QCD factors a1 and a2 beyond leading logarithms versus factorization in non-leptonic heavy meson decays Original Research Article

We calculate the QCD factors a1 and a2, entering the tests of factorization in non-leptonic heavy meson decays, beyond the leading logarithmic approximation in three renormalization schemes (NDR, HV, DRED). We investigate their μ dependence and the renormalization scheme dependence. We point out that a1 for B-decays depends very weakly on ΛMS, μ and the choice of the renormalization scheme. For ΛMS(5) = 225 ± 85 MeV and 4 GeV ⩽ μ ⩽ 8 GeV we find a1 = 1.01 ± 0.02 in accordance with phenomenology. The ΛMS, μ and scheme dependences of a2 are on the other hand sizable. Interestingly, for the NDR scheme we find a2NDR = 0.20 ± 0.05, in the ball park of recent phenomenological results and substantially larger than leading order estimates. However a2HV = 0.16 ± 0.05 and a2DRED = 0.15 ± 0.05. Implications of these findings for the tests of factorization in B-decays and D-decays are critically discussed.