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We explore the potential of a combined analysis of the decays$\tau^{-}\to\pi^{-}\pi^{0}\nu_{\tau}$ and $\tau^{-}\to K^{-}K_{S}\nu_{\tau}$ inthe determination of the $\rho(1450)$ and $\rho(1700)$ resonance properties inthe frame of resonance Chiral Theory supplemented by dispersion relations. Onthe one hand, we take advantage of the very precise data on the modulus squaredof the pion vector form factor $|F_{V}^{\pi}|^{2}$ obtained by Belle to carryout a very dedicated analysis of the region where these resonances come up intoplay. Our study provides an improved treatment of the systematic theoreticalerrors and, as a most important result, we conclude that they dominate over thefit uncertainties in the determination of the $\rho(1450)$ and $\rho(1700)$pole parameters and tend to be larger than in other determinations quoted inthe literature where these errors were ignored or underestimated. The resultsof our analysis are summarized in numerical tables for the form factor modulusand phase, including both statistical and systematic errors, that can be foundas ancillary material of this paper. As a byproduct, we also determine thelow-energy observables of the pion vector form factor and the $\rho$-poleposition. On the other hand, we benefit from the recent experimental data forthe transition $\tau^{-}\to K^{-}K_{S}\nu_{\tau}$ released by BaBar to performa first analysis of its decay spectrum and discuss the role of these resonancesin this decay. We point out that higher-quality data on the $K^{-}K_{S}$ decaychannel will allow compete with the $|F_{V}^{\pi}|^{2}$ ones and improve thedetermination of the $\rho(1450)$ and $\rho(1700)$ resonance parameters as aresult of a combined analysis. We hope our study to be of interest for presentand future experimental analysis of these decays.

A dispersive analysis of the pion vector form factor and $\tau^{-}\to K^{-}K_{S}\nu_{\tau}$ decay