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 ($\varepsilon_{eτ} = |\varepsilon_{eτ}|e^{iϕ_{eτ}}$) into the discrete-layer matter Hamiltonian across the DUNE baseline ($L = 1300\text{ km}$), we analyze the state evolution for both neutrino ($ν_μ\to ν_e$) and antineutrino ($\barν_μ\to \barν_e$) appearance channels over the broadband energy spectrum $E_ν\in [0.5, 8.0]\text{ GeV}$. Our analysis demonstrates that complex NSI phases imprint distinct, energy-dependent spectral dispersions onto the open-path geometric holonomies $Φ_g^{(n)}$ and their $\mathcal{CP}$-conjugate counterparts. By clarifying that these geometric phases manifest through gauge-invariant interference terms $ΔΓ_{nm}$ rather than asymptotic single-channel measurements, we construct the $\mathcal{CP}$-violating geometric phase differences $ΔΦ_g^{\mathrm{CP}}$. We show that the interplay between these geometric dispersions and the matter-potential sign reversal under $\mathcal{CP}$-conjugation forces the neutrino and antineutrino degeneracy bands to intersect at non-parallel angles in the two-dimensional $(δ_{\mathrm{CP}}, ϕ_{eτ})$ 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.