  We consider the properties of the ground state of bottomium. The $\Upsilon$
mass is evaluated to two loops, and including leading higher order
[$O(\alpha_s^5\log\alpha_s)$] and $m_c^2/m_b^2$ corrections. This allows us to
present updated values for the pole mass and $\bar{MS}$ mass of the $b$ quark:
$m_b=5022\pm58$ MeV, for the pole mass, and $\bar{m}_b(\bar{m}_b)=4286\pm36$
MeV for the $\bar{MS}$ one. The value for the \msbar mass is accurate including
and $O(\alpha_s^3)$ corrections and leading orders in the ratio $m_c^2/m_b^2$.
We then consider the wave function for the ground state of $\bar{b}b$, which is
calculated to two loops in the nonrelativistic approximation. Taking into
account the evaluation of the matching coefficients by Beneke and Signer one
can calculate, in principle, the width for the decay $\Upsilon\to e^+e^-$ to
order $\alpha_s^5$. Unfortunately, given the size of the corrections it is
impossible to produce reliable numbers. The situation is slightly better for
the ground state of toponium, where a decay width into $e^+e^-$ of 11 -- 14 keV
is predicted.
