Tetraquarks: Mesons with two $b$ quarks

We look for the existence of stable (by strong interactions) tetraquarks, mesons containing two heavy antiquarks and two light quarks, specifically a $|{\bar b}{\bar b}qq\rangle$ state. This state is viewed as two $|{\bar b}q\rangle$ particles bound by a potential due to the exchange of the four light pseudoscalar and vector mesons, namely the $\pi,\ \eta,\ \rho$ and $\omega$. Couplings of these particles are obtained by the use of heavy quark symmetry. We find that the $I=0,\ J=1$ state is bound for a large range of parameters, while all other states are not bound (the $I=1,\ J=0$ system may be bound for some parameters at the extreme range of their allowed values). We discuss the reasons why the techniques used cannot be extended to mesons containing two $c$ quarks or a $c$ and $b$ quark.