{"id":"f7a9ccf8-c46c-4451-aafc-996bc58a4545","arxiv_id":"2512.10586","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":3.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"RG evolution from a high flavor scale breaks exact μ-τ reflection symmetry in the MSSM neutrino sector, with the breaking pattern depending on the choice of tanβ for both normal and inverted mass orderings.","lead":"The paper runs renormalization group equations in the MSSM starting from exact μ-τ reflection symmetry at a high scale and tracks how the symmetry breaks at low energies, with special attention to how different values of tanβ change the outcome for normal and inverted neutrino mass orderings. A smart generalist might read it to see how supersymmetric flavor models can be connected to current neutrino data through scale-dependent effects.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Fixed SUSY breaking scale Λ_s=7 TeV without variation or Λ_FS specification makes RG-induced breaking sensitive to untested scale choice","rationale":"The identified concern matches the reader’s weakest assumption exactly and is the single point where the numerical claim is least secured: the results are outputs of a specific integration interval whose length is not varied. No other internal inconsistency is visible from the given description, so the verdict remains UNVERDICTED.","tokens_in":1774,"tokens_out":375,"duration_ms":25170,"concrete_test":"Re-run the full RGE integration for the same three high-scale parameter sets that fit at Λ_s=7 TeV, but with Λ_s changed to 1 TeV and to 10 TeV (keeping Λ_FS fixed); check whether the low-energy neutrino angles, mass-squared differences, and CP phases still lie inside the 3ν global-fit 3σ ranges and whether the relative ordering of breaking strength among the three tanβ benchmarks remains unchanged.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that exact μ-τ reflection symmetry at Λ_FS, when evolved via the full coupled RGEs down through the MSSM regime to the EW scale with Λ_s fixed at exactly 7 TeV, produces low-energy observables that fit 3ν data for chosen high-scale parameters, with tanβ modulating the breaking. Because the deviation from symmetry (e.g., θ23 away from 45°) accumulates proportionally to log(Λ_FS/Λ_s) and depends on the MSSM beta functions (which incorporate tanβ via Yukawa running), fixing Λ_s without showing results for other values or stating Λ_FS renders the quantitative tanβ dependence and the “suitable parameters” fit specific to this arbitrary choice rather than robust.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1964,"tokens_out":483,"duration_ms":42355,"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":[{"comment":"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.","section":"Abstract and methodology"},{"comment":"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.","section":"Abstract and parameter fitting"}],"minor_comments":[{"comment":"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.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[{"response":"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_made":"partial","referee_comment":"[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."},{"response":"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_made":"yes","referee_comment":"[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."}],"tokens_in":1436,"tokens_out":598,"duration_ms":31766,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core of this work is a numerical RG evolution of neutrino parameters in the MSSM starting from exact μ-τ reflection symmetry imposed at a high flavor scale. They integrate the coupled equations down to the electroweak scale with the SUSY breaking scale fixed at 7 TeV, then tune the high-scale inputs so the low-energy masses, angles, and phases match 3ν global fits. The new piece is the explicit scan over three tanβ benchmarks and the side-by-side comparison of normal versus inverted ordering to see how the symmetry breaking accumulates differently.","headline":"This paper runs standard MSSM neutrino RGEs from exact μ-τ reflection symmetry at high scale and shows tanβ modulating the low-energy breaking, but the results hinge on a fixed 7 TeV SUSY scale and fitted high-scale parameters.","tokens_in":2469,"tokens_out":208,"would_cite":false,"duration_ms":12709,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean (J-uniqueness, Aczél classification)","rs_theorem":null,"paper_passage":"Starting from an exact μ–τ reflection symmetry imposed at a high flavor symmetry scale Λ_FS, we run the complete set of coupled RGEs for neutrino masses, mixing angles, and CP-violating phases down to the electroweak scale... We consider a specific value of the SUSY breaking scale, Λ_s=7 TeV... three benchmark choices [tanβ=10,30,58]"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/ArithmeticFromLogic.lean (LogicNat recovery, orbit embedding)","rs_theorem":null,"paper_passage":"the RGEs for the mass eigenvalues in the SM and MSSM exhibit distinct forms... C_SM=−3/2, C_MSSM=1... α_MSSM≈6y_t²−6/5 g_1²−6g_2²"}],"headline":"Standard MSSM neutrino RGE analysis with tanβ benchmarks is orthogonal to RS forcing chain","alignment":"orthogonal","rationale":"The paper's central machinery consists of solving 19 coupled one-loop RGEs for neutrino masses, PMNS angles, and CP phases in the MSSM (above Λ_s=7 TeV) matched to SM (below), starting from exact μ-τ reflection symmetry at Λ_FS and fitting high-scale free parameters to low-energy 3ν data for three tanβ values. This is conventional effective-field-theory phenomenology with adjustable high-scale inputs and a fixed SUSY threshold. It shares no structural elements with the RS framework (e.g., J(x)=½(x+x⁻¹)−1, φ-ladder, 8-tick periodicity, or parameter-free derivations from a single distinction). No RS theorem (reality_from_one_distinction, J-uniqueness via Aczél, Alexander-duality D=3 forcing, etc.) is engaged or contradicted.","tokens_in":54698,"confidence":"high","tokens_out":468,"duration_ms":13095,"cache_read_input_tokens":32896,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"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.","keywords":["neutrino mixing","mu-tau reflection symmetry","renormalization group evolution","MSSM","tan beta","normal ordering","inverted ordering","CP phases"],"falsifier":"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.","tokens_in":2669,"feed_emoji":"","tokens_out":733,"duration_ms":27133,"temperature":0.7,"pith_summary":"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.","feed_headline":"RG flow breaks μ-τ symmetry by amount set by tanβ","feed_subtitle":"Running the full neutrino RGEs in the MSSM from a high-scale exact symmetry reproduces data and shows how the Higgs ratio controls the low-","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["MSSM RG breaks μ-τ symmetry","tanβ determines μ-τ breaking in neutrinos","High-scale μ-τ symmetry broken by MSSM flow","RG evolution disrupts exact μ-τ reflection","Neutrino μ-τ symmetry split by tanβ in SUSY"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["MSSM RG breaks μ-τ symmetry","tanβ determines μ-τ breaking in neutrinos","High-scale μ-τ symmetry broken by MSSM flow","RG evolution disrupts exact μ-τ reflection","Neutrino μ-τ symmetry split by tanβ in SUSY"]},"model":"grok-4.3","cost_usd":0.004292,"raw_usage":{"total_tokens":2169,"prompt_tokens":689,"num_sources_used":0,"completion_tokens":73,"cost_in_usd_ticks":42924500,"prompt_tokens_details":{"text_tokens":689,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1407,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":689,"tokens_out":73,"duration_ms":18043,"temperature":1.0,"reasoning_tokens":1407,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-16T23:20:59.414345+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"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.","supporting_citations":[],"review_version":1}