Nonleptonic $\Lambda_b$ decays to $D_s(2317)$, $D_s(2460)$ and other final states in Factorization

Abstract

We consider nonleptonic Cabibbo--allowed $\Lambda_b$ decays in the factorization approximation. We calculate nonleptonic decays of the type $ \Lambda_b \to \Lambda_c P $ and $ \Lambda_b \to \Lambda_c V $ relative to $\bar{B}_d \to D^+ P$ and $\bar{B}_d \to D^+ V$ where we include among the pseudoscalar states(P) and the vector states(V) the newly discovered $D_s$ resonances, $D_s(2317)$ and $D_s(2460)$. In the ratio of $\Lambda_b$ decays to $D_s(2317)$ and $D_s(2460)$ relative to the $\bar{B}_d$ decays to these states, the poorly known decay constants of $D_s(2317)$ and $D_s(2460)$ cancel leading to predictions that can shed light on the nature of these new states. In general, we predict the $\Lambda_b$ decays to be larger than the corresponding $\bar{B}_d$ decays and in particular we find the branching ratio for $\Lambda_b \to \Lambda_c D_s(2460)$ can be between four to five times the branching ratio for $\bar{B}_d \to D^+ D_s(2460)$. This enhancement of $\Lambda_b$ branching ratios follows primarily from the fact that more partial waves contribute in $\Lambda_b$ decays than in $\bar{B}_d$ decays. Our predictions are largely independent of model calculations of hadronic inputs like form factors and decay constants.