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

Abstract

In the heavy quark limit, the heavy baryon ${\Lambda }_Q$ (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 ${\Lambda }_Q$ in the leading order of $1/m_Q$ 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 ${\Lambda }_b\to {\Lambda }_c$ is obtained numerically from our model. Comparison with other model calculations are also presented. It seems that the Isgur-Wise function for ${\Lambda }_b\to {\Lambda }_c$ drops faster than that for $B\to D$. The differential and total decay widths for ${\Lambda }_b\to {\Lambda }_{c}l\bar{\nu }$ are given in the limit $m_{b,c}\to \infty$.

Comments: 14 pages, 4 Postscript figures