Deuteron electromagnetic form factor: Data analysis and asymptotic behavior

Abstract

Available data on the deuteron electromagnetic form factor are analyzed with a view to obtaining information on its asymptotic behavior and extrapolating into the timelike region. For data analysis we adopt an $\frac{N}{D}$ method where the $N$ and the $D$ functions are assumed to represent the anomalous and the two-pion cut contributions, respectively. The $D$ function is represented by an effective-range-type formula and the $N$ function by optimized polynomial expansion in Laguerre polynomials in terms of a parabolic conformally mapped variable. Contrary to the earlier cases of data analysis on the proton and the pion form factor by such representation, the presence of the exponential weight function for Laguerre-polynomial expansion of the $N$ function provides a very effective method of parametrizing the data with economy of parameters. Existing data on $A(t)$ are consistent with an asymptotic behavior $\frac{\mathrm{exp}[\ensuremath{-}0.931{(\mathrm{ln}t)}^{2}]}{{t}^{3}}$. The deuteron charge radius is computed to be 2.02 fm. The formula smoothly extrapolates into the timelike region without showing any evidence of resonance peaks. The magnitude of the form factor near threshold of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{d}d$ is found to be $|A(14 \mathrm{Ge}{\mathrm{V}}^{2})|=1.765\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$.