QCD FACTOR-A(1) AND FACTOR-A(2) BEYOND LEADING LOGARITHMS VERSUS FACTORIZATION IN NONLEPTONIC HEAVY MESON DECAYS

We calculate the QCD factors a(1) and a(2), 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 mu dependence and the renormalization scheme dependence. We point out that a(1) for B-decays depends very weakly on Lambda(MS), mu and the choice of the renormalization scheme. For Lambda(MS)/((5)) = 225 +/- 85 MeV and 4 GeV less than or equal to mu less than or equal to 8 GeV we find a(1) = 1.01 +/- 0.02 in accordance with phenomenology. The lambda(MS), mu and scheme dependences of a(2) are on the other hand sizable. Interestingly, for the NDR scheme we find a(2)(NDR) = 0.20 +/- 0.05, in the ball park of recent phenomenological results and substantially larger than leading order estimates. However a(2)(HV) = 0.16 +/- 0.05 and a(2)(DRED) = 0.15 +/- 0.05. Implications of these findings for the tests of factorization in B-decays and D-decays are critically discussed.