Pion electromagnetic formfactor in the space-like region and $P$-phase $\delta^1_1(s)$ of $\pi\pi$ scattering from the value of the modulus of formfactor in the time-like region.

Abstract

The problem of determining the pion electromagnetic formfactor $F(q^2)$ in the space-like region from the value of its modulus in the time-like region is solved by the formfactor analyticity. If $F(q^2)$has no zeroes in the complex plane then the formfactor in the space-like region is determined uniquely. If $F(q^2)$has zeroes in the complex plane $q^2$ it can be obtained in the space-like region within narrow limits using experimental data from the time-like region. The formfactor phase $\phi(s)$ which coincides with the $P$-wave phase $\delta^1_1(s)$ of the $\pi\pi$ scattering is calculated. The value of the pion radius has been improved.