# Noncyclic geometric phases and helicity transitions for neutrino oscillations in a magnetic field

## TL;DR

This paper investigates how geometric phases influence neutrino spin and flavor transitions in magnetic fields, providing analytical expressions and exploring effects in astrophysical environments like the Sun and neutron stars.

## Contribution

It introduces analytical formulas for noncyclic geometric phases in neutrino oscillations and analyzes their impact in rotating and nonrotating magnetic fields.

## Key findings

- Geometric phases affect neutrino spin and flavor transitions.
- Analytical expressions for noncyclic geometric phases are derived.
- Effects of magnetic field rotation and boundary crossing are examined.

## Abstract

We show that neutrino spin and spin-flavor transitions involve nonvanishing geometric phases. The geometric character of neutrino spin rotation is explored by studying the neutrino spin trajectory in the projective Hilbert space representation and its relation to the geometric phase. Analytical expressions are derived for noncyclic geometric phases. Several calculations are performed for different cases of rotating and nonrotating magnetic fields in the context of solar neutrinos and neutrinos produced inside neutron stars. Also the effects of adiabaticity, critical magnetic fields and cross boundary effects in the case of neutrinos emanating out of neutron stars are examined.