Higher excitations of $\omega$ and $\phi$ in dilepton spectra

We consider lepton pair production via two-hadron annihilation through various isoscalar vector mesons within hot, baryon-free matter. This is tantamount to constructing effective form factors which we model using a vector-meson-dominance approach and compare with experiment. In particular, we consider the reactions $\pi\rho\to e^+e^-$ and $\bar K K^{*}(892)$ + c.c. $\to e^+e^-$. We find that $\omega(1390)$ and $\phi(1680)$ are visible in the mass spectrum for the thermal production rate above the $\pi^{+}\pi^{-} \to e^+e^-$ tail and even above the $\pi a_{1}\to e^+e^-$ results---both of which were considered important in their respective mass regions.