b\bar{b}$ bottomonium interpretation respectively, and are
termed as exotic states. In August 2003 a state X(3872), was discovered [K.
Abe\textit{\ et al.} (Belle Collaboration), Phys. Rev. Lett. \textbf{91},
262001 (2003) [arXiv:hep-ex/0309032]] and in December 2007 a state Y(10890) was
reported [K. F. Chen \textit{et. al.} [Belle Collaboration], Phys. Rev. Lett.
\textbf{100}, 112001 (2008) [arXiv:0710.2577]. One possible interpretation of
such exotic state is that they are tetraquark (diquark-antiquark) states.
Applying knowledge of non-relativistic constituent quark model, we calculate
the spectrum of hidden charm and bottom exotic mesons within
diquark-antidiquark model. We investigate that X(3872) is $1^{++}$ state of the
kind $X_{[cq]}=([cq]_{S=1}[ \bar{c}\bar{q}]_{S=0})_{S\mathrm{-wave}}$, and
Y(10890) is $1^{--}$ state of the kind
$Y_{[bq]}=([bq]_{S=0}[\bar{b}\bar{q}]_{S=0})_{\mathrm{P-wave}}$ and calculate
the decay modes of these exotic states, further supporting X(3872) and Y(10890)
as tetraquark (diquark-antidiquark) states and resolve the puzzling features of
the data. We study the radiative decays of these states, using the idea of
Vector Meson Dominance (VMD), which we hope will increase an insight about
these tetraquark states.
