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Heavy quark decays provide a very advantageous investigation to test theStandard Model (SM). Recently, promising experiments with \textit{b} quark, aswell as the analysis of the huge data sets produced at the B factories, haveled to an increasing study and sensitive measurements of relative \textit{b}quark decays. In this thesis, I calculate various observables in thesemi-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 differentLorentz structures. The results are relevant for the coming measurement of thissemi-leptonic decay at LHC \textit{b} experiment in CERN, and also providetheoretical predictions to refine the physics beyond the SM.

Semi-leptonic Decay of Lambda-b in the Standard Model and with New Physics