Genuine leptonic CP violation or non-standard neutrino interactions: disentangling the $\delta_{CP}\simeq-\pi/2$ hint in long-baseline oscillation data

The Forero–Huber analysis (Phys. Rev. Lett. 117, 031801, 2016) showed that the preference for a Dirac CP phase $\delta_{CP}\simeq-\pi/2$ seen in T2K and NOvA long-baseline data can be reproduced, with statistically indistinguishable $\chi^2$, by CP-conserving non-standard neutrino interactions (NSI) in propagation ($\varepsilon_{e\tau}=|\varepsilon|e^{i\varphi}$ with $\varphi=\pi$, $|\varepsilon|=0.3$). The open question is whether the now-strengthened $\delta_{CP}$ preference reflects genuine CP violation within the standard three-flavor framework or NSI-mimicked new physics, and what quantitative experimental capabilities — exposure, energy resolution, systematic-error control, and baseline complementarity at DUNE and T2HK/Hyper-Kamiokande — are required to discriminate the two hypotheses.

Background

Neutrino oscillations arise because the three known neutrino flavor states are quantum mixings of three mass eigenstates, described by the PMNS mixing matrix, which is parameterized by three mixing angles and one Dirac CP phase $\delta_{CP}$; values of $\delta_{CP}$ different from $0$ or $\pi$ violate CP symmetry in the lepton sector. Long-baseline accelerator experiments — T2K (295 km baseline, Japan) and NOvA (810 km, USA) — measure the appearance of $\nu_e$ from a $\nu_\mu$ beam and the corresponding antineutrino channel to constrain $\delta_{CP}$, with the mixing angle $\theta_{13}$ tightly fixed by reactor experiments such as Daya Bay. Around 2014–2016 these data showed a mild preference for $\delta_{CP}\simeq-\pi/2$, i.e. nearly maximal CP violation.

When neutrinos propagate through matter, coherent forward scattering on electrons modifies the oscillation probabilities (the Wolfenstein matter effect); in the Standard Model this adds a known potential proportional to the electron density. Non-standard neutrino interactions (NSI) are a model-independent way to parameterize new neutral-current-like interactions of neutrinos with matter fermions: dimensionless couplings $\varepsilon_{\alpha\beta}$ enter the propagation Hamiltonian as an additive matter potential, introducing three real diagonal and three complex off-diagonal parameters (eight new physical parameters in total, one combination being redundant), some of which can carry new CP-violating phases.

Forero and Huber (Phys. Rev. Lett. 117, 031801, 2016) simulated T2K and NOvA under the assumption that CP is conserved in the neutrino sector (true $\delta_{CP}=\pi$) but that real, CP-conserving NSI of the form $\varepsilon_{e\tau}=0.3\,e^{i\varphi}$ with $\varphi=\pi$ are present (fixing $\varepsilon_{e\mu}=\varepsilon_{ee}=0$ and assuming normal mass ordering, i.e. two lighter mass states plus a heavier one). The reconstructed $\delta_{CP}$ then clusters near $-\pi/2$, and the $\chi^2$ distributions of the standard and NSI cases nearly coincide: the observed hint for maximal CP violation could equally well be CP-conserving new physics. NSI of this size are not excluded by neutrino data; although NSI generated above the electroweak scale face stringent charged-lepton constraints, interactions generated below that scale can evade them.

Disentangling the two interpretations is the task of the next-generation experiments: DUNE (1300 km baseline, high-energy beam, USA) and T2HK/Hyper-Kamiokande (295 km, a very large water-Cherenkov detector, Japan), whose different baselines matter because NSI effects grow with the amount of matter traversed while genuine CP effects do not. Related degeneracies are known: with NSI, an inverted mass ordering with a flipped $\theta_{12}$ octant and $\delta_{CP}\to\delta_{CP}+\pi$ (the 'dark-side' or LMA-D solution, disfavored below the $2\sigma$ level only by the composition dependence of solar-matter propagation) can fit the data, and coherent neutrino–nucleus scattering data from COHERENT constrain some NSI combinations.

Problem Statement

Determine whether the observed preference for $\delta_{CP}\simeq-\pi/2$ in long-baseline accelerator neutrino oscillation data (T2K, NOvA, and their reactor-constrained combination) is genuine CP violation within the standard three-flavor framework, or whether it can be mimicked — fully or in part — by non-standard neutrino interactions in propagation. This requires: (a) a complete mapping of the degeneracy between the standard CP-violating interpretation and NSI interpretations across the full propagation-NSI parameter space (the complex $\varepsilon_{\alpha\beta}$ matrix, both mass orderings, consistently combined with relevant source/detector NSI effects — non-standard interactions acting in neutrino production or detection rather than in propagation — where they apply), respecting all external constraints (solar, atmospheric, reactor, and coherent-scattering data), establishing whether CP-conserving or CP-violating NSI allowed by current bounds can reproduce the observed data as well as the standard interpretation; and (b) a quantitative determination of the experimental requirements — statistical exposure, energy resolution, systematic-error control, and baseline/facility complementarity, e.g. DUNE together with T2HK/Hyper-Kamiokande — needed to exclude the NSI-mimicking hypotheses and establish (or refute) genuine leptonic CP violation. The theoretical viability of sizable sub-electroweak NSI, for which the source noted ample room from both experimental and theoretical perspectives, has since been demonstrated by explicit models and enters the problem as a consistency requirement on any NSI hypothesis invoked.

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