Mass splittings and matrix elements of mesons and baryons containing a single heavy quark

We present a study in the quenched approximation of the $B$ parameter $B_B$ and the decay constant $f_B$ using heavy-quark propagators implemented in the static approximation, and light-quark propagators computed using an $O(a)$-improved fermion action. We find a value of $\Bbstat$ close unity, and discuss the systematic errors entering into the calculation. $\fbstat$ is extracted using a variational fitting technique in order to obtain a reliable estimate of the ground state. In the second part of the talk, we describe an exploratory study of baryons containing a single heavy quark, computed using the $O(a)$-improved fermion action. We obtain masses generally in good agreement with experiment in both the charm and beauty sectors. We also report preliminary results for the form factor $G_1$ in the semi-leptonic $\Lambda_b \rightarrow \Lambda_c$ transition.