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International Conference on High Energy Physics (ICHEP)

Expressing CP Violation in Terms of Bargmann Invariants and Geometric Phases in Kaon Decays and Baryogenesis

Swarup Sangiri

Published Dec 17, 2024• 0 citations
Publisher

Abstract

We studied the CP violating phases in the neutral kaon oscillations and decays in the effective field theory of kaons, without going into the quark level, and connected the CP violating parameters to the Bargmann invariants and hence to the geometric phases. We extended this approach to demonstrate how the CP violating parameters appearing in the process of baryogenesis are related to the Bargmann invariants, and hence with the geometric phases of those systems. We then concluded on the applications of such a generalized treatment of CP violating phases.

DOI
10.22323/1.476.0480

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We studied the CP violating phases in the neutral kaon oscillations and decays in the effective field theory of kaons, without going into the quark level, and connected the CP violating parameters to the Bargmann invariants and hence to the geometric phases. We extended this approach to demonstrate how the CP violating parameters appearing in the process of baryogenesis are related to the Bargmann invariants, and hence with the geometric phases of those systems. We then concluded on the applications of such a generalized treatment of CP violating phases.
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We present a study of the properties of Bargmann Invariants (BIs) and Null Phase Curves (NPCs) in the theory of the geometric phase for finite dimensional systems. A recent suggestion to exploit the Majorana theorem on symmetric SU(2) multispinors is combined with the Schwinger oscillator operator construction to develop efficient operator-based methods to handle these problems. The BI is described using intrinsic unitary invariant angle parameters whose algebraic properties as functions of Hilbert space dimension are analyzed using elegant group theoretic methods. The BI-geometric phase connection, extended by the use of NPCs, is explored in detail, and interesting new experiments in this subject are pointed out.
We present a theory of the geometric phase based logically on the Bargmann invariant of quantum mechanics, and null phase curves in ray space, as the fundamental ingredients. Null phase curves are themselves defined entirely in terms of the (third order) Bargmann invariant, and it is shown that these are the curves natural to geometric phase theory, rather than geodesics used in earlier treatments. The natural symplectic structure in ray space is seen to play a crucial role in the definition of the geometric phase. Logical consistency of the formulation is explicitly shown, and the principal properties of geometric phases are deduced as systematic consequences.