Nonfactorization and the decays $D_s^{+}\to \varphi {\pi }^{+},\varphi {\rho }^{+}$ and $\varphi l^{+}{\nu }_l$

Abstract

In six chosen scenarios for the $q^2$ dependence of the form factors involved in $D_s^{+}\to \varphi$ 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 $R_{sl}=\Gamma (D_s^{+}\to \varphi l^{+}{\nu }_l)/\Gamma (D_s^{+}\to \varphi {\pi }^{+})$ and $R_h=\Gamma (D_s^{+}\to \varphi {\rho }^{+})/\Gamma (D_s^{+}\to \varphi {\pi }^{+})$ 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 $q^2$.

Comments: 15 pages, Latex, four figure (available on request);