Dispersion Calculation of Isoscalar3πandKK¯Electromagnetic Form Factors

Abstract

Using dispersion theory and the assumption that the three-pion cut is well represented by the $\ensuremath{\rho}\ensuremath{\pi}$ cut, the $I=0$, $J=1 \ensuremath{\rho}\ensuremath{\pi}$ and $K\overline{K}$ scattering amplitudes are calculated from a matrix integral equation, using only right-hand cuts, in an effective-range-type approximation. Subtraction constants are determined by the experimental masses and widths of the isoscalar vector resonances. There are no ghosts (spurious first-sheet poles) in the model. The $\ensuremath{\rho}\ensuremath{\pi}$ and $K\overline{K}$ isoscalar form factors are calculated and compared to the available ${e}^{+}{e}^{\ensuremath{-}}$ colliding-beam data near the $\ensuremath{\omega}$ and $\ensuremath{\varphi}$ masses. The isoscalar charge radii are also computed. The agreement of the model with the experimental values is satisfactory. An estimate $\ensuremath{\Gamma}(\ensuremath{\rho}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\gamma})\ensuremath{\simeq}40$ keV is obtained (the decay has not yet been observed).