  Heavy quark decays provide a very advantageous investigation to test the
Standard Model (SM). Recently, promising experiments with \textit{b} quark, as
well as the analysis of the huge data sets produced at the B factories, have
led to an increasing study and sensitive measurements of relative \textit{b}
quark decays. In this thesis, I calculate various observables in the
semi-leptonic decay process $\Lambda_{b}\to \Lambda_{c}\tau\bar{\nu}_{\tau}$
both in the SM and in the presence of New Physics (NP) operators with different
Lorentz structures. The results are relevant for the coming measurement of this
semi-leptonic decay at LHC \textit{b} experiment in CERN, and also provide
theoretical predictions to refine the physics beyond the SM.
