Multiple solutions in extracting physics information from experimental data

TL;DR

This paper discusses the issue of multiple mathematical solutions in extracting physical parameters from experimental data and proposes a rule to identify the physically meaningful solution based on minimal amplitude magnitudes.

Contribution

It introduces a simple rule for selecting the physical solution among multiple mathematical solutions in amplitude analysis, supported by examples and consistent with previous literature.

Findings

Multiple solutions are common in amplitude fits.

The minimal amplitude magnitude rule aligns with previous practices.

Testing this rule in future experiments is recommended.

Abstract

Multiple solutions exist in various experimental situations whenever the sum of several amplitudes is used to fit the experimentally measured distributions, such as the cross section, the mass spectrum, or the angular distribution. We show a few examples where multiple solutions were found, while only one solution was reported in the publications. Since there is no existing rules found in choosing any one of these solutions as the physics one, we propose a simple rule which agrees with what have been adopted in previous literatures: the solution corresponding to the minimal magnitudes of the amplitudes must be the physical solution. We suggest test this rule in the future experiments.