The electromagnetic pion form factor and its phase

In this work, we employ a dispersion relation that allows to recover the electromagnetic form factor of the pion from its modulus along the unitarity cut. Unlike the standard dispersive approach, this method extends in a straightforward manner above the inelastic region, allowing us to obtain the form factor’s phase, as well as its real and imaginary parts. As applications, we extract the $P$-wave $\pi \pi$ phase shift, the octet form factor, derive bounds in the spacelike region, and offer insights into the onset of perturbative QCD.