https://doi.org/10.1140/epjc/s10052-026-15853-3
Regular Article - Theoretical Physics
Bargmann invariants and correlated geometric 
-violating structures in neutral meson systems
Physics Department, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India
a
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Received:
1
April
2026
Accepted:
17
May
2026
Published online:
1
June
2026
Abstract
Bargmann invariants provide a rephasing-invariant description of phase relations among quantum states and offer a geometric perspective on interference phenomena. In this work, we investigate their role in neutral meson systems by constructing cyclic products involving the heavy and light mass eigenstates together with decay-projected states arising from correlated meson decays. Explicit expressions for third-order and fourth-order invariants are obtained in terms of mixing parameters and decay amplitudes. The analysis shows that the associated geometric phases encode -sensitive interference effects between meson–antimeson mixing and decay amplitudes and become trivial in the -conserving limit. Expressing the decay amplitudes in terms of CKM matrix elements reveals quartic combinations with analogous rephasing-invariant weak-phase structure to that of the Jarlskog invariant. We further introduce a rephasing-invariant ratio constructed from third- and fourth-order Bargmann invariants, which isolates correlated -violating structures that cannot, in general, be factorized into independent decay-channel contributions and can enhance sensitivity to small deviations from symmetry. The invariants can also be related to parameters governing time-dependent asymmetries in neutral meson decays, thereby providing a geometric interpretation of observable -violating interference effects.
© The Author(s) 2026
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