Anatomy of the pQCD Approach to the Baryonic Decays $\Lambda_b \to p\pi, p K$

Abstract

We calculate the CP-averaged branching ratios and CP-violating asymmetries for the two-body charmless hadronic decays $\Lambda_b \to p \pi, pK$ in the perturbative QCD (pQCD) approach to lowest order in $\alpha_s$. The baryon distribution amplitudes involved in the factorization formulae are considered to the leading twist accuracy and the distribution amplitudes of the proton are expanded to the next-to-leading conformal spin (i.e., "P" -waves), the moments of which are determined from QCD sum rules. Our work shows that the contributions from the factorizable diagrams in $\Lambda_b \to p \pi, pK$ decays are much smaller compared to the non-factorizable diagrams in the conventional pQCD approach. We argue that this reflects the estimates of the $\Lambda_b \to p$ transition form factors in the $k_T$ factorization approach, which are found typically an order of magnitude smaller than those estimated in the light-cone sum rules and in the non-relativistic quark model. As an alternative, we adopt a hybrid pQCD approach, in which we compute the factorizable contributions with the $\Lambda_b \to p$ form factors taken from the light cone QCD sum rules. The non-factorizable diagrams are evaluated utilizing the conventional pQCD formalism which is free from the endpoint singularities. The predictions worked out here are confronted with the recently available data from the CDF collaboration on the branching ratios and the direct CP asymmetries for the decays $ \Lambda_b \to p \pi$, and $\Lambda_b \to p K$. The asymmetry parameter $\alpha$ relevant for the anisotropic angular distribution of the emitted proton in the polarized $\Lambda_b$ baryon decays is also calculated for the two decay modes.