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arxiv: 2606.20830 · v1 · pith:NKBYOBICnew · submitted 2026-06-18 · ✦ hep-ph · hep-ex

When CPT Violation Hides in Plain Sight: How CP Measurements Are Compromised and How to Fix Them

Miaochen Jin , Gabriela Barenboim , Carlos A. Arg\"uelles , Pablo Fern\'andez-Men\'endez , Ivan Martinez-Soler This is my paper

Pith reviewed 2026-06-26 16:15 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords CPT violationneutrino oscillationsCP phaselong-baseline experimentsatmospheric neutrinosDUNEmass splitting asymmetrydegeneracy
0
0 comments X

The pith

A constant difference in neutrino and antineutrino atmospheric mass splittings produces an energy-dependent phase shift that is degenerate with δ_CP in long-baseline appearance data.

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

The paper establishes that CPT violation appearing only as an asymmetry δΔm²₃₁ between neutrino and antineutrino mass splittings generates an effective phase φ_eff(E) that enters the appearance asymmetry exactly as a shift in the CP phase does. This functional degeneracy means a standard CPT-conserving fit to data from experiments such as DUNE can return a value of δ_CP displaced from the true one once |δΔm²₃₁| exceeds about 0.3×10^{-3} eV². Atmospheric neutrino observations are shown to break the degeneracy because they constrain the same mass splitting without the same CP-phase dependence. Existing IceCube-DeepCore and KM3NeT/ORCA data already set |δΔm²₃₁| ≤ 0.57×10^{-3} eV² at 90% CL, and planned upgrades are projected to reach 10^{-4} eV² sensitivity within a decade.

Core claim

CPT violation parametrized as a constant difference δΔm²₃₁ ≡ Δm̄²₃₁ − Δm²₃₁ between neutrino and antineutrino atmospheric mass splittings induces an effective energy-dependent phase shift φ_eff(E) that is functionally identical to δ_CP inside the long-baseline appearance asymmetry ⟨ΔP⟩; a CPT-conserving analysis therefore misattributes the effect to δ_CP, with the bias becoming severe for |δΔm²₃₁| ≳ 0.3×10^{-3} eV² at DUNE, while atmospheric data from IceCube-DeepCore (7.74 yr) and KM3NeT/ORCA-6 (433 kt-yr) constrain |δΔm²₃₁| ≤ 0.57×10^{-3} eV² at 90% CL.

What carries the argument

The effective phase shift φ_eff(E) generated by the constant CPT-violating mass-splitting difference δΔm²₃₁, which enters the oscillation probability asymmetry in the same functional form as the CP phase δ_CP.

If this is right

  • A CPT-conserving analysis of DUNE data returns a biased δ_CP once |δΔm²₃₁| exceeds roughly 0.3×10^{-3} eV².
  • The existing tension between T2K and NOνA best-fit δ_CP values can be reduced if a small CPT violation is allowed.
  • Atmospheric neutrino data supply an independent limit on δΔm²₃₁ that removes the degeneracy for long-baseline CP extractions.
  • IceCube Upgrade and full ORCA data will reach a 1σ sensitivity of 10^{-4} eV² on |δΔm²₃₁| within a decade.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Global neutrino oscillation fits should include δΔm²₃₁ as a free parameter when extracting δ_CP rather than fixing it to zero by assumption.
  • The same effective-phase mechanism may affect other appearance-channel analyses that have not yet been checked for this degeneracy.
  • A nonzero δΔm²₃₁ signal would motivate re-analysis of reactor disappearance data to test consistency with the assumed form of CPT violation.

Load-bearing premise

CPT violation is assumed to appear exclusively as a constant shift in the atmospheric mass splitting with no additional violations in mixing angles or other parameters.

What would settle it

A joint fit in which atmospheric data bound |δΔm²₃₁| above 0.3×10^{-3} eV² while long-baseline appearance data are still described by a single δ_CP value would confirm the degeneracy; a tight atmospheric bound together with a DUNE result that deviates from the CPT-conserving prediction would challenge it.

Figures

Figures reproduced from arXiv: 2606.20830 by Carlos A. Arg\"uelles, Gabriela Barenboim, Ivan Martinez-Soler, Miaochen Jin, Pablo Fern\'andez-Men\'endez.

Figure 1
Figure 1. Figure 1: FIG. 1. CP–CPT degeneracy at DUNE [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Illustration of the CP, CPT, and effective CP [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. CP–CPT degeneracy manifolds for T2K (295 km, solid blue) and NOvA (810 km, dashed red) in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. CPT-induced bias on [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Two-dimensional confidence contours in the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Two-dimensional [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Projected sensitivity to CPT violation as a [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

The extraction of the leptonic charge-parity (CP)-violating phase $\delta_{\rm CP}$ from long-baseline neutrino oscillation experiments rests on the assumption of charge-parity-time (CPT) conservation. We show that CPT violation, parametrized as an asymmetry $\delta\Delta m^2_{31} \equiv \Delta\bar{m}^2_{31} - \Delta m^2_{31}$ between neutrino and antineutrino mass splittings, induces an effective, energy-dependent phase shift $\phi_{\rm eff}(E)$ that is functionally degenerate with $\delta_{\rm CP}$ in the appearance asymmetry $\langle\Delta P\rangle$. This has a profound implication for long-baseline experiments, where the tension between T2K and NO$\nu$A CPT-conserving best-fit $\delta_{\rm CP}$ values can be significantly alleviated by a CPT-violating truth; and a CPT-conserving fit can miss the true CP phase entirely for $|\delta\Delta m^2_{31}|\gtrsim 0.3\times10^{-3}~\text{eV}^2$ for DUNE. We then demonstrate that atmospheric neutrino telescopes provide the natural tool to resolve this degeneracy: using existing data from IceCube-DeepCore (7.74 yr) and KM3NeT/ORCA-6 (433 kt-yr), we derive a world-leading constraint on CPT-violation at $| \delta\Delta m^2_{31}|\leq 0.57\times10^{-3}~\text{eV}^2$ at 90% CL. With the IceCube Upgrade and full ORCA detector, we can reach a $1\sigma$ constraint at $10^{-4}~\text{eV}^2$ within a decade, providing the independent CPT constraint needed to ensure that DUNE's $\delta_{\rm CP}$ measurement is unambiguous.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper claims that CPT violation parametrized solely as a constant difference δΔm²₃₁ between neutrino and antineutrino mass splittings induces an energy-dependent effective phase shift φ_eff(E) that is functionally degenerate with δ_CP in the long-baseline appearance asymmetry ⟨ΔP⟩. This degeneracy can alleviate the T2K–NOνA tension in δ_CP and cause a CPT-conserving fit to miss the true CP phase in DUNE for |δΔm²₃₁| ≳ 0.3×10^{-3} eV². Atmospheric neutrino data from IceCube-DeepCore (7.74 yr) and KM3NeT/ORCA-6 (433 kt-yr) are used to set a 90% CL limit |δΔm²₃₁| ≤ 0.57×10^{-3} eV², with future upgrades projected to reach 10^{-4} eV².

Significance. If the claimed functional degeneracy survives binned likelihoods and the atmospheric constraint is robust, the work would be significant for neutrino oscillation phenomenology: it identifies a previously under-appreciated systematic that can bias δ_CP extraction in long-baseline experiments and demonstrates that existing atmospheric data already provide a useful independent CPT test. The forward-calculation approach and use of public data sets are positive features.

major comments (1)
  1. [Abstract] Abstract (paragraph on effective phase shift): the assertion that φ_eff(E) ∝ δΔm²₃₁ L/(4E) is functionally degenerate with a constant δ_CP must be demonstrated explicitly in a binned DUNE likelihood; the explicit 1/E energy dependence cannot be absorbed by a single constant phase across the 0.5–8 GeV range, so the integrated-asymmetry degeneracy does not automatically imply that a CPT-conserving fit misses the true CP phase in realistic analyses.
minor comments (1)
  1. [Abstract] The numerical constraint |δΔm²₃₁| ≤ 0.57×10^{-3} eV² at 90% CL is quoted without an accompanying error budget, baseline comparison, or description of the fit procedure used on the IceCube-DeepCore and ORCA data sets.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review. The point raised about demonstrating the degeneracy explicitly in a binned DUNE likelihood is well taken, and we address it directly below. We are prepared to strengthen the manuscript with additional analysis to substantiate the claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph on effective phase shift): the assertion that φ_eff(E) ∝ δΔm²₃₁ L/(4E) is functionally degenerate with a constant δ_CP must be demonstrated explicitly in a binned DUNE likelihood; the explicit 1/E energy dependence cannot be absorbed by a single constant phase across the 0.5–8 GeV range, so the integrated-asymmetry degeneracy does not automatically imply that a CPT-conserving fit misses the true CP phase in realistic analyses.

    Authors: We agree that the explicit 1/E dependence of φ_eff(E) is not identical to a constant δ_CP and that this distinction matters for binned analyses. Our abstract statement is grounded in the degeneracy observed in the integrated appearance asymmetry ⟨ΔP⟩, which is the dominant driver of δ_CP sensitivity. Nevertheless, the referee correctly notes that this does not automatically guarantee a bias in realistic binned likelihood fits. To resolve the concern, we will add an explicit binned DUNE likelihood study in the revised manuscript, comparing CPT-conserving fits to data generated with nonzero δΔm²₃₁. This will quantify any residual bias in the extracted δ_CP across the 0.5–8 GeV range and clarify the conditions under which the effect persists. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central constraint from independent external datasets

full rationale

The paper's derivation proceeds by parametrizing CPT violation as a constant δΔm²₃₁, computing its effect on the appearance asymmetry via the oscillation phase (a forward calculation), and then fitting that parameter to separate atmospheric neutrino datasets (IceCube-DeepCore 7.74 yr and KM3NeT/ORCA-6 433 kt-yr). These datasets are external and not derived from the long-baseline experiments under discussion. No self-citations appear load-bearing, no fitted inputs are relabeled as predictions, and no ansatz or uniqueness claim reduces the result to its own inputs by construction. The degeneracy statement is presented as a calculational observation rather than a statistical fit to the same data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard three-flavor oscillation framework plus one additional CPT-violating parameter; no new particles or forces are introduced.

axioms (2)
  • standard math Neutrino oscillations are described by the standard three-flavor PMNS framework with the usual mixing angles and mass splittings.
    Invoked when defining the appearance probability and the effective phase shift.
  • domain assumption CPT violation is fully captured by a constant difference δΔm²₃₁ between neutrino and antineutrino mass splittings, with no CPT violation in mixing angles or other parameters.
    This is the parametrization chosen in the abstract to induce φ_eff(E).

pith-pipeline@v0.9.1-grok · 5900 in / 1605 out tokens · 26672 ms · 2026-06-26T16:15:04.683194+00:00 · methodology

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Reference graph

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    The right-most panels show the aggregated flux of both currents. This is only for the purpose of demonstrating that the two basins fit better in aggregate than the null hypothesis with CP conservation; in the actual fit the two horn currents are binned separately. Supplemental Methods and Tables – S1 SUPPL. FIG. 2. CP–CPT degeneracy analysis at the DUNE b...

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    The subtraction ηj −η nom j ensures that the slope terms vanish at the nominal hypersurface point, leaving only the intercept correction

    is the linear response slope to the IceCube detector nuisance parameter ηj. The subtraction ηj −η nom j ensures that the slope terms vanish at the nominal hypersurface point, leaving only the intercept correction. The final expectationE IC i is obtained by applying these category-wise correction factors to the flux-reweighted histograms and summing over t...