Analysis of the QCD - improved factorization in B → J / ψK

We consider the exclusive decay B → J/ψK using the QCD-improved factorization method in the heavy quark limit. It is shown that the decay amplitude is factorizable in this limit and nonfactorizable contributions are calculable from first principles in perturbation theory. Also the spectator contributions at order αs are finite and suppressed in the heavy quark limit. We present the result at next-to-leading order in strong interaction, and leading order in 1/mb in the heavy quark limit. Exclusive nonleptonic decays of B mesons have received a lot of attention since they are observed in experiments at CLEO, BABAR and BELLE [1]. They offer the opportunity to test the unitarity of the Cabibbo-KobayashiMaskawa (CKM) triangle, the CP violation and to observe new physics effects. Quantitative understanding of nonleptonic decays of B mesons is difficult since there are final-state interactions which are intrinsically nonperturbative in nature. However, when there is large momentum transfer to final-state mesons such as the two-body decays of B mesons into two light mesons, we can systematically calculate the decay rate using perturbation theory in the heavy quark limit. Beneke et al. [2] considered general two-body nonleptonic decays of B mesons extensively. The general idea is that in the limit mb ≫ ΛQCD, the hadronic matrix elements can be schematically represented as 〈M1M2|O|B〉= 〈M1|j1|B〉〈M2|j2|0〉 × [ 1 + ∑ rnα n s +O(ΛQCD/mb) ] , (1) 1 e-mail address: [email protected] Preprint submitted to Elsevier Preprint 28 April 2008 where M1, M2 are final-state mesons and O is a local current-current operator in the weak effective Hamiltonian. If we neglect radiative corrections in αs and power corrections in ΛQCD, we get the factorization result with a form factor times a decay constant. At higher order in αs, this simple factorization is broken, but the corrections can be calculated systematically in terms of shortdistance Wilson coefficients and meson light-cone distribution amplitudes. We call this the QCD-improved factorization. When we use the light-cone meson wave functions for exclusive decays, the transition amplitude of an operator Oi in the weak effective Hamiltonian is given by