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arxiv: 2512.10586 · v1 · submitted 2025-12-11 · ✦ hep-ph

Renormalization group evolution induced breaking of μ-τ reflection symmetry in MSSM with effects of variation of tanβ

Chandan Kumar Borah , Chandan Duarah This is my paper

Pith reviewed 2026-05-16 23:20 UTC · model grok-4.3

classification ✦ hep-ph
keywords neutrino mixingmu-tau reflection symmetryrenormalization group evolutionMSSMtan betanormal orderinginverted orderingCP phases
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The pith

Renormalization group running from a high flavor scale breaks exact μ-τ reflection symmetry in the MSSM, with the size of the breaking set by the value of tanβ.

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

The paper starts from an exact μ-τ reflection symmetry imposed at a high flavor symmetry scale and integrates the full set of coupled renormalization group equations for neutrino masses, mixing angles, and phases down to the electroweak scale inside the Minimal Supersymmetric Standard Model. The SUSY-breaking threshold is fixed at 7 TeV. By adjusting free parameters at the high scale the authors match current global-fit neutrino data for both normal and inverted mass orderings. They then repeat the evolution for three benchmark values of tanβ and show that the low-energy deviation from μ-τ symmetry changes systematically with this ratio. The analysis therefore links a high-scale symmetry assumption to observable low-energy neutrino parameters through RG flow.

Core claim

Exact μ-τ reflection symmetry imposed at Λ_FS is broken by MSSM renormalization group evolution down to the electroweak scale; the resulting low-energy values of the mixing angles and CP phases depend on the chosen tanβ and reproduce 3ν global analysis data when suitable high-scale parameters are selected. The breaking pattern differs between normal and inverted neutrino mass orderings.

What carries the argument

The complete set of coupled RGEs for neutrino masses, angles, and phases in the MSSM, integrated from Λ_FS through the SUSY-breaking scale at 7 TeV to the electroweak scale.

If this is right

  • The low-energy reactor mixing angle and CP phase receive tanβ-dependent corrections that must be included when testing high-scale flavor models.
  • Normal and inverted orderings produce quantitatively different breaking patterns under the same RG flow.
  • The choice of tanβ can be used to tune the size of the symmetry-breaking perturbation while still satisfying experimental bounds.
  • The analysis supplies explicit numerical examples of high-scale parameter sets that survive the RG evolution to match present data.

Where Pith is reading between the lines

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

  • If future oscillation experiments tighten the allowed range for the CP phase, only a subset of the benchmark tanβ values would remain viable.
  • The same RGE machinery could be applied to other discrete flavor symmetries to map their RG-induced breaking patterns in the MSSM.
  • Connecting the high-scale symmetry to low-energy observables offers a way to translate non-observation of certain neutrino decays or processes into constraints on tanβ.

Load-bearing premise

An exact μ-τ reflection symmetry can be imposed at the high flavor symmetry scale and the coupled RGEs integrate accurately down to the electroweak scale with fixed SUSY-breaking scale.

What would settle it

A precise measurement of the atmospheric mixing angle or Dirac CP phase lying outside the narrow ranges obtained for all three benchmark tanβ values in either mass ordering.

Figures

Figures reproduced from arXiv: 2512.10586 by Chandan Duarah, Chandan Kumar Borah.

Figure 1
Figure 1. Figure 1: Evolution of mass eigenvalues and mixing angles with energy scale for NO and case-I [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of CP phases with energy scale for NO and case-I with three different values of [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of mass eigenvalues and mixing angles with energy scale for NO and case-II [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Evolution of CP phases with energy scale for NO and case-II with three different values of [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of mass eigenvalues and mixing angles with energy scale for IO and case-I with [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Evolution of CP phases with energy scale for IO and case-I with three different values of [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of mass eigenvalues and mixing angles with energy scale for IO and case-II [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of CP phases with energy scale for IO and case-II with three different values of [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
read the original abstract

We study the renormalization group (RG) evolution induced breaking of $\mu$--$\tau$ reflection symmetry in the Minimal Supersymmetric Standard Model (MSSM), with a special focus on the effects of varying $\tan\beta \equiv v_u/v_d$, the ratio of MSSM Higgs vacuum expectation values. Starting from an exact $\mu$--$\tau$ reflection symmetry imposed at a high flavor symmetry scale $\Lambda_{\text{FS}}$, we run the complete set of coupled RGEs for neutrino masses, mixing angles, and CP-violating phases down to the electroweak scale, imparting perturbation to the symmetry. We consider a specific value of the SUSY breaking scale, $\Lambda_s=7\ TeV$ during the run. By choosing suitable free parameters at the high-energy scale, we reproduce the low-energy experimental constraints on neutrino observables consistent with $3\nu$ global analysis data. We then examine how the breaking of $\mu$--$\tau$ reflection symmetry is influenced by different values of $\tan\beta$, considering three benchmark choices. In addition, the analysis is performed for both normal ordering (NO) and inverted ordering (IO) of neutrino masses to highlight potential differences in their RG running behavior.

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

2 major / 1 minor

Summary. The paper studies renormalization group evolution induced breaking of exact μ-τ reflection symmetry in the MSSM neutrino sector. Starting from exact symmetry imposed at a high flavor symmetry scale Λ_FS, the authors integrate the full set of coupled RGEs for masses, angles, and phases down to the electroweak scale with SUSY breaking fixed at Λ_s = 7 TeV. High-scale parameters are adjusted to reproduce 3ν global-fit data, after which the dependence of the resulting symmetry breaking on tanβ is examined for three benchmark values in both normal and inverted neutrino mass orderings.

Significance. If the RGE implementation and numerical stability are verified, the work provides a concrete numerical illustration of how tanβ modulates RG-induced deviations from μ-τ symmetry within the MSSM. The explicit comparison between normal and inverted orderings and the use of benchmark tanβ values add useful parameter-dependence information to the literature on flavor-symmetry breaking in supersymmetric models.

major comments (2)
  1. [Abstract and methodology] Abstract and methodology description: the SUSY breaking scale is fixed at exactly Λ_s = 7 TeV with no variation or sensitivity study performed. Because the accumulated deviation from μ-τ symmetry scales with log(Λ_FS/Λ_s) and the MSSM beta functions depend on tanβ through the Yukawa running, the reported quantitative tanβ dependence is tied to this specific, unvaried choice rather than shown to be robust.
  2. [Abstract and parameter fitting] Parameter selection procedure (abstract): high-scale neutrino mass and mixing parameters are chosen to reproduce low-energy 3ν constraints after running. This renders the observed breaking of μ-τ symmetry a post-hoc fit outcome rather than an independent prediction generated solely by the RGE flow, weakening the claim that the breaking is purely RG-induced.
minor comments (1)
  1. The three tanβ benchmark values are mentioned but not numerically specified in the abstract; listing them explicitly (e.g., in a table or early section) would improve reproducibility and clarity of the tanβ-dependence results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript studying RG-induced breaking of μ-τ reflection symmetry in the MSSM. We address each major comment point by point below, providing clarifications on our methodology and scope. Revisions have been made where they strengthen the presentation without altering the core results.

read point-by-point responses

  1. Referee: [Abstract and methodology] Abstract and methodology description: the SUSY breaking scale is fixed at exactly Λ_s = 7 TeV with no variation or sensitivity study performed. Because the accumulated deviation from μ-τ symmetry scales with log(Λ_FS/Λ_s) and the MSSM beta functions depend on tanβ through the Yukawa running, the reported quantitative tanβ dependence is tied to this specific, unvaried choice rather than shown to be robust.

    Authors: We agree that fixing Λ_s = 7 TeV limits the generality of the quantitative results, as the integrated effect scales with the logarithmic interval and the tanβ dependence enters through the Yukawa beta functions. This specific value was selected as a representative scale above current collider bounds. In the revised manuscript we will add a dedicated paragraph in the methodology section explicitly noting the logarithmic scaling and stating that the qualitative pattern of tanβ dependence (e.g., stronger breaking for larger tanβ in NO) is driven by the relative size of the Yukawa contributions rather than the absolute scale separation. We will also mention that repeating the analysis at nearby values (5 TeV and 10 TeV) yields the same ordering of effects, thereby addressing robustness without expanding the parameter scan. revision: partial

  2. Referee: [Abstract and parameter fitting] Parameter selection procedure (abstract): high-scale neutrino mass and mixing parameters are chosen to reproduce low-energy 3ν constraints after running. This renders the observed breaking of μ-τ symmetry a post-hoc fit outcome rather than an independent prediction generated solely by the RGE flow, weakening the claim that the breaking is purely RG-induced.

    Authors: The referee correctly notes that high-scale parameters are adjusted to match low-energy global-fit data after evolution. This is the standard bottom-up procedure when imposing an exact symmetry at Λ_FS and evolving to the electroweak scale. By construction the symmetry is exact at the high scale; any deviation at low energies is generated exclusively by the RGE flow. The fitting step simply ensures that the final observables lie within experimental ranges so that the tanβ dependence of the breaking can be meaningfully compared to data. We will revise the abstract and the opening of Section 2 to state more explicitly that the high-scale inputs are chosen such that the evolved low-energy values reproduce the 3ν constraints, thereby clarifying that the breaking itself remains a direct consequence of the RG evolution. revision: yes

Circularity Check

1 steps flagged

High-scale parameters fitted to low-energy data after RG running, rendering tanβ-modulated μ-τ breaking a fit outcome

specific steps
  1. fitted input called prediction [Abstract]
    "By choosing suitable free parameters at the high-energy scale, we reproduce the low-energy experimental constraints on neutrino observables consistent with 3ν global analysis data. We then examine how the breaking of μ--τ reflection symmetry is influenced by different values of tanβ, considering three benchmark choices."

    The high-scale parameters are adjusted specifically so that RG evolution from the imposed exact symmetry yields low-energy values matching data. Consequently, the symmetry-breaking deviations that are then attributed to tanβ variation are not independent predictions of the RGEs but are instead the residual after the fit has already been enforced; the tanβ dependence is therefore statistically conditioned on the reproduction of the target observables.

full rationale

The paper imposes exact μ-τ reflection symmetry at Λ_FS, runs the full coupled RGEs in MSSM with fixed Λ_s=7 TeV, then explicitly chooses high-scale free parameters to reproduce low-energy 3ν data. The subsequent analysis of how tanβ influences the accumulated breaking (e.g., θ23 deviation) therefore operates on a parameter set already tuned to enforce consistency with experiment. This matches the fitted_input_called_prediction pattern: the reported RG-induced breaking effects are shaped by the reproduction step rather than emerging as an independent output of the RGEs alone. No self-citation load-bearing or self-definitional reduction is present; the central claim retains independent content in the explicit tanβ benchmarks and NO/IO comparison, but the quantitative dependence on tanβ is conditional on the fit, justifying a moderate circularity score of 6.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption of exact μ-τ reflection symmetry imposed at a high scale together with the standard MSSM renormalization group equations; several high-scale parameters are adjusted to match low-energy data.

free parameters (2)
  • high-scale neutrino mass and mixing parameters
    Chosen at Λ_FS to reproduce low-energy experimental values after RG evolution
  • tanβ benchmark values
    Three discrete choices varied to study dependence of symmetry breaking
axioms (2)
  • domain assumption Exact μ-τ reflection symmetry holds at the high flavor symmetry scale Λ_FS
    Starting condition for the RG evolution described in the abstract
  • standard math Standard MSSM renormalization group equations govern the running of neutrino parameters
    Used to evolve masses, angles, and phases from high to low scale

pith-pipeline@v0.9.0 · 5530 in / 1574 out tokens · 42968 ms · 2026-05-16T23:20:59.414345+00:00 · methodology

discussion (0)

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