A Levinson's theorem for particle form factors

TL;DR

This paper extends Levinson's theorem to relate the asymptotic phase behavior of particle form factors to their underlying electromagnetic interaction properties.

Contribution

It introduces a specialized version of Levinson's theorem for analyzing the asymptotic phases of form factors in particle physics.

Findings

Form factors are multi-valued complex functions with phases tending to multiples of π.

The theorem links phase asymptotics to hadron electromagnetic interaction properties.

Provides a theoretical framework for analyzing form factor phase behavior.

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.