Infinite momentum frame calculation of semileptonic heavyΛb→Λctransitions including HQET improvements

Abstract

We calculate the transition form factors that occur in heavy $\Lambda$-type baryon semileptonic decays as e.g. in $\Lambda_{b} \to \Lambda_{c}^{+} + l^{-} + \bar{\nu}_{l} $. We use Bauer-Stech-Wirbel type infinite momentum frame wave functions for the heavy $\Lambda$-type baryons which we assume to consist of a heavy quark and a light spin-isospin zero diquark system. The form factors at $ q^{2} = 0 $ are calculated from the overlap integrals of the initial and final $\Lambda$-type baryon states. To leading order in the heavy mass scale the structure of the form factors agrees with the HQET predictions including the normalization at zero recoil. The leading order $\omega$-dependence of the form factors is extracted by scaling arguments. By comparing the model form factors with the HQET predictions at ${\cal O}(1/m_{Q})$ we obtain a consistent set of model form factors up to ${\cal O}(1/m_{Q})$. With our preferred choice of parameter values we find that the contribution of the non-leading form factor is practically negligible. We use our form factor predictions to compute rates, spectra and various asymmetry parameters for the semi-leptonic decay $\Lambda_{b} \to \Lambda_{c}^{+} + l^{-} + \bar{\nu}_{l} $.