QCD Factors a1 and a2 Beyond Leading Logarithms Versus Factorization in Non-Leptonic Heavy Meson Decays

Abstract

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 $\text{Lms}$, $\mu$ and the choice of the renormalization scheme. For ${\text{Lms}}^{(5)}=225\pm 85MeV$ and $4GeV\le \mu \le 8GeV$ we find $a_1=1.01\pm 0.02$ in accordance with phenomenology. The $\text{Lms}$, $\mu$ and scheme dependences of $a_2$ are on the other hand sizable. Interestingly, for the NDR scheme we find $a_2^{NDR}=0.20\pm 0.05$, in the ball park of recent phenomenological results and substantially larger than leading order estimates. However $a_2^{HV}=0.16\pm 0.05$ and $a_2^{DRED}=0.15\pm 0.05$. Implications of these findings for the tests of factorization in B-decays and D-decays are critically discussed.

Comments: 17 pages, MPI-PhT/94-60, TUM-T31-75/94. (LATEX FILE) (no figures)