A Levinson's theorem for particle form factors

Abstract

We present and demonstrate a version of Levinson's theorem especially dedicated to the asymptotic behavior of form factor phases. Indeed, as required by analyticity, form factors are multi-valued complex functions of a square four-momentum defined in the complex plane with a cut along the positive real axis. Their phases evaluated on the upper edge of this cut, i.e., on the time-like region, tend asymptotically to integer multiples of $\pi$ radians. The Levinson's theorem establishes a univocal relation between such multiples and properties of form factors related to the dynamics of the electromagnetic interaction of the corresponding hadrons.