The Inverse Problem: Extracting Time-Like from Space-Like Data

Abstract

A practical strategy is presented and successfully implemented to determine form factors in the time-like but unphysical (below threshold) region using dispersion relations, in a model independent way without any bias towards expected resonances. Space and time-like data have been employed along with a regularization scheme to unfold and solve the integral equations. Remarkably, resonance structures with peaks for the $\rho(770)$, $\rho'(1600)$ and a structure near the $N\bar N$ threshold are automatically generated. The $\Phi$ peak is invisible thus refuting suggestions about any sizeable $s\bar s$ content in the nucleon.