Analysis of two-body nonleptonicBdecays involving light mesons in the standard model

We report a theoretical analysis of the exclusive nonleptonic decays of the $B^{\pm }$ and $B^0$ mesons into two light mesons, some of which have been measured recently by the CLEO Collaboration. Our analysis is carried out in the context of an effective Hamiltonian based on the standard model (SM), using next-to-leading order perturbative QCD calculations. We explicitly take into account the $O\left({\alpha }_s\right)$ penguin-loop diagrams of all four-Fermi operators and the $O\left({\alpha }_s\right)$ tree-level diagram of the chromomagnetic dipole operator, and give a prescription for including their effects in nonleptonic two-body decays. Using a factorization ansatz for the hadronic matrix elements, we show that existing data, in particular, the branching ratios $\mathcal{B}{(B}^{\pm }\to {\eta }^{\prime }{K}^{\pm }),\hspace{0.5em}\hspace{0.5em}\mathcal{B}{(B}^{\pm }\to {\pi }^{\pm }{K}^0),\hspace{0.5em}\hspace{0.5em}\mathcal{B}\left(B^0{(B}^0¯\right)\to {\pi }^{\mp }{K}^{\pm })$, and $\mathcal{B}{(B}^{\pm }\to \omega h^{\pm }{\left)\right(h}^{\pm }={\pi }^{\pm }{,K}^{\pm })$, can be accounted for in this approach. Thus, theoretical scenarios with a substantially enhanced Wilson coefficient of the chromomagnetic dipole operator (as compared to the SM) and/or those with a substantial color-singlet $c\overline{c}$ component in the wave function of ${\eta }^{\prime }$ are not required by these data. We predict, among other decay rates, the branching ratios for the decays $B^0{(B}^0¯)\to {\pi }^{\pm }{\pi }^{\mp }$ and $B^{\pm }\to {\pi }^0{\pi }^{\pm }$, which are close to the present experimental limits. Implications of some of these measurements for the parameters of the CKM matrix are presented.