Determination of the Photoproduction Phase of $\phi$ Mesons

We have measured wide-angle electron-positron pairs from the reaction $\gamma +\mathrm{C}\to \mathrm{C}+e^{+}+e^{-}$ in the invariant-mass region $920<m<\mathrm{}1080\mathrm{}$ MeV/${\mathit{c}}^2$ for incident photon energy $6<k<\mathrm{}7.4\mathrm{}$ GeV. The photoproduction amplitude of the $\phi$ meson was found to deviate from pure imaginary by 25° ± 15° corresponding to a ratio of the real to imaginary part of the $\phi$-nucleon amplitude of $\beta ={-0.48\mathrm{}}_{-0.45\mathrm{}}^{+0.33\mathrm{}}$. The forward photoproduction cross section ${\left[d\sigma \right(\gamma +C\to C+\phi (\phi \to e^{+}{e}^{-})\left)dt\right]}_{t=0\mathrm{}}$ was found to be 96 ± 14 nb/${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$.