Study of the semileptonic decay \Lambda_b^0 \to \Lambda_c^+ l^- \bar{\nu}_l

Within the framework of a nonrelativistic quark model we evaluate the six form factors associated to the \Lambda_b^0 \to \Lambda_c^+ l^- \bar{\nu}_l semileptonic decay. The baryon wave functions were evaluated using a variational approach applied to a family of trial functions constrained by Heavy Quark Symmetry (HQS). We use a spectator model with only one-body current operators. For these operators we keep up to first order terms on the internal (small) heavy quark momentum, but all orders on the transferred (large) momentum. Our result for the partially integrated decay width is in good agreement with lattice calculations. Comparison of our total decay width to experiment allows us to extract the V_{cb} Cabbibo-Kobayashi-Maskawa matrix element for which we obtain a value of |V_{cb}|=0.047\pm 0.005 in agreement with a recent determination by the DELPHI Collaboration. Furthermore, we obtain the universal Isgur-Wise function with a slope parameter \rho^2=0.98 in agreement with lattice results.