  We examine in detail the semi-leptonic decay $\Lambda_b \to \Lambda_c
\tau{\bar \nu}_{\tau}$, which may confirm previous hints, from the analogous
$B$ decay, of a new physics beyond the standard model. First of all, starting
from rather general assumptions, we predict the partial width of the decay.
Then we analyze the effects of five possible new physics interactions, adopting
in each case five different form factors. In particular, for each term beyond
the standard model, we find some constraints on the strength and phase of the
coupling, which we combine with those found by other authors in analyzing the
analogous semi-leptonic decays of $B$. Our analysis involves some dimensionless
quantities, substantially independent of the form factor, but which, owing to
the constraints, turn out to be strongly sensitive to the kind of non-standard
interaction. We also introduce a criterion thanks to which one can discriminate
among the various new physics terms: the left-handed current and the
two-higgs-doublet model appear privileged, with a neat preference for the
former interaction. Lastly, we suggest a differential observable that could, in
principle, help to distinguish between the two cases.
