Semi-Leptonic Decays of \Lambda_c and \Lambda_b Baryons involving Heavy to Light Transitions and the determination of V_{ub}

We calculate the semi-leptonic decays of $\Lambda_c$ and $\Lambda_b$ baryons which involve transitions of a heavy quark to a light quark. In a previous work we used data on the Cabibbo favoured non-leptonic decays of charmed baryons $\Lambda_c \rightarrow \Lambda \pi^{+}$ and $\Lambda_c \rightarrow \Sigma^{+} \pi^{0 }$ to obtain information on the form factors in the $c \rightarrow s $ transition. This form factor informations is used to study the semi-leptonic decay $\Lambda_c \rightarrow \Lambda l \nu $. Using SU(3) symmetry and HQET it is shown how a knowledge of form factors in $\Lambda_c \rightarrow \Lambda l \nu $ can be applied to $\Lambda_b \rightarrow p l \nu $ decay and used to measure $|V_{ub}/V_{cs}|^{2} $.