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, $D_s ^+ \rightarrow \phi \pi^+$, 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 $D\rightarrow \bar{K}\pi, \bar{K} \rho, \bar{K}^{*} \pi, D_s^+ \rightarrow \eta \pi^+$, $\eta' \pi^+$, $\eta \rho^+ ,\eta' \rho^+$, and for $B^0 \rightarrow D^- \pi^+$ and $D^- \rho^+$ from the hadronic and semileptonic decay data.