arXiv subjects

Swarup Sangiri

Publications and source records attributed to Swarup Sangiri.

7 recordsLinked to original sources

arXiv2026

Geometric Phases in Two-Level Mixing: From Neutral Mesons to Holonomic Qubits and Topological Majorana Modes

We investigate the geometric structure of a Hermitian two-level mixing Hamiltonian motivated by neutral meson oscillations and its connections with qubit, fermionic, and topological descriptions. Mapping the Hamiltonian to an effective qubit representation, we analyze the geometric phase associated with cyclic parameter evolution on the Bloch sphere. Without identifying the complex mixing phase with a physical CP-violation observable, we interpret it as a CP-like geometric parameter controlling the azimuthal orientation of the Hamiltonian vector and its reversal under phase conjugation. Third-order Bargmann invariants constructed from the eigenstates yield an associated discrete phase whose dependence on the mixing parameters is examined alongside the continuous geometric construction. The cyclic evolution is also represented as a single-qubit $R_z$ phase operation and expressed through Majorana bilinears. Extending the construction to the momentum-dependent Bogoliubov-de Gennes Hamiltonian of the Kitaev chain, we relate momentum-space winding to the topological regimes and the quantized Berry (Zak) phase in the real-parameter model, while the corresponding Bargmann construction approaches the global phase in the continuum limit. Together, these results provide a geometric perspective connecting phase structure, qubit operations, fermionic representations, and momentum-space topology within related two-level Hamiltonians.

hep-ph↗

arXiv2026

A Geometric Framework for CPT Violation in Neutral Meson Mixing Using Biorthogonal Bargmann Invariants

We develop a geometric framework for characterizing CPT violation in neutral meson systems using Bargmann invariants formulated within a biorthogonal description of the non-Hermitian effective Hamiltonian governing neutral meson mixing. Interpreting CPT violation as a relative geometric deformation of the heavy- and light-state mixing directions in projective flavor space, we construct a fourth-order Bargmann invariant together with its CP-conjugate counterpart involving the physical mass eigenstates and experimentally accessible decay channels. From the phase of a rephasing-invariant product of these invariants, we define a geometric observable that isolates the CPT-violating contribution. The resulting formalism identifies the channel dependence of the geometric response and yields a selection criterion for decay-mode combinations exhibiting linear sensitivity to CPT violation. We further relate the geometric deformation to the Lorentz-violating coefficients of the Standard-Model Extension, showing that the resulting observable inherits the characteristic sidereal modulation of the SME framework. The present work provides a complementary geometric perspective on CPT violation in neutral meson mixing and establishes a foundation for future phenomenological studies of geometric signatures of CPT and Lorentz violation.

hep-ph↗

arXiv2026

Correlation-Induced Interferometric Geometric Phase Difference in Entangled Neutral Meson Systems

We investigate the phase structure associated with correlated evolution in entangled neutral meson systems. Working within a rephasing-invariant interferometric framework, we construct the time-dependent interferometric geometric phase associated with the antisymmetric entangled neutral meson state undergoing nonunitary evolution. Exploiting the natural factorization of the overlap amplitude into global propagation and interference contributions, we derive an explicit expression for the phase in terms of the mass and decay-width differences that govern neutral meson mixing. To place the entangled phase in context, we derive the corresponding interferometric geometric phases accumulated by independently evolving neutral mesons within the same framework. This comparison naturally leads to the introduction of a correlation-induced interferometric geometric phase difference, $Δγ=γ_{\rm g}^{\rm{ent}}-γ_{\rm g}^{(1)}-γ_{\rm g}^{(2)}$, defined as the deviation of the entangled interferometric geometric phase from the sum of the associated single-meson phases. We show that this quantity characterizes the nonadditive phase structure generated by correlated meson evolution and originates from interference between propagation pathways that have no analogue in isolated meson dynamics. The resulting phases depend solely on the eigenvalue differences governing neutral meson oscillations and decay. The system-dependent behavior of the interferometric geometric phases and the correlation-induced phase difference is analyzed across different neutral meson families, illustrating how the underlying mixing dynamics shape the resulting phase correlations. Our results provide an interferometric characterization of entangled neutral meson evolution and highlight the role of entanglement in generating nonadditive phase structures associated with correlated meson dynamics.

hep-ph↗

arXiv2026

Connected Sequential Bargmann Invariants and CP-Sensitive Geometric Correlation Structures in Neutral Meson Systems

We investigate connected sequential geometric structures in correlated neutral meson systems within the framework of Bargmann invariants. Building upon previously developed third- and fourth-order rephasing-invariant geometric structures involving decay-projected conditional states, we introduce a connected sequential fourth-order Bargmann invariant in which the decay-projected states associated with two decay channels are linked through a direct overlap between the corresponding projected states. This construction incorporates explicit projection-projection correlations within the cyclic overlap chain. The connected sequential invariant encodes the geometric relation between decay-projected states, thereby extending the geometric correlation framework developed for correlated neutral meson systems. To characterize the resulting geometric structures, we define rephasing-invariant ratios that quantify connected sequential correlations and provide a direct comparison with the previously studied disconnected geometric correlations. The behavior of these quantities is analyzed in the regime of small CP violation using the standard rephasing-invariant interference parameters together with a small-asymmetry expansion. We show that the connected sequential ratios exhibit characteristic scaling behaviors governed by both mixing asymmetry and relative interference-phase alignment, leading to geometric scaling properties distinct from those of the disconnected structures. We further discuss the geometric interpretation of the connected sequential invariants and their possible relevance to correlated neutral meson systems. The resulting framework extends the hierarchy of Bargmann invariant geometric correlations associated with neutral meson mixing and decay, providing a complementary geometric perspective on CP-sensitive interference phenomena.

hep-ph↗

arXiv2026

Bargmann Invariants and Correlated Geometric CP-Violating Structures in Neutral Meson Systems

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 CP-sensitive interference effects between meson-antimeson mixing and decay amplitudes and become trivial in the CP-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 CP-violating structures that cannot, in general, be factorized into independent decay-channel contributions and can enhance sensitivity to small deviations from CP symmetry. The invariants can also be related to parameters governing time-dependent CP asymmetries in neutral meson decays, thereby providing a geometric interpretation of observable CP-violating interference effects.

hep-ph↗

arXiv2022

Geometric Phases in Kaon Decays and Baryogenesis

We studied the formalism for construction of Bargmann invariants (BIs) as quantum mechanical geometric phases and identified the CP invarince with the rephasing invariant phases in neutral kaon system, kaon decays, baryogenesis and leptogenesis. We develop this formalism to express the CP violation in terms of the Bargmann invariants, which allow us to interpret them as geometric phases. We then comment on the application of such generalized treatment of CP phases.

hep-ph↗

arXiv2020

Bargmann Invariants, Geometric Phases and Recursive Parametrization with Majorana Fermions

A generalized connection between the quantum mechanical Bargmann invariants and the geometric phases was established for the Dirac fermions. We extend that formalism for the Majorana fermions by defining proper quantum mechanical ray and Hilbert spaces. We then relate both the Dirac and Majorana type Bargmann invariants to the rephasing invariant measures of CP violation with the Majorana neutrinos, assuming that the neutrinos have lepton number violating Majorana masses. We then generalize the recursive parametrization for studying any unitary matrices to include the Majorana fermions, which could be useful for studying the neutrino mixing matrix.

hep-ph↗