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, $D_s ^+ \rightarrow ϕπ^+$, 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 $D\rightarrow \bar{K}π, \bar{K} ρ, \bar{K}^{*} π, D_s^+ \rightarrow ηπ^+$, $η' π^+$, $ηρ^+ ,η' ρ^+$, and for $B^0 \rightarrow D^- π^+$ and $D^- ρ^+$ from the hadronic and semileptonic decay data.