Ds+→φρ+decay

Abstract

Motivated by the experimental measurement of the decay rate \ensuremath{\Gamma} and longitudinal polarization ${P}_{L}$ in the Cabibbo favored decay ${D}_{s}^{+}\ensuremath{\rightarrow}\ensuremath{\varphi}{\ensuremath{\rho}}^{+},$ we study theoretical predictions within the context of the factorization approximation invoking several form factor models. We obtain agreement with experiment for both \ensuremath{\Gamma} and ${P}_{L}$ by using experimentally measured values of the form factors ${A}_{1}^{{D}_{s}\ensuremath{\varphi}}(0),$ ${A}_{2}^{{D}_{s}\ensuremath{\varphi}}(0),$ and ${V}^{{D}_{s}\ensuremath{\varphi}}(0)$ in the semileptonic decay ${D}_{s}^{+}\ensuremath{\rightarrow}\ensuremath{\varphi}{l}^{+}{\ensuremath{\nu}}_{l}.$ We also include in our calculation the effect of the final state interaction by working with the partial wave amplitudes $S,$ $P,$ and $D.$ A numerical calculation shows that the decay amplitude is dominated by the $S$ wave, and that the polarization is sensitive to the interference between $S$ and $D$ waves. The range of the phase difference ${\ensuremath{\delta}}_{\mathrm{SD}}={\ensuremath{\delta}}_{S}\ensuremath{-}{\ensuremath{\delta}}_{D}$ accommodated by experimental error in ${P}_{L}$ is large.