The data on the electromagnetic pion form factor and P-wave isovector ππ phase-shift are definitely consistent

Abstract

The data for the absolute value of the pion form factor (free of the omega-meson contribution) are combined with the P-wave isovector pi pi phase-shift. The resultant real and imaginary parts of the pion form factor are described by means of a Pade-type approximation. All the data which involve pion form factor experimental points from the range of momenta -0.8432 GeV²2, the pion charge radius and the P-wave isovector pi pi phase-shift in the elastic region (including also the generally accepted value of the scattering length a₁¹) are mutually consistent. The data themselves reveal through a Pade-type approximation that the consistency can be achieved only if the pion form factor left-hand cut from the second Riemann sheet is taken into account. In almost all the Pade-type approximations considered one stable pion form factor zero is found in the space-like region; this might indicate the existence of a diffraction minimum in the differential cross section for elastic e^- pi scattering as a consequence of the constituent structure of the pion, as in the case of electron elastic scattering on nuclei.