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Neutrino mass ordering obscured by non-standard interactions

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Allowing electron-tau flavor-changing neutral-current interactions completely erases the current 2.4σ normal-ordering preference from T2K and NOvA; with those interactions, inverted ordering is even mildly favored.

desk verdict A well-executed robustness study: allowing e-tau NSI flips the T2K/NOvA mass-ordering preference from 2.4σ normal to 0.7σ inverted, though the washout size hinges on a self-referential relaxation of the 90% NSI bound. read the letter →

arxiv 1908.06992 v2 pith:NGGFUBOJ submitted 2019-08-19 hep-ph hep-ex

Francesco Capozzi , Sabya Sachi Chatterjee , Antonio Palazzo This is my paper · ORCID
classification hep-phhep-ex
keywords neutrinomassorderingnon-standardinteractionse-tauNSIT2KNOvAlong-baselineoscillationsmattereffectsCPviolation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is trying to establish that the current ~2.4σ preference for normal neutrino mass ordering, extracted from T2K and NOvA long-baseline data under the standard three-flavor assumption, disappears as soon as neutral-current non-standard interactions (NSI) of the flavor-changing e-tau type are allowed in the fit. Concretely, the difference in fit quality between normal and inverted ordering changes from Δχ² ≈ −5.6 (favoring normal ordering) in the standard model to Δχ² ≈ +0.5 (mildly favoring inverted ordering) once εeτ is included. The reason this matters is that the neutrino mass ordering is one of the main open questions in particle physics, and experiments are being designed around a discovery that this result shows would be contingent on the absence of a specific class of new physics.

What carries the argument

The argument runs on an analytic decomposition of the νμ→νe appearance probability, $P_{\mu e}\simeq P_0+P_1+P_2$, where $P_0$ is the standard leading term set by $\theta_{13}$, $P_1$ is the standard solar-atmospheric interference, and $P_2$ is a matter-induced NSI interference term proportional to $V_{CC}\,|\varepsilon|$ and to the CP-phase combination $\delta+\varphi_{\varepsilon}$. For $\varepsilon_{e\tau}$ the coefficients in $P_2$ enter with opposite signs for the two mass orderings because the sign of $\Delta m^2_{31}$ flips, while the larger matter potential in NOvA ($v\simeq0.14$) relative to T2K ($v\simeq0.05$) makes the term big enough to reshape the predicted event ellipses. This extra interference term supplies the freedom that lets inverted ordering reproduce the data.

What would settle it

Re-run the same T2K+NOvA fit with an external 90% C.L. constraint $|\varepsilon_{e\tau}|\le0.36$ imposed as a hard prior. Since the inverted-ordering best fit sits at $|\varepsilon_{e\tau}|\approx0.39$, that minimum would move to the boundary and pay a penalty of roughly $((0.39-0.36)/\sigma_{\rm ext})^2$ in $\chi^2$; if independent data (e.g., atmospheric neutrinos or coherent elastic neutrino-nucleus scattering) tighten the bound to $|\varepsilon_{e\tau}|\lesssim0.3$, the penalty would exceed 4 and the normal-ordering preference would re-emerge. A published global fit with updated T2K/NOvA data that keeps $|\varepsilon_{e\tau}|<0.3$ at 90% C.L. would falsify the washout claim.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is an ambiguity: the same T2K and NOvA appearance data that select normal ordering in the standard three-flavor framework can be described just as well by inverted ordering once a complex flavor-changing coupling εeτ between electron and tau neutrinos is introduced. The best fit in inverted ordering sits at |εeτ| ≈ 0.39 with phase φeτ ≈ 1.30π, and the preference for nonzero NSI in that ordering is 2.5σ; in normal ordering the corresponding preference is only 0.7σ. Because both orderings then fit the data equally well, the inferred ordering is no longer determined by these two experiments.

Load-bearing premise

The washout relies on allowing $|\varepsilon_{e\tau}|$ to rise to about 0.39, well above the 90% bound (≈0.36) quoted from current global analyses; that bound can only be relaxed if the same T2K/NOvA data driving the NSI preference are imported into the constraint, so if independent data hold the coupling below roughly 0.3, the inverted-ordering fit is penalized and the normal-ordering preference survives.

Editorial extensions

If this is right

  • Any claim that T2K and NOvA favor normal ordering is conditional on the standard model (or at least on small $\varepsilon_{e\tau}$); the 2.4σ preference is not a property of the data alone.
  • The washout is specific to the e-tau sector: for $\varepsilon_{e\mu}$, normal ordering keeps a 2.5σ preference, so the confusion is not generic to all NSI.
  • DUNE can in principle break the degeneracy, but only if the CP phase $\delta$ stays close to its current best-fit value around $1.5\pi$; otherwise its ordering sensitivity drops below 2σ over broad ranges of $\delta$.
  • Simulations of T2HK and T2HKK show little ability to resolve the confusion, making DUNE the most promising future long-baseline experiment.
  • Complementary probes such as atmospheric neutrinos and JUNO, which are less affected by matter-enhanced NSI, become necessary to pin the ordering down.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the large $|\varepsilon_{e\tau}|\simeq0.39$ preferred in inverted ordering is real physics, then the current mass-ordering tension is arguably the first hint of non-standard neutrino interactions, and the normal-ordering preference is an artifact of assuming their absence.
  • The same $P_2$ mechanism should also contaminate global fits that combine reactor, accelerator, and atmospheric data; a testable extension is to redo the global NMO fit with $\varepsilon_{e\tau}$, $\varepsilon_{ee}$, and $\varepsilon_{\mu\tau}$ varied simultaneously, which could shift or strengthen the ambiguity.
  • Because the paper fixes solar parameters and treats $\theta_{13}$ through a reactor prior, the stability of the washout could be re-examined with those parameters free; that is a direct check of whether the conclusion changes under a different statistical treatment.
  • A practical consequence is that future long-baseline analyses should present the ordering preference as a function of NSI parameters rather than quoting a single significance, since the significance is prior-dependent.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper re-analyzes the combined T2K and NOvA data using the GLoBES package with the public NSI tool, asking whether the ~2.4sigma preference for the normal mass ordering (NO) survives when neutral-current non-standard interactions of the flavor-changing e-tau type are allowed. In the standard three-flavor fit the authors reproduce the NO preference (chi^2_SM,NO - chi^2_SM,IO ~ -5.6), while in the SM+epsilon_e-tau fit the difference becomes chi^2_SM+NSI,NO - chi^2_SM+NSI,IO ~ +0.5, i.e., a mild preference for inverted ordering (IO), thereby washing out the NO indication. The paper also presents an analytical expansion of the nu_mu->nu_e probability to explain the effect, and DUNE projections in the Supplemental Material. The authors explicitly note a caveat: the IO best fit requires |epsilon_e-tau| ~ 0.39, above the 90% bound quoted from the earlier global analysis, and they argue that the newer T2K/NOvA data would relax that bound.

Significance. If the central claim holds, it would demonstrate that the current normal-ordering hint from T2K and NOvA is not robust against a well-motivated class of new physics, which is an important message for the community. The analysis is reproducible in principle: it uses publicly released experimental data, the public GLoBES framework, and the public NSI simulation tool. The analytical decomposition of the appearance probability is a pedagogically useful illustration of why epsilon_e-tau can alter the ordering discrimination. However, the quantitative significance of the washout is conditional on the assumption that independent constraints on |epsilon_e-tau| are weak enough to accommodate the large IO best-fit value; this assumption is not validated inside the paper.

major comments (2)
  1. [Theoretical framework and Fig. 2] The IO best fit is located at |epsilon_e-tau| ~ 0.39 (Fig. 2, right panel), which is above the 90% C.L. upper bound |epsilon_e-tau| <~ 0.36 quoted in the Theoretical framework section from Refs. [41] and [39]. The authors anticipate that including the new T2K/NOvA data would sensibly relax the bound, but the data used to infer this relaxation are the same appearance data whose ordering preference is being erased. The paper does not include the most constraining independent probes, in particular atmospheric neutrino data (Super-K, IceCube) and COHERENT, even though the Conclusions state that complementing the study with atmospheric data would be interesting. This matters because if independent constraints keep |epsilon_e-tau| below roughly 0.3, the IO fit would be penalized and the NO preference would likely survive. I ask the authors to quantify this dependence, e.g., by profiling over a range of external upper bounds on |epsilon_e-tau| or by adding a representative atmospheric constraint, and to adjust the abstract and conclusions if the washout disappears under such a bound.
  2. [Supplemental Material, Fig. S1] The DUNE sensitivity projection assumes a true value |epsilon_e-tau| = 0.2, described as intermediate between the best-fit values found for NO and IO. In the real-data analysis the NO best fit is |epsilon_e-tau| ~ 0.09 and the IO best fit is ~ 0.39, so the chosen true value is not derived from the fit. If the true value were closer to the IO best fit, the DUNE sensitivity could be even worse than shown; if closer to the NO best fit, it could be better. The stated conclusion that DUNE can resolve the ambiguity only for delta near 1.5pi is therefore sensitive to an unquantified assumption. The authors should show the DUNE sensitivity as a function of the assumed true |epsilon_e-tau| (including values near the IO best fit) and, ideally, with a prior based on an updated external bound.
minor comments (5)
  1. [Introduction] The text says 'three mixing angles theta12, theta13, theta13'; the third angle should be theta23.
  2. [Eq. (11) and surrounding discussion] The analytical probability expansion is first-order in |epsilon| and is justified by the claim that |epsilon| is small, of order 0.2, yet the same paragraph anticipates best-fit values up to |epsilon| ~ 0.4. The authors should state explicitly that the analytic expression is illustrative and that the numerical GLoBES results use the full Hamiltonian.
  3. [Supplemental Material] The sentence 'We have also marginalized over Delta m^2_31 in the test, where we have taken the true value equal to 2.49 x 10^-3 eV^2 obtained from the real data analysis' is confusing; presumably the true value is fixed and the test value is profiled.
  4. [Fig. 2 and Numerical Results] The contours in Fig. 2 are drawn for 1 d.o.f., but the text quotes the significance of the preference for nonzero |epsilon_e-tau| as 2.5sigma; the connection between the contour level and the quoted significance (e.g., the Delta chi^2 between the best fit and |epsilon_e-tau| = 0) should be made explicit.
  5. [Theoretical framework] A brief comment on why epsilon_ee and epsilon_mu-tau are not included in the scan would be helpful, especially since epsilon_mu-tau is tightly bounded by atmospheric data while epsilon_ee is not obviously negligible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim is a conditional model-comparison fit to external data, not a prediction derived from its own inputs.

full rationale

The paper's central result is a conditional: if e-tau NSI are allowed and fitted to T2K plus NOvA appearance data, the normal-ordering preference drops from about 2.4 sigma to about 0.7 sigma. This is obtained by a direct GLoBES fit to public event data, not by assuming the conclusion. The NSI parameters are free in the fit (Eqs. 8-15) and are marginalized; the chi-square difference is computed from the fitted event rates. The analytic probability decomposition is standard perturbation theory and does not encode the ordering answer. The only potentially self-referential input is the paper's own caveat that the quoted 90% bound |epsilon_e_tau| < 0.36 would be relaxed if the new T2K/NOvA data are included; the IO best fit lies at 0.39. That is a robustness gap (the external global constraint is not re-evaluated) rather than a circular reduction: the conclusion is explicitly conditional on NSI existing, and the fit is transparent about the parameter values. The DUNE simulation likewise uses an explicit assumption ('true value |epsilon_e_tau| = 0.2, which is intermediate between the values we find as best fits'), not a prediction forced by construction. Self-citations to the authors' global fit [3] are used only for fixed solar parameters and are not load-bearing. No equation reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the standard 3-flavor oscillation framework plus a freely fitted electron-tau NSI coupling. The decisive input is not a new measurement but the allowance of a large |ε_eτ|, with external constraints deferred to a cited bound that the paper argues would relax. No new entities are introduced.

free parameters (4)
  • |ε_eτ| (NSI coupling strength) = 0.39 in IO best fit, 0.09 in NO best fit
    The central washout of the normal-ordering preference is driven by allowing this coupling to float up to values near or above the quoted 90% bound of 0.36 (Fig. 2).
  • φ_eτ (NSI CP phase) = 1.30π in IO best fit, 1.42π in NO best fit
    The phase controls the sign and amplitude of the NSI interference term in Eq. (11), and its fitted value determines which ordering provides the better fit.
  • |ε_eμ| (secondary NSI coupling) = 0.15 in NO, 0.10 in IO
    Fitted in the same analysis but shown not to erase the ordering preference; included for completeness.
  • Profiled oscillation parameters θ23, δ, Δm31^2, θ13 = marginalized; θ23 and δ profiles shown in Fig. 3
    Standard 3-flavor parameters are left free in the fit, with θ13 receiving a reactor prior. The ordering comparison is a profile likelihood over these parameters.
assumptions (6)
  • domain assumption Three-flavor neutrino mixing with the standard PMNS parameterization and the Wolfenstein matter potential, as used in Eq. (5).
    The entire analysis is framed in the 3-flavor framework plus NSI; this is the background theory the paper relies on.
  • domain assumption NSI are described by the dimension-six operator in Eq. (1) and the effective propagation Hamiltonian in Eq. (5).
    The paper assumes NSI enter as non-diagonal matter potential terms; alternative new-physics structures are not considered.
  • domain assumption Constant matter density along the baseline with Ye about 0.5.
    Used in Eq. (6) for V_CC and in the probability expressions; Earth crust composition is treated as uniform.
  • standard math The perturbative expansion P ≈ P0 + P1 + P2 in Eqs. (8)-(11) is valid for the small parameters θ13, v, α and |ε|.
    This expansion is used for interpreting the degeneracy; numerical results come from GLoBES, so the expansion is illustrative.
  • ad hoc to paper The upper bound on |ε_eτ| can be as large as about 0.36 and would relax with the new dataset, permitting best-fit values near 0.39 in IO.
    The closing of the ordering gap relies on this coupling being allowed to be large; external constraints from atmospheric data and COHERENT are not included in the fit.
  • domain assumption NSI sectors other than ε_eτ and ε_eμ (for example ε_ee and ε_μτ) can be neglected.
    The paper justifies ignoring ε_μτ via the atmospheric bound quoted in footnote [40], but does not fully explore simultaneous effects.

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Cite this review

Pith. "Pith review of Neutrino mass ordering obscured by non-standard interactions." pith.science (2026). https://pith.science/paper/NGGFUBOJ

@misc{pith2026190806992,
  author       = {Pith},
  title        = {Pith review of: Neutrino mass ordering obscured by non-standard interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NGGFUBOJ}},
  note         = {Machine review of arXiv:1908.06992}
}
abstract

One of the major open questions in particle physics is the issue of the neutrino mass ordering (NMO). The current data of the two long-baseline experiments NO$\nu$A and T2K, interpreted in the standard 3-flavor scenario, provide a $\sim2.4\sigma$ indication in favor of the normal neutrino mass ordering. We show that such an indication is completely washed out if one assumes the existence of neutral-current non-standard interactions (NSI) of the flavor changing type involving the $e-\tau$ flavors. This implies that the claim for a discovery of the NMO will require a careful consideration of the impact of hypothetical NSI.

Figures

Figures reproduced from arXiv: 1908.06992 by the authors.

Figure 1
Figure 1. FIG. 1. Bievents plot for the T2K (left panel) and NO [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Estimates of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 14, 2026 · model on record in the stance chip above.