Topological Diagnostics of CP Degeneracies in Long-Baseline Neutrino Oscillations with Non-Standard Interactions via Pancharatnam Open-Path Phases

Abstract

We investigate the topological signatures of neutral-current Non-Standard Interactions (NSI) in long-baseline neutrino oscillations by extending the open-path Pancharatnam geometric phase framework. Incorporating off-diagonal vector couplings (${\epsilon }_{e\tau }=|{\epsilon }_{e\tau }|e^{i{\varphi }_{e\tau }}$) into the discrete-layer matter Hamiltonian across the DUNE baseline ($L=1300\text{ km}$), we analyze the state evolution for both neutrino (${\nu }_{\mu }\to {\nu }_e$) and antineutrino (${\bar{\nu }}_{\mu }\to {\bar{\nu }}_e$) appearance channels over the broadband energy spectrum $E_{\nu }\in [0.5,8.0]\text{ GeV}$. Our analysis demonstrates that complex NSI phases imprint distinct, energy-dependent spectral dispersions onto the open-path geometric holonomies ${\Phi }_g^{(n)}$ and their $\mathcal{C}\mathcal{P}$-conjugate counterparts. By clarifying that these geometric phases manifest through gauge-invariant interference terms $\Delta {\Gamma }_{nm}$ rather than asymptotic single-channel measurements, we construct the $\mathcal{C}\mathcal{P}$-violating geometric phase differences $\Delta {\Phi }_g^{\mathrm{CP}}$. We show that the interplay between these geometric dispersions and the matter-potential sign reversal under $\mathcal{C}\mathcal{P}$-conjugation forces the neutrino and antineutrino degeneracy bands to intersect at non-parallel angles in the two-dimensional $({\delta }_{\mathrm{CP}},{\varphi }_{e\tau })$ parameter space. This non-trivial topological intersection isolates a unique physical solution, providing a robust, independent diagnostic capable of breaking persistent parameter degeneracies even under realistic calorimetric energy smearing.