  The analytical expressions and the numerical values of the renormalisation
constants of ${\cal O}(a)$ improved static-light currents are given at one-loop
order of perturbation theory in the framework of Heavy Quark Effective Theory:
the static quark is described by the HYP action and the light quark is
described either with the Clover or the Neuberger action. These factors are
relevant to extract from a lattice computation the decay constants $f_B$,
$f_{B_S}$ and the set of bag parameters $B_i$ associated with $B-\bar{B}$
mixing phenomenology in the Standard Model and beyond.
