Nonadditive Geometric Phase and Correlated CP Effects in Entangled Neutral Meson Systems

TL;DR

This paper explores the geometric phase in entangled neutral meson systems, revealing how CP violation influences the geometric structure and demonstrating that entanglement induces unique geometric effects not reducible to single-particle contributions.

Contribution

It introduces a formulation of the time-dependent geometric phase for entangled mesons, highlighting the entanglement-induced geometric effects and their relation to CP violation in these systems.

Findings

Geometric phase cannot be expressed as a sum of single-meson contributions.

CP violation affects the geometric phase through mixing parameters.

The geometric structure remains sensitive to mixing parameters and entanglement.

Abstract

We investigate the geometric structure associated with CP-violating dynamics in entangled neutral meson systems. We formulate the time-dependent geometric phase for the correlated two-meson state and analyze its system-dependent behavior across different neutral meson mixing scenarios. We demonstrate that the geometric phase associated with the entangled state cannot, in general, be expressed as a sum of independent single-meson contributions, indicating the presence of genuinely entanglement-induced geometric effects. Furthermore, we show how CP violation enters the geometric phase through mixing, leading to a rephasing-invariant geometric structure of correlated evolution that remains indirectly sensitive to the mixing parameters. These results clarify the geometric characterization of entanglement and CP violation in neutral meson systems.