Generalized factorization in non-leptonic two-body B-decays: a critical look Original Research Article

We reanalyze critically the generalized factorization hypothesis in non-leptonic two-body B-decays discussed recently by several authors. In particular we address the determination of the factorization scale μf and of the non-perturbative parameters ξ1NF(mb) and ξ2NF (mb) which are supposed to measure non-factorizable contributions to hadronic matrix elements with ξiNF(μf) = 0. We emphasize that both μf and ξiNF(mb) are renormalization scheme dependent and we demonstrate 3nalytically and numerically that for any chosen scale μf = O(mb) it is possible to find a renormalization scheme for which ξ1NF(μf) = ξ2NF(μf) = 0. The existing data indicate that such “factorization schemes” differ from the commonly used schemes NDR and HV. Similarly we point out that the recent extractions of the effective number of colours Neff from two-body non-leptonic B-decays while μ and renormalization scheme independent suffer from gauge dependences and infrared dependences.