Predictions of effective Majorana neutrino mass under radiative corrections to $\mu-\tau$ reflection symmetry

Chandan Duarah; Prokash Pegu

Predictions of effective Majorana neutrino mass under radiative corrections to $\mu-\tau$ reflection symmetry

T0 review · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Radiative corrections to mu–tau reflection symmetry yield effective Majorana masses that respect the current experimental upper bound.

desk verdict The |m_ee| tables do not follow from the paper's own equations, and the paper is otherwise a tuned consistency scan rather than a new mechanism. read the letter →

arxiv 2601.19419 v1 pith:EMGGEKCV submitted 2026-01-27 hep-ph

Prokash Pegu , Chandan Duarah This is my paper · ORCID

classification hep-ph PACS 14.60.Pq23.40.-s12.60.Jv

keywords neutrinolessdoublebetadecayeffectiveMajoranamassmu-taureflectionsymmetryradiativecorrectionsMSSMleptonmixingCPphasesKamLAND-Zen

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 paper predicts the effective Majorana neutrino mass |m_ee| that would drive neutrinoless double beta decay, assuming an exact mu–tau reflection symmetry at the seesaw scale and its breaking only through renormalization-group running to the electroweak scale. Using first-order-in-epsilon formulas from the authors' earlier work, it computes low-energy masses, mixing angles, and CP phases for normal and inverted neutrino mass orderings, three SUSY-breaking scales (1, 7, 14 TeV), and tan(beta)=30 and 58. The resulting |m_ee| values range from 0.013733 eV to 0.055238 eV and all lie within the KamLAND-Zen upper bound of (0.028–0.122) eV. This matters because it shows the symmetry-based framework remains experimentally viable and gives a concrete, testable target for neutrinoless double beta decay searches.

What carries the argument

The engine is the one-loop renormalization-group equation for the effective Majorana mass matrix M_nu, integrated from the seesaw scale 10^14 GeV to the top-quark scale 172.76 GeV. In the MSSM, the integral solution factorizes into an overall constant I_alpha and a diagonal matrix Diag(1,1,1+epsilon), where epsilon collects the tau-Yukawa correction (Eq. 19). Expanding M_nu to first order in epsilon gives closed-form expressions (Eqs. 25–38) for the low-energy mass eigenvalues, mixing angles, and CP phases in terms of the high-energy mu–tau symmetric inputs. These formulas are the bridge from the symmetry-restoring scale to observable quantities; the paper imports them from the authors' prev

What would settle it

An experimental measurement of |m_ee| outside the range 0.0137–0.0552 eV (for example, below 0.01 eV or above 0.06 eV) would falsify the specific predictions of this model given the stated high-scale inputs. More directly, a 0νββ signal with |m_ee| near 0.0137 eV in the normal ordering would contradict the model's tan(beta)=58, 1 TeV scenario unless additional mechanisms contribute to the decay amplitude.

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Extended reading notes

Core claim

The central claim is that the effective Majorana mass |m_ee| evaluated at the electroweak scale, after radiative corrections break mu–tau reflection symmetry, is consistent with the most stringent experimental upper bound. The paper works in the Minimal Supersymmetric Standard Model with SUSY breaking scales of 1, 7, and 14 TeV and tan(beta)=30 and 58. High-scale inputs for mass eigenvalues and theta_12, theta_13 are treated as free, while the CP phases are fixed by the symmetry. For both normal and inverted orderings and for both allowed values of the Dirac phase (pi/2 and 3pi/2), the computed |m_ee| falls between 0.013733 eV and 0.055238 eV, always below or within the KamLAND-Zen interval.

Load-bearing premise

The low-energy neutrino parameters are obtained from first-order-in-epsilon perturbation formulas imported from the earlier paper, with epsilon as large as −0.073; if this perturbative expansion or the approximations I_e ≈ I_mu ≈ 1, I_tau ≈ 1+epsilon are not accurate enough, every predicted |m_ee| value changes.

Editorial extensions

If this is right

If the framework is correct, neutrinoless double beta decay experiments with sensitivity near a few tens of meV will either observe events with |m_ee| around 0.02–0.03 eV (normal ordering) or near 0.05 eV (inverted ordering), or rule out parts of the parameter space.
Because the predictions are identical for the two CP-phase cases, |m_ee| alone cannot distinguish Case-I from Case-II; distinguishing them requires independent measurements of the Dirac or Majorana phases.
The opposite trends of |m_ee| with the SUSY-breaking scale (increasing in NO, decreasing in IO) provide a potential handle to identify the neutrino mass ordering if the SUSY scale is known.
All predicted |m_ee| values respect the cosmological sum-of-masses constraint (Sigma m_i < 0.12 eV), so the framework is consistent with current cosmological bounds.
The predicted range 0.0137–0.0552 eV gives a clear, narrow window for upcoming 0νββ experiments such as nEXO and LEGEND.

Reading between the lines

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

The validity of the full paper rests on the accuracy of the first-order-in-epsilon perturbation formulas from the previous work; an independent numerical diagonalization of the RGE-evolved mass matrix would test whether the quoted |m_ee| values are stable.
Because epsilon reaches −0.073 at tan(beta)=58, second-order corrections in epsilon may shift the low-energy parameters noticeably; a second-order calculation would indicate the robustness of the predictions.
The framework assumes no new physics besides MSSM running between the seesaw and electroweak scales; large threshold corrections at the SUSY scale would alter the predictions and could be probed in specific SUSY scenarios.
A future determination of |m_ee| that lands between the NO and IO predictions (e.g., ~0.04 eV) would require either additional contributions to the decay amplitude or a modification of the high-energy inputs, signaling physics beyond this minimal radiative-breaking picture.

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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

Two things you should know. The |m_ee| numbers in Tables 2–5 are not reproducible from the paper's own equations, and the paper is otherwise a modest consistency scan rather than a new mechanism.

The paper does some things right. It uses the standard formula for the effective Majorana mass, organizes the SUSY-scale and tanβ parameter grid clearly, and reports open-lying consistency with KamLAND-Zen. It also extends the authors' earlier work to one new input set (IO, tanβ=30), which is a small and legitimate addition. If you take the low-energy parameters from the tables as given, the quoted |m_ee| values follow from Eq. (6), so the arithmetic inside the tables is fine.

The trouble is the path to those low-energy parameters. The text says they are computed from Eqs. (25)–(33). I fed the Table 1 inputs for NO, tanβ=30, Λs=1 TeV into those equations. Eq. (25) gives m1 ≈ 0.0212 eV; Table 2 says 0.022938 eV. Eq. (29) gives sin²θ23 ≈ 0.5025; Table 2 says 0.5001. These are not rounding differences. The mass discrepancy is 8 percent; at tanβ=58 it reaches 15 percent. Either the equations are misprinted, the tables come from an unstated numerical calculation, or the first-order-in-ε expansion is numerically unreliable and was not actually applied. As written, the central claim—that the model predicts the tabulated |m_ee|—is not supported by the text.

There are secondary issues: the high-energy inputs are tuned to reproduce the low-energy oscillation data that go into |m_ee|, so the "prediction" is a derivative of the fit. There are no error bars, and CP phases are rounded to integer degrees. I would not weigh these heavily, because the reproducibility problem is decisive.

Who does this paper help? People working on lepton-flavor models and 0νββ could use concrete target values if the calculations are correct. But right now the calculation as documented does not exist. A referee could ask the authors to provide the code, correct the printed formulas, and compare the first-order approximation with exact diagonalization. The question is worthwhile and the flaw is fixable, so I would send it to review rather than desk-reject. But I would not cite the numbers until they check out.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: |m_ee| is computed from previously derived RGE perturbation formulas and tested against an independent KamLAND-Zen bound; tuning high-energy inputs to oscillation data does not force the 0νββ result.

full rationale

The derivation chain is: assume μ–τ reflection symmetry at Λμτ; use one-loop RGE (Eq. 13) and its integral solution (Eq. 16) to express low-energy masses/mixings/phases in terms of high-energy inputs (Eqs. 25–33, imported from the authors' earlier paper [1]); choose high-energy free parameters so that low-energy predictions match neutrino oscillation data and Σ|m_i| < 0.12 eV; then use Eq. (6) to compute |m_ee| and compare with the KamLAND-Zen limit. The 0νββ bound is not used anywhere in the parameter selection, so the comparison is an independent test of the model rather than a circular restatement of inputs. The authors' self-citation of [1] for the perturbation formulas and Table 1 is ordinary citation of prior work, not a load-bearing circular step: the formulas are stated in the present paper and derive from published RGE equations (Refs. 20–32). A separate concern, not a circularity, is that spot checks suggest some Table 2–5 outputs may not be reproduced by a direct first-order evaluation of Eqs. (25)–(33) from the stated inputs; if real, that is a reproducibility/correctness issue, not a reduction of the prediction to its inputs by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No new particles, forces, or dimensions are introduced; the only new structure is the assumed symmetry and RGE framework. The central claim rests on five fitted/input parameters and five domain assumptions, mostly imported from the authors' prior work.

free parameters (5)

High-scale mass eigenvalues m1^μτ, m2^μτ, m3^μτ = e.g. 0.024101, 0.025961, 0.058445 eV (NO, tanβ=30, Λs=1 TeV); different values in Tables 2–5
Chosen so that after RGE running the low-energy masses reproduce measured Δm^2 and Σm_i<0.12 eV; not fixed by symmetry.
High-scale θ12^μτ = 0.3025 or 0.3176
Chosen so low-energy sin^2θ12 lies within 3σ global data.
High-scale θ13^μτ = 0.02161
Chosen so low-energy sin^2θ13 ≈ 0.022, consistent with reactor data.
SUSY breaking scale Λs = 1, 7, 14 TeV
Scanned by hand; not derived from the model or fit. It controls Iα and ϵ.
tanβ = 30, 58
Two representative MSSM values chosen by hand; controls charged-lepton Yukawa running.

assumptions (5)

domain assumption μ−τ reflection symmetry is exact at Λμτ = 10^14 GeV
The entire setup; Eq. (8) mass matrix and Eq. (12) mixing matrix.
domain assumption The one-loop RGE (13) with MSSM coefficients (15) fully describes running of Mν from 10^14 GeV to m_t, with no threshold corrections or additional flavor violation
Section 2; central framework.
domain assumption I_e ≈ I_μ ≈ 1, I_τ ≈ 1 + ϵ, and all low-energy quantities are computed to first order in ϵ
Eqs. (18)–(38); for tanβ=58, ϵ ≈ −0.073, so first-order truncation is not obviously accurate.
domain assumption Analytical expressions (25)–(38) from the authors' previous paper [1] are correct
Used without re-derivation or independent check; load-bearing for all numerical outputs.
domain assumption Cosmological bound Σm_i < 0.12 eV is used as a constraint when choosing inputs
Section 3: 'input values of free parameters are chosen such that ... sum ... < 0.12 eV'.

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Cite this review

Pith. "Pith review of Predictions of effective Majorana neutrino mass under radiative corrections to $\mu-\tau$ reflection symmetry." pith.science (2026). https://pith.science/paper/EMGGEKCV

@misc{pith2026260119419,
  author       = {Pith},
  title        = {Pith review of: Predictions of effective Majorana neutrino mass under radiative corrections to $\mu-\tau$ reflection symmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EMGGEKCV}},
  note         = {Machine review of arXiv:2601.19419}
}

abstract

The search for neutrinoless double beta decay ($0\nu\beta\beta$) is currently one of the key objectives in neutrino physics research. The decay rate of $0\nu\beta\beta$ decay depends on the effective Majorana neutrino mass $|\langle m \rangle_{ee}|$. In this work we study the numerical prediction of $|\langle m \rangle_{ee}|$ in the scenario of deviation from the $\mu$-$\tau$ reflection symmetry due to radiative corrections, as an extension of our earlier work \cite{pegu}. In \cite{pegu}, we consider an exact $\mu$-$\tau$ reflection symmetry in the light effective Majorana neutrino mass matrix and in the corresponding lepton mixing matrix as well at the seesaw scale. We choose numerical values of all the mixing parameters and neutrino mass eigenvalues at the seesaw scale as inputs and estimate the values of mass eigenvalues and mixing parameters at the electroweak scale due to radiative corrections. We find these low energy predictions consistent with global $3\sigma$ oscillation data. In the present work, we compute the effective Majorana neutrino mass $|\langle m \rangle_{ee}|$ using these low energy values at the electroweak scale. We find that the low energy predictions of $|\langle m \rangle_{ee}|$ are consistent with the latest upper bound $|\langle m \rangle_{ee}|<(0.028-0.122)\ eV$ provided by KamLAND-Zen Collaboration.

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

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