{"id":"3b47b9fe-f890-46bf-9db6-9dd84bcb79dd","arxiv_id":"1909.01560","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":8,"one_line_summary":"A Δ(27) flavor-symmetric type-II seesaw model reproduces neutrino oscillation data only after an ad hoc diagonal perturbation is added, and its CP violation predictions reduce to parameter scans.","lead":"This paper builds a neutrino mass model using three scalar triplets and two extra Higgs doublets with a Δ(27) flavor symmetry, then scans its parameters to match neutrino oscillation data and estimates lepton flavor violation. A generalist might read it to see how model parameters are squeezed by oscillation, cosmology, and rare-decay constraints.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Treatment of the CP phase δ is internally inconsistent: Section II.B sets δ = 0 to diagonalize the mass matrix (Eq. 17), but Sections III.B and IV vary the same δ to generate δ_CP, J_CP, and the leptogenesis asymmetry, so those CP-violating predictions do not follow from the model.","rationale":"Central claim: the Δ(27)-symmetric type-II seesaw extension (two extra Higgs doublets, three scalar triplets, and a diagonal perturbation ε) simultaneously accounts for the measured mass-squared differences, three mixing angles, nonzero δ_CP, baryon asymmetry from triplet leptogenesis, and LFV rates. For this to be true, one self-consistent input set must yield all of these observables. The least secure link is the phase δ. Section II.B imposes δ = 0 to diagonalize the mass matrix: Eq. (16) is real only for δ = 0, and Eq. (17) plus the masses in Eq. (15) rest on that choice. Sections III.B and IV then vary the same δ to produce δ_CP, J_CP, and the leptogenesis asymmetry (Eqs. 29–31, Fig. 7, Fig. 12). These two uses conflict: with ε ≠ 0, the off-diagonal element after the U13(θ, δ) rotation acquires an imaginary part −2cs ε sinδ, so the matrix cannot be diagonalized for any δ ≠ 0. The CP-violating claims are therefore not consequences of the model as written. The reader's weakest assumption is the perturbation ε in Eq. (10). That concern is valid: without ε, |m1| = |m3| and Δm²31 vanishes, and the authors concede the term requires unspecified extra fields. I agree ε is load-bearing, but the authors flag it openly, and adding fields to generate ε is a conceivable completion. The δ inconsistency is sharper because it is presented as a derivation while being internally contradictory, and it strikes at the paper's claimed advances (δ_CP and leptogenesis) rather than at an acknowledged placeholder. The paper does deserve some credit: the TBM block-diagonalization at δ = 0, the TM1 mixing relations in Eq. (29), and the LFV formulas of Eqs. (52)–(55) are standard and correctly recycled; the failure is in the model-to-observable connection, not in those formulas. The analytic and numeric checks above would settle whether any δ ≠ 0 point can simultaneously diagonalize Eq. (10) and yield the stated CP observables; I expect they cannot. The reader's REJECT verdict stands.","tokens_in":21770,"tokens_out":21999,"duration_ms":205639,"concrete_test":"Analytic check: compute the (1,3) entry of U^T_13 M_bd U_13 using M_bd from Eq. (11) and U_13(θ, δ) from Eq. (14). For real m11, m13, m33 its imaginary part is −2 c s ε sinδ, which cannot vanish for the required ε ≠ 0 and δ ≠ 0; hence the model's mass matrix is not diagonalized at any point with a nonzero CP phase, and the eigenvalues in Eq. (15) are only valid at δ = 0. Numeric check: take an allowed point of Fig. 7 with δ_CP ≠ 0, reconstruct M_ν = U_PMNS diag(m1, m2, m3) U^T_PMNS using Eq. (27) and the masses from Eq. (15), and verify it equals the model matrix in Eq. (10); it will not. Also evaluate Eq. (49) at the scanned parameters: Im[(M†_ν M_ν)_ii] = 0 identically, so the plotted CP asymmetry has no source within the model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing concern is the internal inconsistency in the treatment of δ. Section II.B fixes δ = 0 for the diagonalization: the sentence 'For rest of our analysis we will use δ = 0' precedes Eq. (17), and Eq. (16) itself contains the term 2i ε sinδ in the denominator, so only at δ = 0 is the U13 rotation in Eq. (14) real and able to diagonalize the block matrix in Eq. (11). The mass eigenvalues in Eq. (15) are therefore valid only for δ = 0. Yet Sections III.B and IV treat the same δ as a free parameter: sin²θ23 depends on cosδ (Eq. 29), J_CP is proportional to sinδ (Eq. 30), δ_CP is displayed in Fig. 7, and the triplet CP asymmetry is plotted against δ in Fig. 12. Concretely, with M_bd from Eq. (11), the imaginary part of the (1,3) element of U^T_13 M_bd U_13 is −2cs ε sinδ, which is nonzero for any δ ≠ 0 once the necessary ε ≠ 0 is present; no complex phase structure justifying δ ≠ 0 is constructed, and the scanned phases φ_ba, φ_ca in Eq. (20) are never connected to δ. The CP-violating and leptogenesis results are thus imposed by hand, not derived. A secondary but real issue is the ad hoc diagonal perturbation ε in Eq. (10), which the paper explicitly admits requires unspecified additional fields; without ε, |m1| = |m3| in Eq. (9) and Δm²31 vanishes. The reader emphasized ε; I find the δ inconsistency more damaging because it is presented as a working derivation rather than an acknowledged placeholder. Relatedly, the simplified CP asymmetry in Eq. (49) is identically zero as written, since Im[(M†_ν M_ν)_ii] = 0 for any complex matrix M_ν, so the leptogenesis CP source is never specified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a type-II seesaw extension of the Standard Model with a Δ(27) flavor symmetry, adding two SU(2)_L Higgs doublets and three scalar triplets. The light neutrino mass matrix is assumed to have a form that can be block-diagonalized by the tribimaximal mixing matrix and then fully diagonalized by a U13 rotation. A diagonal perturbation ε is added by hand to break an exact degeneracy of the light neutrino masses. The authors scan their model parameters to reproduce the observed neutrino mass-squared differences and mixing angles, derive the Dirac CP phase, the effective Majorana mass, scalar-triplet leptogenesis, and the branching ratios of μ→eγ and μ→3e. The central claims are that the model reproduces all current neutrino oscillation data, including nonzero θ13 and δ_CP, and gives testable predictions for neutrinoless double beta decay, leptogenesis, and lepton flavor violation.","tokens_in":22211,"tokens_out":9789,"duration_ms":90248,"significance":"If the derivation were correct, the model would be a useful example of a discrete flavor symmetry producing trimaximal-like mixing with several phenomenological consequences. The paper is clearly organized and uses standard type-II seesaw and LFV formulas, and it does compare with the 3σ ranges of global neutrino oscillation fits. However, the predictive power is severely limited: the neutrino mass spectrum requires an ad hoc perturbation ε with no field-theoretic origin, and the CP-violating predictions rest on an internally inconsistent treatment of the phase δ. Moreover, the leptogenesis asymmetry as written in Eq. (49) is identically zero. With at least ten free inputs used to fit the oscillation observables, the agreement shown is consistency rather than prediction. These issues undermine the central claims of the manuscript in its present form.","major_comments":[{"comment":"The treatment of the phase δ is internally inconsistent. The manuscript fixes δ = 0 for the diagonalization: Eq. (16) contains a term 2i ε sinδ in the denominator, and the text before Eq. (17) states 'For rest of our analysis we will use δ = 0.' For δ ≠ 0 with ε ≠ 0, the matrix U13^T M_bd U13 is not diagonal; its (1,3) element acquires an imaginary part -2 c s ε sinδ (in addition to real terms). Nevertheless, Sections III.B and IV treat the same δ as a free parameter: sin²θ23 depends on cosδ in Eq. (29), J_CP is proportional to sinδ in Eq. (30), δ_CP is displayed in Fig. 7, and the scalar-triplet CP asymmetry is plotted against δ in Fig. 12. No mechanism is constructed that would generate a nonzero δ while preserving the block-diagonal form, and the scanned phases φ_ba, φ_ca, φ_εa in Eq. (20) are never connected to δ. Consequently, the CP-violating predictions are imposed by hand, not derived from the model.","section":"II.B, Eqs. (14)-(17); III.B; IV"},{"comment":"The diagonal perturbation ε is introduced without a symmetry origin. The text acknowledges that it 'can also be generated by the inclusion of additional fields,' but no such fields are specified. Without ε, the eigenvalues in Eq. (9) give |m1| = |m3|, so Δm²31 vanishes and the oscillation data cannot be reproduced. The agreement with the neutrino mass splittings is therefore entirely dependent on this unmodeled parameter. The adjacent sentence saying 'two eigenvalues m1 and m2 are degenerate' is also a misstatement: Eq. (9) shows that m1 and m3 have equal magnitude.","section":"II.B, Eq. (10)"},{"comment":"The simplified CP asymmetry for the lightest scalar triplet is written as ε^{ℓ_i}_{Δ1} ∝ Im[(M_ν^† M_ν)_{ii}]. Since M_ν^†M_ν is Hermitian, its diagonal entries are real, so this expression is identically zero. The flavored asymmetry in Eq. (48) requires products of distinct triplet matrices, Im[(M_{Δα}^† M_{Δβ})_{ii}], which do not reduce to a diagonal element of a single Hermitian matrix. The leptogenesis curves in Figs. 12 and 13 therefore do not follow from the stated equations.","section":"IV.A, Eq. (49)"},{"comment":"The numerical analysis is a scan over at least ten free inputs (|a|, ε, α1, α2, α3, φ_ba, φ_ca, φ_εa, θ, δ) used to fit the two mass-squared differences and the three mixing angles. The 'predictions' for δ_CP, |mee|, and the LFV rates are then evaluated at the same scanned parameter points, so the agreement with oscillation data is a fit rather than a test of the model. No χ², confidence-level, or number-of-degrees-of-freedom statistic is reported, making it impossible to assess the statistical significance of the claimed 'restricted range of parameter space for α1.'","section":"III, Eq. (20) and Figs. 4-9"}],"minor_comments":[{"comment":"There are numerous typos and OCR artifacts, e.g., 'Yukuwa' should be 'Yukawa,' 'corelation' should be 'correlation,' and 'fllowing' should be 'following.' These should be corrected in a revised version.","section":"Throughout"},{"comment":"The expression for δ_CP in Eq. (31) is not well defined as written and appears to be dimensionally inconsistent; please clarify the intended formula or remove it if it is not used in the numerical analysis.","section":"III.B, Eq. (31)"},{"comment":"The relation Y_B = κ·c·ε_{Δ1}/g* is only schematic; the washout factor κ is not evaluated, so the final baryon asymmetry is not actually determined from the model parameters.","section":"IV, Eq. (50)"},{"comment":"The scalar potential and symmetry-breaking discussion mention 'flavon fields,' but Table I does not include any flavon fields. Please clarify how the Δ(27) symmetry is broken to obtain the VEV alignments used in Section II.","section":"VIII.C, Appendix"},{"comment":"The text and the figure caption disagree on whether the left panel shows δ or θ; please correct the inconsistency.","section":"Fig. 12"}],"recommendation":"reject","confidential_remarks":"The two central issues (the inconsistent treatment of δ and the vanishing CP-asymmetry in Eq. (49)) are load-bearing, and the ad hoc ε parameter means the neutrino mass matrix is not fully derived from the model. These problems cannot be fixed by a minor revision; the numerical results as presented do not support the paper's conclusions. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know first. The paper is a systematic Δ(27) type-II seesaw scan and, as scans go, it is rather complete: it derives the charged-lepton and neutrino mass textures, walks through TBM→U13 diagonalization, scans the parameter space against oscillation data, and maps the surviving regions onto 0νββ, μ→eγ, and μ→3e observables. The presentation is clear and the experimental bounds are current. The second thing is that the CP-violating and leptogenesis results do not follow from the model as written. The phase δ is fixed to zero in Section II.B to make the U13 rotation diagonalize the block mass matrix, but the same δ is later varied to produce δ_CP, J_CP, and the triplet CP asymmetry. And the simplified asymmetry in Eq. (49) is identically zero, since Im[(Mν†Mν)_ii] vanishes for every i. Those plots are imposed by hand, not derived.\n\nWhere the paper earns credit: the charged-lepton sector is kept diagonal by the symmetry, so the entire mixing problem sits in the neutrino sector; the analytic steps up to Eq. (17) are legible; and the phenomenological correlations in Figs. 8, 14, and 16 are useful. The citation pattern is honest and anchors the construction in earlier Δ(27) and A4 work. The trouble is that by the same anchoring, the mixing ansatz UPMNS = UTBM·U13·P is the standard trimaximal texture from refs. [67, 69, 80, 81], and the only genuinely new ingredient is the diagonal ε perturbation. The paper explicitly admits ε would need additional fields; without it, |m1| = |m3| and Δm^2_31 vanishes. So the novel element is also the least justified.\n\nUnderneath that, the numerical analysis is a parameter fit rather than a prediction. With |a|, α1, α2, α3, three phases, θ, and δ all scanned, reproducing six oscillation observables is not surprising, and the later constraints on mee and LFV inherit the scan. That is a common pattern in this literature, but it means the concluding claim—that the model explains δ_CP, leptogenesis, and LFV—overstates what has been shown.\n\nMy recommendation: don't cite it and don't publish it as is. A serious editor could still send it to a referee because the paper is substantial and the flaws are instructive, but the referee should reject unless the authors either restrict to δ=0 and drop the δ_CP and leptogenesis claims, or construct the missing fields, redo the diagonalization with complex phases, and fix Eq. (49). The useful part is the scan template; the model part is not yet a model.","headline":"A systematic Δ(27) type-II seesaw scan whose CP-violating and leptogenesis claims are not derived: δ is set to zero for the diagonalization and then varied to make the plots, and Eq. (49) is identically zero.","tokens_in":22852,"tokens_out":7309,"would_cite":false,"duration_ms":75101,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["14.60.Pq","12.60.Fr"],"model":"deepseek-v4-flash","headline":"The paper claims that a Delta(27)-symmetric type-II seesaw extension of the Standard Model reproduces the observed neutrino masses, mixing angles, CP phase, baryon asymmetry, and lepton-flavor-violating rates.","keywords":["type-II seesaw","Delta(27) flavor symmetry","neutrino mass and mixing","reactor mixing angle","leptogenesis","lepton flavor violation","neutrinoless double beta decay","scalar triplet"],"falsifier":"Build the scalar potential for the stated $\\Delta(27)$ field content and check whether its vacuum alignment produces a diagonal perturbation $\\epsilon$: the model is falsified if the minimum forces $\\epsilon=0$ (leaving two degenerate light neutrinos) or gives an off-diagonal $\\epsilon$-texture, because then the predicted mixing angles contradict the measured reactor angle.","tokens_in":21485,"feed_emoji":"⚛️","tokens_out":10574,"duration_ms":93010,"temperature":0.7,"pith_summary":"The paper claims that a single discrete flavor symmetry, $\\Delta(27)$, can organize a type-II seesaw extension of the Standard Model that matches the measured neutrino oscillation data. With two additional Higgs doublets fixing the charged-lepton masses and three scalar triplets generating neutrino masses, the model produces a neutrino mass matrix that is diagonalized by tribimaximal mixing together with one further rotation. A small common perturbation added to the diagonal entries splits the two degenerate light masses, and the resulting parameters then yield the non-zero reactor angle, the Dirac CP phase, a sum of neutrino masses within the cosmological bound, and an effective Majorana mass in the reach of upcoming neutrinoless double $\\beta$ decay experiments. The same TeV-scale triplets generate the baryon asymmetry through leptogenesis and give lepton-flavor-violating rates for muon decays near current bounds. If correct, the model would tie several independent neutrino observables to just a few parameters.","feed_headline":"Delta(27) flavor symmetry reproduces neutrino data","feed_subtitle":"A type-II seesaw model ties neutrino masses, CP violation, leptogenesis, and rare muon decays to one symmetry.","key_machinery":"The load-bearing object is the light neutrino mass matrix $M_\\nu = \\begin{pmatrix} a+\\epsilon & c & b \\\\ c & b+\\epsilon & a \\\\ b & a & c+\\epsilon \\end{pmatrix}$ in the $\\Delta(27)$ basis, together with the two-step diagonalization $U = U_{\\text{TBM}}\\cdot U_{13}\\cdot P$. The tribimaximal matrix $U_{\\text{TBM}}$ (the mixing pattern with $\\sin^2\\theta_{12}=1/3$, $\\sin^2\\theta_{23}=1/2$, $\\theta_{13}=0$) block-diagonalizes the matrix; the perturbation $\\epsilon$ splits the degenerate pair, and the $U_{13}$ rotation with angle $\\theta$ and phase $\\delta$ produces a non-zero $\\theta_{13}$, a deviated $\\theta_{23}$, and CP violation. All subsequent predictions, from the mixing angles and $J_{CP}$ to Majorana phases, neutrinoless double $\\beta$ decay, triplet leptogenesis, and muon lepton-flavor-violating rates, are derived from this same matrix and its diagonalization.","core_discovery":"In the paper's own terms, the central result is that an $SU(2)_L$ extension with three $\\Delta(27)$-triplet scalar fields plus two additional Higgs doublets realizes the type-II seesaw in a phenomenologically complete way: it reproduces the current $3\\sigma$ ranges of the solar, atmospheric, and reactor mixing angles, the two mass-squared differences, and the Dirac CP phase. The key step is the structure of the neutrino mass matrix, which before perturbation is diagonalized by the tribimaximal matrix and has two degenerate eigenvalues; adding a universal diagonal perturbation $\\epsilon$ lifts the degeneracy, and a further $U_{13}$ rotation with angle $\\theta$ and phase $\\delta$ relates the observable mixing to the model parameters. The authors conclude that all mixing angles can be reproduced for a restricted range of the parameter $\\alpha_1$, and the model simultaneously gives a total neutrino mass $\\sum m_\\nu$ consistent with cosmology, an effective Majorana mass $|m_{ee}|$ relevant for neutrinoless double $\\beta$ decay, TeV-scale scalar triplet leptogenesis with the observed baryon asymmetry, and lepton-flavor-violating branching ratios near present bounds.","pith_inferences":["If the diagonal $\\epsilon$ is ever traced to explicit fields, its flavor-diagonal texture becomes the model's decisive prediction: an $\\epsilon$ that is not diagonal would alter the block structure that produces the successful mixing-angle relations.","The $U_{\\text{TBM}}\\cdot U_{13}$ mixing ansatz is not unique to $\\Delta(27)$; the same perturbation logic could be transplanted to other discrete flavor groups, so the specific claim of the paper is that $\\Delta(27)$ supplies the matrix texture, and that is what a direct symmetry-breaking calculation would have to check.","A future measurement of $\\delta_{CP}$ combined with a bound on $\\mu\\to e\\gamma$ would select disjoint regions of the $\\theta$--$v_\\Delta$ parameter space, turning this model into a concrete target that muon experiments can probe.","If the $\\Delta(27)$ scalar potential fixes the phases that the paper's scan leaves free, the allowed $\\alpha_1$ range found here could shrink or disappear, so the claimed restricted range is not yet a prediction from the symmetry alone."],"forward_implications":["The model reproduces, within $3\\sigma$, the observed values of $\\Delta m^2_{21}$, $|\\Delta m^2_{31}|$, $\\sin^2\\theta_{12}$, $\\sin^2\\theta_{23}$, and $\\sin^2\\theta_{13}$, with the Dirac CP phase $\\delta_{CP}$ as a correlated output.","The predicted sum of neutrino masses lies in the range $0.12$ to $0.29$ eV, compatible with cosmological bounds, and the effective Majorana mass $|m_{ee}|$ is correlated with the lightest neutrino mass and with $\\theta$, giving a concrete target for neutrinoless double beta decay searches.","The TeV-scale decay of the lightest scalar triplet can generate the observed baryon asymmetry through flavored leptogenesis, with the CP asymmetry controlled by the same $\\theta$ and $\\delta$ that govern neutrino mixing.","The branching ratios for $\\mu\\to e\\gamma$ and $\\mu\\to 3e$ are expressed through the same PMNS matrix and light neutrino masses; for TeV-scale triplets they fall near the current experimental upper limits, making the framework testable in upcoming muon experiments."],"supporting_citations":[{"why":"Supplies the tribimaximal mixing matrix $U_{\\text{TBM}}$ used to block-diagonalize the neutrino mass matrix.","marker":"[45]"},{"why":"Gives the $\\Delta(27)$-symmetric form of the neutrino mass matrix that the model starts from.","marker":"[70]"},{"why":"Establishes the near-tribimaximal $\\Delta(27)$ framework that this type-II seesaw extension builds on.","marker":"[66]"},{"why":"Provides the global-fit neutrino oscillation parameters shown in Table II that the numerical scan must match.","marker":"[74]"},{"why":"Provides the neutrino mass-ordering and cosmological constraints used to set the oscillation ranges.","marker":"[75]"},{"why":"Gives the flavored scalar-triplet leptogenesis formulas used to compute the CP asymmetry.","marker":"[83]"},{"why":"Links triplet seesaw to leptogenesis and justifies using TeV-scale triplet decays for the baryon asymmetry.","marker":"[33]"}],"fun_headline_variants":["Triplet seesaw under Delta(27) cracks neutrino puzzle","One symmetry for neutrino mass, leptogenesis, and LFV","Delta(27) symmetry unifies neutrino mass, leptogenesis, LFV","Type-II seesaw with Delta(27) fits all neutrino data","TeV-scale triplets tie neutrinos to leptogenesis"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire fit rests on a small diagonal perturbation $\\epsilon$ that is added by hand to every diagonal entry of the neutrino mass matrix; the paper states that it could come from extra fields but does not construct them, and without $\\epsilon$ the two lighter neutrino masses are equal, so the oscillation data cannot be reproduced.","fun_headline_variants_meta":{"raw":{"variants":["Triplet seesaw under Delta(27) cracks neutrino puzzle","One symmetry for neutrino mass, leptogenesis, and LFV","Delta(27) symmetry unifies neutrino mass, leptogenesis, LFV","Type-II seesaw with Delta(27) fits all neutrino data","TeV-scale triplets tie neutrinos to leptogenesis"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001344,"raw_usage":{"total_tokens":5484,"prompt_tokens":991,"completion_tokens":4493,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":607,"completion_tokens_details":{"reasoning_tokens":4404}},"tokens_in":607,"tokens_out":4493,"duration_ms":31731,"temperature":1.0,"reasoning_tokens":4404,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:14:27.676499+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build the scalar potential for the stated $\\Delta(27)$ field content and check whether its vacuum alignment produces a diagonal perturbation $\\epsilon$: the model is falsified if the minimum forces $\\epsilon=0$ (leaving two degenerate light neutrinos) or gives an off-diagonal $\\epsilon$-texture, because then the predicted mixing angles contradict the measured reactor angle.","supporting_citations":[{"cited_title":"A Redetermination of the Neutrino Mass-Squared Difference in Tri-Maximal Mixing with Terrestrial Matter Effects","cited_arxiv_id":"hep-ph/9904297","evidence_quote":"Supplies the tribimaximal mixing matrix $U_{\\text{TBM}}$ used to block-diagonalize the neutrino mass matrix."},{"cited_title":"Maximal CP violation in lepton mixing from a model with Delta(27) flavour symmetry","cited_arxiv_id":"1206.7072","evidence_quote":"Gives the $\\Delta(27)$-symmetric form of the neutrino mass matrix that the model starts from."},{"cited_title":"The SNO+ Experiment","cited_arxiv_id":"0810.3694","evidence_quote":"Establishes the near-tribimaximal $\\Delta(27)$ framework that this type-II seesaw extension builds on."},{"cited_title":"A 3-3-1 model with right-handed neutrinos based on the $\\Delta\\left(27\\right)$ family symmetry","cited_arxiv_id":"1601.05062","evidence_quote":"Provides the global-fit neutrino oscillation parameters shown in Table II that the numerical scan must match."}],"review_version":1}