Experimental tests of factorization in charmless nonleptonic two-body<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>decays

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 nonleptonic decays $\stackrel{\ensuremath{\rightarrow}}{B}PP,PV,VV,$ involving the lowest-lying light pseudoscalar $(P)$ and vector $(V)$ mesons in the standard model. We work out the parametric dependence of the decay rates, making use of the currently available information on the weak mixing matrix elements, form factors, decay constants, and quark masses. 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 $\stackrel{\ensuremath{\rightarrow}}{B}\mathrm{PP}$ decays ${(B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\eta}}^{\ensuremath{'}}, {B}^{0}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\eta}}^{\ensuremath{'}}, {B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}, {B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}^{0},$ and charge conjugates) are dominated by the ${N}_{c}$-stable QCD penguin transitions (class-IV transitions) and their estimates are consistent with the data. The measured charmless $\stackrel{\ensuremath{\rightarrow}}{B}\mathrm{PV} {(B}^{+}\ensuremath{\rightarrow}\ensuremath{\omega}{K}^{+}, {B}^{+}\ensuremath{\rightarrow}\ensuremath{\omega}{h}^{+})$ and $\stackrel{\ensuremath{\rightarrow}}{B}\mathrm{VV}$ transition $(\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{K}^{*}),$ on the other hand, belong to the penguin (class-V) and tree (class-III) transitions. The class-V penguin transitions are ${N}_{c}$ sensitive and/or involve large cancellations among competing amplitudes, making their decay rates in general more difficult to predict. Some of these transitions may also receive significant contributions from annihilation and/or final state interactions. We propose a number of tests of the factorization framework in terms of the ratios of branching ratios for some selected $\stackrel{\ensuremath{\rightarrow}}{B}{h}_{1}{h}_{2}$ 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 $\stackrel{\ensuremath{\rightarrow}}{B}{h}_{1}{h}_{2}$ decays on the CKM phenomenology is emphasized by analyzing a number of decay rates in the factorization framework.