What are effective $a_1$ and $a_2$ in two-body hadronic decays of D and B mesons?

Abstract

Through a specific example of two-body color-favored charm decay, $D_s^{+}\to \varphi {\pi }^{+}$, we illustrate how an effective and complex (unitarized) $a_1$, denoted by $a_1^{U,eff}$, may be defined such that it includes nonfactorized, annihilation and inelastic final state interaction (fsi) effects. The procedure can be generalized to color-suppressed processes to define an effective, and complex $a_2^{U,eff}$. We determine $|a_1^{U,eff}|$ and, where relevant, $|a_2^{U,eff}|$ for $D\to \bar{K}\pi ,\bar{K}\rho ,{\bar{K}}^{\ast }\pi ,D_s^{+}\to \eta {\pi }^{+}$, ${\eta }^{\prime }{\pi }^{+}$, $\eta {\rho }^{+},{\eta }^{\prime }{\rho }^{+}$, and for $B^0\to D^{-}{\pi }^{+}$ and $D^{-}{\rho }^{+}$ from the hadronic and semileptonic decay data.

14 pages,Latex,no figures