On the ambiguity of determination of interfering resonances parameters

TL;DR

This paper derives the general solutions for parameters of interfering Breit-Wigner resonances, revealing the maximum number of solutions based on roots of characteristic equations and extending to complex resonance forms under certain conditions.

Contribution

It provides a comprehensive mathematical framework for understanding the ambiguity in determining interfering resonance parameters, including the maximum number of solutions and their properties.

Findings

Number of solutions does not exceed 2^{N-1} for N resonances.

Multiple solutions exist for complex resonance forms under specific amplitude conditions.

The solutions are linked to roots of a characteristic equation.

Abstract

The general form of solutions for parameters of interfering Breit-Wigner resonances is found. The number of solutions is determined by the properties of roots of corresponding characteristic equation and does not exceed $2^{N-1}$, where $N$ is the number of resonances. For resonances of more complicated form, provided that their amplitudes satisfy certain conditions, for any $N\ge2$ multiple solutions also exist.