Exploration of CPT violation via time-dependent geometric quantities embedded in neutrino oscillation through fluctuating matter

TL;DR

This paper introduces a novel method using time-dependent geometric quantities, like the geometric phase on a Poincare sphere, to detect CPT violation in neutrino oscillations influenced by fluctuating matter, with potential experimental applications.

Contribution

It develops an analytic framework mapping neutrino oscillations onto a Poincare sphere and links geometric phases to CPT violation, offering a new approach for experimental detection.

Findings

The radius of the Poincare sphere depends on the CP-violating angle.

Time-dependent geometric phase is strongly enhanced during neutrino propagation.

Simulation suggests feasible detection of CPT violation via NMR-like experiments.

Abstract

We propose a new approach to explore CPT violation of neutrino oscillation through a fluctuating matter based on time-dependent geometric quantities. By mapping the neutrino oscillation onto a Poincare sphere structure, we obtain an analytic solution of master equation and further define the geometric quantities, i.e., radius of Poincare sphere and geometric phase. We find that the mixing process between electron and muon neutrinos can be described by the radius of Poincare sphere that depends on the intrinsic CP-violating angle. Such a radius reveals a dynamic mechanism of CPT-violation, i.e., both spontaneous symmetry breaking and Majorana-Dirac neutrino confusion. We show that the time-dependent geometric phase can be used to find the neutrino nature and observe the CPT-violation because it is strongly enhanced under the neutrino propagation. We further show that the time-dependent geometric phase can be easily detected by simulating the neutrino oscillation based on fluctuating magnetic fields in nuclear magnetic resonance, which makes the experimental observation of CPT-violation possible in the neutrino mixing and oscillation.