Isgur-Wise Function for ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ in B-S Approach

In the heavy quark limit, the heavy baryon ${\mathrm{\Lambda }}_Q$ (Q=b or c) can be regarded as composed of a heavy quark and a scalar light diquark which has good spin and flavor quantum numbers. Based on this picture we establish the Bethe-Salpeter (B-S) equation for ${\mathrm{\Lambda }}_Q$ in the leading order of $1\mathrm{/}{m}_Q$ expansion. With the kernel containing both the scalar confinement and one-gluon-exchange terms we solve the B-S equation numerically. The Isgur-Wise function for ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ is obtained numerically from our model. Comparison with other model calculations are also presented. It seems that the Isgur-Wise function for ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ drops faster than that for $B \to D$\mathrm{.}Thedifferentialandtotaldecaywidthsfor$\Lambda_b \to \Lambda_c l \bar{\nu}$aregiveninthelimit$m_{b,c}\to \infty$.