# A scheme to fix multiple solutions in amplitude analyses

## TL;DR

This paper addresses the problem of multiple equivalent solutions in amplitude analyses of particle decays and proposes a scheme to resolve them by fixing certain parameters, validated through toy simulations.

## Contribution

It introduces a novel method to fix free parameters in amplitude analyses to eliminate multiple solutions, enhancing analysis accuracy.

## Key findings

- The proposed scheme effectively resolves multiple solutions in simulated data.
- A new method for aligning helicities across decay chains is developed.
- Validation with toy data confirms the approach's robustness.

## Abstract

Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better understanding of the underlying dynamics. For special cases, where two spin-1/2 particles and two (pseudo-)scalar particles are present in the process, multiple equivalent solutions are found due to intrinsic symmetries in the summed probability density function. In this paper, the problem of multiple solutions is discussed and a scheme to overcome this problem is proposed by fixing some free parameters. Toys are generated to validate the strategy. A new approach to align helicities of initial- and final-state particles in different decay chains is also introduced.