Can the Pion's Charge Radius be Large?

Abstract

Analyticity has been used to derive dispersive inequalities which bound the spacelike behavior of the pion's charge form factor in terms of the timelike variation of the modulus of the form factor and the $p$-wave $\pi \pi$ scattering phase shift. The large charge radius, suggested by the Serpukhov-UCLA measurement of $\pi e$ scattering, is only compatible with timelike data which involve a large $p$-wave $\pi \pi$ phase shift just above threshold.