The phase of the electromagnetic form factor of the pion

We employ a dispersion relation that allows to recover the phase of the electromagnetic form factor of the pion from its absolute value above threshold. Compared to alternative approaches building on the phase, this approach builds on experimental input directly accessible at colliders. Employing the precise datasets from the $e^+e^-\to\pi^+\pi^-$ reaction, we obtain the phase of the electromagnetic form factor up to $2.5$~GeV, well beyond standard dispersive approaches. In addition, we separate the isovector and isoscalar components, that allows to extract the $P$-wave $\pi\pi$ phase shift. We also provide relevant results, including the radius of the form factor and bounds in the spacelike region. Last, but not least, the study assess potential systematic uncertainties from the interpolation method and potential zeros of the form factor.
Comment: 25 pages, 11 figures. Results provided in ancillary file. Version accepted for publication in PRD. Includes substantial additions and discussion on systematics