Systematic error studies for the charged particle EDM measurement proposal

TL;DR

This paper develops a method to analyze systematic errors in charged particle EDM measurements by solving the T-BMT equation and simulating lattice imperfections, improving understanding of potential false signals.

Contribution

It introduces a novel averaging method based on the Bogoliubov-Krylov Mitropolski approach to accurately evaluate spin evolution and systematic errors in EDM experiments.

Findings

Validated the convergence of numerical simulations

Provided analytical estimates for systematic errors

Enhanced understanding of spin dynamics at the polarimeter

Abstract

Proposals aimed at measuring the Electric Dipole Moment (EDM) for charged particles require a good understanding of the systematic errors that can contribute to a vertical spin buildup mimicking the EDM signal to be detected. In what follows, a method of averaging emanating from the Bogoliubov-Krylov Mitropolski method is employed to solve the T-BMT equation and calculate the Berry phases arising for the storage ring frozen spin concept. The formalism employed proved to be particularly useful to determine the evolution of the spin at the observation point, i.e. at the location of the polarimeter. Several selected cases of lattice imperfections were simulated and benchmarked with the analytical estimates. This allowed the proof of the convergence of the numerical simulations and helped gain better understanding of the systematic errors.