Combined nonrelativistic constituent quark model and heavy quark effective theory study of semileptonic decays ofΛbandΞbbaryons

Abstract

We present the results of a nonrelativistic constituent quark model study of the semileptonic decays $\Lambda_b^0 \to \Lambda_c^+ l^- {\bar \nu}_l$ and $\Xi_b^0 \to \Xi_c^+ l^- {\bar \nu}_l$. We work on coordinate space, with baryon wave functions recently obtained from a variational approach based on heavy quark symmetry . We develop a novel expansion of the electroweak current operator, which supplemented with heavy quark effective theory constraints, allows us to predict the baryon form factors and the decay distributions for all $q^2$ (or equivalently $w$) values accessible in the physical decays. Our results for the partially integrated longitudinal and transverse decay widths, in the vicinity of the $w=1$ point, are in excellent agreement with lattice calculations. Comparison of our integrated $\Lambda_b-$decay width to experiment allows us to extract the $V_{cb}$ Cabbibo-Kobayashi-Maskawa matrix element for which we obtain a value of $|V_{cb}| = 0.040\pm 0.005 ({\rm stat}) ^{+0.001}_{-0.002} ({\rm theory})$ also in excellent agreement with a recent determination by the DELPHI Collaboration from the exclusive ${\bar {\rm B}^0_{\rm d}} \to {\rm D}^{*+}l^-{\bar \nu}_l$ decay. Besides for the $\Lambda_b (\Xi_b)-$decay, the longitudinal and transverse asymmetries, and the longitudinal to transverse decay ratio are $<a_L >=-0.954\pm 0.001 (-0.945\pm 0.002)$, $<a_T >=-0.665\pm 0.002 (-0.628\pm 0.004)$ and $R_{L/T}=1.63\pm 0.02 (1.53\pm 0.04)$, respectively.