Quantum Decoherence at ESSnuSB Experiment

ESSnuSB: M. Ghosh

REVIEW 4 major objections 5 minor 6 references

Quantum Decoherence at ESSnuSB Experiment

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The ESSnuSB experiment can bound quantum decoherence as tightly as DUNE while still measuring CP violation, this proceedings argues.

desk verdict Useful ESSnuSB decoherence proceedings, but Eq. (5) has index typos that make the printed centerpiece formula unreliable. read the letter →

arxiv 2412.11791 v1 pith:3FP6QGOW submitted 2024-12-16 hep-ph hep-ex

ESSnuSB: M. Ghosh This is my paper · ORCID

classification hep-phhep-ex PACS 14.60.Pq

keywords quantumdecoherenceneutrinooscillationsESSnuSBCPviolationLindbladmasterequationlong-baselineexperimentopensystemparameters

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

This proceedings paper argues that the planned ESSnuSB long-baseline neutrino experiment can do double duty: in addition to its primary goal of measuring the CP-violating phase $\delta_{\rm CP}$ at the second oscillation maximum, it can place competitive constraints on quantum decoherence. Using the open-quantum-system (Lindblad) formalism, the author shows that ESSnuSB's sensitivity to the two independent decoherence parameters $\Gamma_{21}$ and $\Gamma_{32}$ is better than the existing MINOS bounds and comparable to the projected DUNE sensitivity. The paper further shows that the CP-violation and CP-precision sensitivities of ESSnuSB are not strongly affected unless the decoherence parameters are large. If correct, the result means the experiment could simultaneously pin down the CP phase and test whether neutrinos lose quantum coherence through interactions with an environment.

What carries the argument

The load-bearing object is the Lindblad master equation, $\partial_t \rho(t) = -i[H,\rho(t)] + D[\rho(t)]$, in the open-quantum-system treatment of decoherence, together with the particular diagonal form of the dissipator $D$. The key identity is $\Gamma_{31} = \Gamma_{21}+\Gamma_{32}-2\sqrt{\Gamma_{21}\Gamma_{32}}$, which reduces the three damping rates to the two independent parameters $\Gamma_{21}$ and $\Gamma_{32}$ that the experiment is claimed to constrain. The machinery works by turning decoherence into an exponential damping factor $e^{-\Gamma_{ij}L}$ on each oscillation-interference term in the probability, so stronger damping means a faster loss of the coherent oscillations. The validity of the whole construction hinges on $D$ staying diagonal in the matter basis, which the paper argues holds at ESSnuSB because the matter effect is small.

What would settle it

Evaluate the full matter-basis dissipator for ESSnuSB's 360 km baseline and the neutrino energies of the second oscillation maximum using a realistic Earth density profile, and compare the probabilities from Eq. (5) with a numerical solution of the Lindblad equation that keeps the off-diagonal dissipator terms; if the contours for $\Gamma_{21}$ and $\Gamma_{32}$ shift by more than the claimed sensitivity, the central claim fails.

Watch

Extended reading notes

Core claim

On its own terms, the central claim is that ESSnuSB, a future experiment with a far detector 360 km from a powerful neutrino source, can constrain the vacuum-form decoherence parameters $\Gamma_{21}$ and $\Gamma_{32}$ with sensitivities in the $10^{-24}$ GeV range, surpassing MINOS and matching DUNE, while preserving the experiment's ability to measure $\delta_{\rm CP}$. The analysis evolves the neutrino density matrix with the Lindblad master equation and takes the dissipator to be diagonal in the vacuum flavour basis, $D = -\mathrm{diag}(\Gamma_{21},\Gamma_{21},0,\Gamma_{31},\Gamma_{31},\Gamma_{32},\Gamma_{32},0)$, with $\Gamma_{31} = \Gamma_{21}+\Gamma_{32}-2\sqrt{\Gamma_{21}\Gamma_{32}}$, so that only two parameters are free. This yields the damped-oscillation probability formula Eq. (5), in which the interference terms are multiplied by $e^{-\Gamma_{ij}L}$. The author states that the formula applies because matter effects at ESSnuSB's baseline and energies are small enough that the vacuum-form dissipator remains effectively diagonal. The constraint curves and the $\delta_{\rm CP}$ sensitivity plots in the proceedings are then presented as evidence for those claims.

Load-bearing premise

The analysis stands on the assumption that matter effects at ESSnuSB are small enough that the vacuum-form dissipator $D$ stays approximately diagonal in the matter basis and Eq. (5) remains valid, a condition the paper asserts without quantifying a threshold, so if that fails the reported $\Gamma_{21}$ and $\Gamma_{32}$ bounds could be biased.

Editorial extensions

If this is right

ESSnuSB would independently constrain both $\Gamma_{21}$ and $\Gamma_{32}$ at the $10^{-24}$ GeV scale, providing decoherence bounds that complement DUNE's expected reach.
The CP-violation and CP-precision sensitivities shown in the proceedings indicate that the extraction of $\delta_{\rm CP}$ remains reliable as long as the decoherence parameters stay small.
Reducing systematic uncertainties from 10% to 2% sharpens the decoherence constraints, so detector calibration improvements translate directly into stronger bounds on environment-induced decoherence.
If no signal is found, the resulting exclusion regions on $\Gamma_{21}$ and $\Gamma_{32}$ would extend the current MINOS limits and serve as a test of decoherence models based on the Lindblad equation.

Reading between the lines

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

Adding ESSnuSB to a combined fit with DUNE and MINOS could break the degeneracy between $\delta_{\rm CP}$ and the decoherence parameters, because the three experiments sample different baselines and matter densities; the proceedings present the sensitivities separately rather than as a joint fit.
Because ESSnuSB's small matter effect makes the vacuum-form dissipator nearly diagonal, its bounds would be the cleanest vacuum-form decoherence limits; extending the same method to higher energies or longer baselines would require including the off-diagonal dissipator terms the paper sets aside.
A direct test of the robustness claim would be a full simultaneous fit to simulated ESSnuSB data with $\delta_{\rm CP}$, $\Gamma_{21}$, and $\Gamma_{32}$ all free, checking whether the best-fit CP phase is biased when decoherence is present; the proceedings show sensitivity curves but not such a marginalized fit.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Matt — short take: this is a four-page proceedings summarizing ESSnuSB's projected sensitivity to the decoherence parameters Gamma21 and Gamma32. The application is new, and the comparison to DUNE and MINOS is plausible. But Eq. (5), the only probability formula shown, has index typos that make it unusable as printed. That doesn't sink the paper if the companion paper [6] is correct, but it should be flagged.

What's genuinely good: the author imports the Lindblad dissipator of Ref [3] (Gomes et al.) without overclaiming, points to the companion JHEP paper for details, and is upfront that the formalism is valid only when matter effects are small. The GLoBES setup with 2%, 5%, 10% systematics is standard. For a proceedings, this is an honest summary.

The soft spots: Eq. (5) has the wrong index structure. The real part should involve products like \tilde U_{alpha i}\tilde U*_{beta i}\tilde U*_{alpha j}\tilde U_{beta j}; what's printed has \tilde U*_{alpha i}\tilde U_{beta i}\tilde U_{beta j}\tilde U*_{beta j}, which is not symmetric in alpha↔beta and doesn't reduce to the no-decoherence limit. The imaginary term uses an undefined index k. Since the quoted sensitivities come from simulations using this formula, a reader cannot reproduce the curves from the text. I'd bet this is a typo in the proceedings, not in the actual analysis, but the author needs to say that explicitly.

Also, the 'matter effect is small' condition is asserted without a quantitative threshold. That matters because the dissipator is defined in vacuum; at higher energies the matter-basis rotation breaks the simple form. The paper acknowledges it but doesn't give the criterion. For a proceedings that's a minor omission, but it matters for judging whether the Gamma21/Gamma32 constraints are biased.

On balance: the abstract's claims are plausible and the paper is transparent about its provenance. It's a useful write-up for ESSnuSB folks, and it deserves referee attention, but only after the Eq. (5) typo is corrected or cross-referenced. I'd accept it pending that fix.

Reading group: maybe. I wouldn't cite it this year, since the full analysis is the companion paper. But worth a skim for anyone tracking decoherence constraints.

Referee Report

4 major / 5 minor

Summary. This proceedings paper studies the sensitivity of the future ESSnuSB long-baseline neutrino experiment to quantum decoherence, using the Lindblad master equation with the dissipation matrix of Ref. [3]. The author presents GLoBES-based sensitivity curves for the two decoherence parameters Gamma21 and Gamma32, compares them with MINOS and DUNE, and studies the impact of decoherence on the measurement of the CP-violating phase delta_CP. The abstract claims that ESSnuSB can constrain the decoherence parameters better than MINOS and comparably to DUNE, and that the CP measurement capability is robust in the presence of decoherence. The paper is short and states that more details are available in the companion paper Ref. [6].

Significance. If the central claims are correct, the paper would indicate that ESSnuSB, a future experiment designed mainly for CP violation at the second oscillation maximum, can also provide competitive bounds on quantum decoherence. This is potentially valuable for the growing effort to test open-quantum-system effects in neutrino oscillations. The paper is transparently based on a companion publication [6] and uses the standard Lindblad formalism, which is a strength. However, as printed, the key oscillation probability formula in Eq. (5) contains index errors that prevent the reader from reproducing or verifying the results, and the matter-effect validity condition is not quantified. These issues are load-bearing for the stated sensitivity claims, so the manuscript needs substantial correction before it can be accepted.

major comments (4)

[Section 1, Eq. (5)] The printed expression for P(nu_alpha -> nu_beta) is not a valid oscillation probability as written. The real part contains the product U~*_{alpha i} U~_{beta i} U~_{beta j} U~*_{beta j}, which is not symmetric under alpha <-> beta and does not reduce to the standard vacuum probability. The imaginary part contains U~*_{alpha k} U~_{beta k} U~_{beta j} U~*_{beta j} with an undefined index k. The standard decoherence formula requires products of the form U~*_{alpha i} U~_{beta i} U~_{alpha j} U~*_{beta j} (or the conjugate). Since all sensitivity curves in Section 3 are obtained from simulations based on this equation, the central claim cannot be independently verified from the text. The author should either correct Eq. (5) or explicitly state that it contains a typographical error and refer the reader to the correct expression in the companion paper [6].
[Section 1, paragraph after Eq. (5)] The statement that the formalism remains valid for ESSnuSB because 'the matter effect is small' is not quantified. The dissipator D is defined in vacuum and becomes off-diagonal in the matter basis; the probability formula in Eq. (5) relies on the dissipator being diagonal in the effective matter basis. A quantitative threshold is needed, for example a condition on the ratio of the matter potential to the relevant Delta m^2/(2E), or an estimate of the induced error in the decoherence parameters. Without such a threshold, the quoted constraints on Gamma21 and Gamma32 could be biased, especially at higher energies where matter effects are larger.
[Section 3, Fig. 1 and Fig. 2] The sensitivity analysis is not reproducible from the text. The figures show constraints for systematic errors of 2%, 5%, and 10%, but the paper does not define how these systematics are implemented in GLoBES (e.g., normalization pulls, energy-scale uncertainties, backgrounds) or how the chi-squared is computed. There are no event rate tables and no statement of the number of events, signal and background normalization, or any priors on oscillation parameters. These details are needed to evaluate the claimed sensitivity and to compare with the MINOS and DUNE results. Since this is a proceedings paper, the author could instead state explicitly that all such details are in Ref. [6], but the present text does not provide that bridge.
[Section 4 and abstract] The comparison 'better than MINOS but comparable to DUNE' is made without specifying the exact source of the MINOS and DUNE constraints. Different analyses may use different parametrizations of the dissipator, different confidence levels, and different treatment of matter effects. The author should state whether the MINOS and DUNE bounds are taken from Refs. [5] and [3] with the same Gamma definitions as in Eq. (3), and whether the comparison is performed at the same confidence level. Without this, the headline comparison may not be apples-to-apples.

minor comments (5)

[Section 1, Introduction] There is a typographical duplication: 'with which which are generally studied' should read 'which are generally studied'.
[Section 1, Eq. (2)] The notation rho_beta(t) in the trace is ambiguous; presumably rho_beta is the projector onto flavour beta. Please define it explicitly.
[Section 1, after Eq. (3)] The dissipator expansion D = D_jk rho_k lambda_j uses rho_k for matrix elements of rho, which conflicts with the use of rho(t) for the density matrix. A different symbol, for example r_k, would improve clarity.
[Section 3, Fig. 1 and Fig. 2] In the figure captions and axis labels, '21' and '32' should be typeset as Gamma_21 and Gamma_32. The horizontal axis label 'log10' is incomplete; it should specify the quantity being plotted, e.g., log10(Gamma/GeV).
[References] Reference [2] should include the full publication data for Lindblad (journal, volume, page, year), which is currently present but the page range would be helpful. Reference [3] is for DUNE, but the comparison to DUNE in the text is not explicit about whether the same reference is used.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analysis is a parameter scan under an imported Lindblad model, and the sensitivity claims are benchmark comparisons rather than derivations that reduce to their own inputs.

full rationale

The paper's derivation chain is a standard phenomenological projection: it adopts a specific Lindblad dissipator from the literature (Eq. 3, from Ref. [3]), uses the corresponding oscillation probability (Eq. 5), and then scans the two decoherence parameters Gamma21 and Gamma32 in a GLoBES simulation of ESSnuSB to produce chi-square sensitivity curves. No step fits a parameter to a subset of data and then renames that fit as a prediction; the scanned parameters are the model inputs, and the output is an expected sensitivity under a chosen true value. The comparison with MINOS and DUNE is a benchmark against published constraints, not a circular reduction. The paper is transparent that the dissipator form is 'the one that is studied in Ref. [3]', so it is an imported model assumption, not a result derived here. The companion paper Ref. [6] is self-cited for details, which is normal for a proceedings and does not carry the load of the argument: the figures and claims are present in this paper. The apparent index inconsistency in Eq. (5) is a correctness or typographical concern, not circularity, because the probability formula is an input assumption rather than a quantity that is defined in terms of the sensitivity result. Overall, the central claims do not reduce to their inputs by construction.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the Lindblad equation and the specific decoherence model imported from Ref. [3]. The only additional assumption is the smallness of matter effects at ESSnuSB, which the paper asserts but does not quantify. No new entities or fitted parameters are introduced beyond the scanned decoherence parameters Gamma21 and Gamma32.

assumptions (3)

standard math Lindblad master equation governs the neutrino density matrix evolution (Eq. 1).
Used as the fundamental evolution equation for the open quantum system; standard in quantum mechanics.
domain assumption Specific dissipator form D = -diag(Gamma21, Gamma21, 0, Gamma31, Gamma31, Gamma32, Gamma32, 0) with Gamma31 related to Gamma21 and Gamma32 (Eqs. 3-4).
This particular decoherence model is adopted from Ref. [3]; different dissipator choices could yield different sensitivities.
domain assumption Matter effects are small enough for ESSnuSB that the vacuum-form probability formula Eq. (5) with matter-modified PMNS matrix remains valid.
The paper states this is valid at ESSnuSB but does not provide a numerical threshold; it is load-bearing for the correctness of the computed constraints.

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Cite this review

Pith. "Pith review of Quantum Decoherence at ESSnuSB Experiment." pith.science (2026). https://pith.science/paper/3FP6QGOW

@misc{pith2026241211791,
  author       = {Pith},
  title        = {Pith review of: Quantum Decoherence at ESSnuSB Experiment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3FP6QGOW}},
  note         = {Machine review of arXiv:2412.11791}
}

abstract

In this proceedings we study the sensitivity of the ESSnuSB experiment to probe quantum decoherence. ESSnuSB is a future long-baseline neutrino oscillation experiment which aims to measure $\delta_{\rm CP}$ by probing the second oscillation maximum. Using the open quantum system formalism for decoherence, we have shown that the sensitivity of ESSnuSB to constrain the decoherence parameters is better than MINOS but comparable to DUNE. We have also shown that the CP measurement capability of ESSnuSB is robust in presence of decoherence.

Figures

Figures reproduced from arXiv: 2412.11791 by the authors.

**Figure 2.** Effect of the decoherence parameters in the 𝛿𝐶𝑃 sensitivity. 4. Conclusion In this proceedings we have studied quantum decoherence in the context of ESSnuSB experiment. Our results show that the sensitivity is better than MINOS [5] and comparable to DUNE [3]. Further, CP sensitivity is not affected much if the decoherence parameters are not very large. For more details see Ref. [6] on which this proceedings is base… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

6 extracted references · 1 canonical work pages

[6]

DecoherenceinneutrinooscillationattheESSnuSBexperiment,

J.Aguilar et al.[ESSnuSB],“DecoherenceinneutrinooscillationattheESSnuSBexperiment,” JHEP 08 (2024), 063 [arXiv:2404.17559 [hep-ex]]. 4

arXiv 2024
[3]

Quantum Decoherence Effects in Neutrino Oscillations at DUNE,

G. Balieiro Gomes, D. V. Forero, M. M. Guzzo, P. C. De Holanda and R. L. N. Oliveira, “Quantum Decoherence Effects in Neutrino Oscillations at DUNE,” Phys. Rev. D100(2019) no.5, 055023 [arXiv:1805.09818 [hep-ph]]

arXiv 2019
[5]

Neutrino oscillation bounds on quantum decoherence,

V. De Romeri, C. Giunti, T. Stuttard and C. A. Ternes, “Neutrino oscillation bounds on quantum decoherence,” JHEP09(2023), 097 [arXiv:2306.14699 [hep-ph]]

arXiv 2023
[1]

TheEuropeanSpallation Source neutrino super-beam conceptual design report,

A. Alekou, E. Baussan, A. K. Bhattacharyya, N. Blaskovic Kraljevic, M. Blennow, M. Bo- gomilov,B.Bolling,E.Bouquerel,O.BuchanandA.Burgman, et al.“TheEuropeanSpallation Source neutrino super-beam conceptual design report,” Eur. Phys. J. ST231 (2022) no.21, 3779-3955 [erratum: Eur. Phys. J. ST232(2023), 15-16] [arXiv:2206.01208 [hep-ex]]

arXiv 2022
[2]

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G.Lindblad,“OntheGeneratorsofQuantumDynamicalSemigroups,”Commun.Math.Phys. 48 (1976), 119

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[4]

Huber, M

P. Huber, M. Lindner and W. Winter, Comput. Phys. Commun. 167 (2005), 195 doi:10.1016/j.cpc.2005.01.003 [arXiv:hep-ph/0407333 [hep-ph]]

arXiv 2005

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [6]

DecoherenceinneutrinooscillationattheESSnuSBexperiment,

J.Aguilar et al.[ESSnuSB],“DecoherenceinneutrinooscillationattheESSnuSBexperiment,” JHEP 08 (2024), 063 [arXiv:2404.17559 [hep-ex]]. 4

arXiv 2024

[2] [3]

Quantum Decoherence Effects in Neutrino Oscillations at DUNE,

G. Balieiro Gomes, D. V. Forero, M. M. Guzzo, P. C. De Holanda and R. L. N. Oliveira, “Quantum Decoherence Effects in Neutrino Oscillations at DUNE,” Phys. Rev. D100(2019) no.5, 055023 [arXiv:1805.09818 [hep-ph]]

arXiv 2019

[3] [5]

Neutrino oscillation bounds on quantum decoherence,

V. De Romeri, C. Giunti, T. Stuttard and C. A. Ternes, “Neutrino oscillation bounds on quantum decoherence,” JHEP09(2023), 097 [arXiv:2306.14699 [hep-ph]]

arXiv 2023

[4] [1]

TheEuropeanSpallation Source neutrino super-beam conceptual design report,

A. Alekou, E. Baussan, A. K. Bhattacharyya, N. Blaskovic Kraljevic, M. Blennow, M. Bo- gomilov,B.Bolling,E.Bouquerel,O.BuchanandA.Burgman, et al.“TheEuropeanSpallation Source neutrino super-beam conceptual design report,” Eur. Phys. J. ST231 (2022) no.21, 3779-3955 [erratum: Eur. Phys. J. ST232(2023), 15-16] [arXiv:2206.01208 [hep-ex]]

arXiv 2022

[5] [2]

OntheGeneratorsofQuantumDynamicalSemigroups,

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Huber, M

P. Huber, M. Lindner and W. Winter, Comput. Phys. Commun. 167 (2005), 195 doi:10.1016/j.cpc.2005.01.003 [arXiv:hep-ph/0407333 [hep-ph]]

arXiv 2005