Nonfactorization and the decays $D_s^+ \to ϕπ^+, ϕρ^+$ and $ϕl^+ ν_l$

In six chosen scenarios for the $q^2$ dependence of the form factors involved in $D_s^+ \rightarrow ϕ$ transition, we have determined the allowed domain of $x = A_2(0) / A_1(0)$ and $y = V(0)/A_1(0)$ from the experimentally measured ratios $R_{sl} = Γ(D_s^+ \rightarrow ϕl^+ ν_l)/Γ(D_s^+ \rightarrow ϕπ^+)$ and $R_h = Γ(D_s^+ \rightarrow ϕρ^+)/Γ(D_s^+ \rightarrow ϕπ^+)$ in a scheme that uses the $N_c =3$ value of the phenomenological parameter $a_1$ and includes nonfactorized contribution. We find that the experimentally measured values of $x$ and $y$ from semileptonic decays of $D_s^+$ favor solutions which have significant nonfactorized contribution, and, in particular, $R_{sl}$ favors solutions in scenarios where $A_1(q^2)$ is either flat or decreasing with $q^2$.

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