Combined nonrelativistic constituent quark model and heavy quark effective theory study of semileptonic decays of Λ_b and Ξ_b baryons

Abstract

We present the results of a nonrelativistic constituent quark model study of the semileptonic decays $\hat{I}{›}_b^0\to \hat{I}{›}_c^{+}{l}^{-}{\bar{\hat{I}}½}_l$ and $\hat{I}{ž}_b^0\to \hat{I}{ž}_c^{+}{l}^{-}{\bar{\hat{I}}½}_l$. 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 $\hat{I}{›}_b-$decay width to experiment allows us to extract the $V_{cb}$ Cabbibo-Kobayashi-Maskawa matrix element for which we obtain a value of $|V_{cb}|=0.040\pm 0.005(\mathrm{stat}{)}_{-0.002}^{+0.001}(\mathrm{theory})$ also in excellent agreement with a recent determination by the DELPHI Collaboration from the exclusive ${\bar{\mathrm{B}}}_{\mathrm{d}}^0\to {\mathrm{D}}^{\ast +}{l}^{-}{\bar{\hat{I}}½}_l$ decay. Besides for the $\hat{I}{›}_b(\hat{I}{ž}_b)-$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.

17 latex pages, 4 figures. Minor changes with respect to the previous version. Accepted for publication in Physical Review D