Experimental Tests of Factorization in Charmless Non-Leptonic Two-Body B Decays

Abstract

Using a theoretical framework based on the next-to-leading order QCD-improved effective Hamiltonian and a factorization Ansatz for the hadronic matrix elements of the four-quark operators, we reassess branching fractions in two-body non-leptonic decays $B\to PP,PV,VV$, involving the lowest lying light pseudoscalar $(P)$ and vector $(V)$ mesons in the standard model. Using the sensitivity of the decay rates on the effective number of colors, $N_c$, as a criterion of theoretical predictivity, we classify all the current-current (tree) and penguin transitions in five different classes. The recently measured charmless two-body $B\to PP$ decays $(B^{+}\to K^{+}{\eta }^{\prime },B^0\to K^0{\eta }^{\prime },B^0\to K^{+}{\pi }^{-},B^{+}\to {\pi }^{+}{K}^0$ and charge conjugates) are dominated by the $N_c$-stable QCD penguins (class-IV transitions) and their estimates are consistent with data. The measured charmless $B\to PV$ $(B^{+}\to \omega K^{+},B^{+}\to \omega h^{+})$ and $B\to VV$ transition $(B\to \varphi K^{\ast })$, on the other hand, belong to the penguin (class-V) and tree (class-III) transitions. The class-V penguin transitions are in general more difficult to predict. We propose a number of tests of the factorization framework in terms of the ratios of branching ratios for some selected $B\to h_1{h}_2$ decays involving light hadrons $h_1$ and $h_2$, which depend only moderately on the form factors. We also propose a set of measurements to determine the effective coefficients of the current-current and QCD penguin operators. The potential impact of $B\to h_1{h}_2$ decays on the CKM phenomenology is emphasized by analyzing a number of decay rates in the factorization framework.

Comments: 64 pages (LaTex) including 13 figures, requires epsfig.sty; submitted to Phys. Rev. D