B→χcJK decays revisited

Recently, the hypothesis that exclusive B decays to charmonia H, such as B →HK, should factorize in the heavy quark limit and non-relativistic limit was not confirmed, when the formalism was applied to P-wave charmonium states, due to the appearance of infrared (IR) divergences. We show that factorization is recovered, if one includes the charmonium bound-state scales mcv, mcv2 into the theoretical framework, and assume them to be intermediate between the heavy quark masses mb, mc and ΛQCD. In this case the IR divergences problem is solved by the introduction of colour-octet operators, not considered before, but necessary for a consistent perturbative calculation of the decay amplitude at order αsv (NLO). The appearance of endpoint singularities at leading twist in the spectator scattering contribution to the amplitude is solved in a similar way. We then provide estimates for the branching fractions