{"id":"94e45f37-90d4-4d12-b59f-2c9c8c414243","arxiv_id":"2504.21701","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A non-supersymmetric modular flavor model with polyharmonic Maass forms and an extended inverse seesaw is fitted to neutrino oscillation data and then used to test 0νββ, LFV, and leptogenesis constraints.","lead":"This paper builds a neutrino mass model without supersymmetry, using special modular functions called polyharmonic Maass forms and an extended inverse seesaw mechanism. The authors then check whether the same model can also respect bounds on neutrinoless double beta decay, charged lepton flavor violation, and the baryon asymmetry of the universe.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The BAU result is internally inconsistent: with v_R=v'=10 TeV and the quoted q_i/Y_i ranges, the 6x6 heavy-neutrino matrix cannot produce the claimed 200-2000 TeV masses.","rationale":"The Reader's weakest assumption targets the unsourced polyharmonic Maass-form expansions in Eq. (A7), and that is a genuine open question that should be resolved by comparison with the cited constructions. However, the most load-bearing failure I find is internal and does not require external input: with the VEVs and coupling ranges explicitly stated in Section VII, the heavy neutrino masses quoted for successful BAU in Section VII.E are impossible. The resonant-leptogenesis claim is therefore not merely under-supported; it contradicts the model's own parameter space. Because baryogenesis via resonant leptogenesis is one of the central advertised results, the current manuscript cannot be accepted as a valid demonstration of the model's viability. A corrected version that uses consistent mass scales, or that revises the parameter ranges and redoes the BAU analysis, could be reconsidered, and the q-expansion verification should still be performed in that revision.","tokens_in":16199,"tokens_out":15006,"duration_ms":157747,"concrete_test":"Diagonalize the 6x6 matrix of Eq. (6.1) in a random scan over the quoted parameter ranges: v_R = v' = 10 TeV, q_i and g_j as specified in Section VII, and Y_i drawn uniformly from the Table V intervals. Record the maximum heavy eigenvalue over at least 10^4 sampled points. If the maximum eigenvalue is always below about 20 TeV, the claimed 200-2000 TeV BAU band in Fig. 8 cannot be reproduced and the inconsistency is confirmed. If any sampled point yields an eigenmass above 200 TeV, the concern is refuted.","verdict_should_be":"REJECT","load_bearing_attack":"Section VII fixes v_R = v' = 10 TeV, Re[q_i] = Im[q_i] in [0.01, 0.1] (so |q_i| is at most about 0.14), g1 = g2 in [10, 50] keV, and Table V limits the Yukawa couplings to |Y_i| below about 1.1. From Eqs. (3.7) and (3.9), every entry of M_R and M_N is at most O(v_R |q_i| |Y_i|), i.e. roughly 5 TeV or below. The 6x6 heavy-neutrino mass matrix in Eq. (6.1) therefore has all entries in the few-TeV range, and its eigenvalues are bounded by that same scale (e.g. by the Frobenius norm or Gershgorin disks). Yet Section VII.E states that for NH the BAU bound is satisfied when the heavy neutrino mass lies between 200 TeV and 2000 TeV (Fig. 8c/d). No point in the stated parameter space can produce an eigenmass of 200 TeV, so the resonant-leptogenesis result cannot be generated by the model as written. This is a purely internal contradiction: it does not depend on the correctness of the polyharmonic q-expansions in Eq. (A7), which the Reader's verdict already questions; even granting those expansions and the leptogenesis formulas, the BAU claim fails.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs a non-supersymmetric left-right asymmetric model with an extended inverse seesaw mechanism, using weight-zero polyharmonic Maass forms for Γ(3) as Yukawa couplings transforming as an A4 triplet. The authors fit the neutrino sector to oscillation data, then compute predictions for 0νββ decay, charged lepton flavor violation, and baryogenesis via resonant leptogenesis, and claim simultaneous consistency with all current experimental bounds.","tokens_in":16611,"tokens_out":10723,"duration_ms":100517,"significance":"If correct, the paper would demonstrate that non-holomorphic modular forms can be used in non-supersymmetric flavor models, and that a TeV-scale setup can accommodate neutrino masses, 0νββ bounds, LFV constraints, and the baryon asymmetry. The direction is timely and the paper attempts to go beyond the usual holomorphic modular-invariant framework. However, the central quantitative claims are not supported as written: the resonant leptogenesis result is internally inconsistent with the stated parameter choices, the 0νββ calculation omits essential numerical inputs, and the claimed 'predictions' of the mixing angles are circular because those angles are used as input to fix the Yukawa couplings. These load-bearing problems prevent acceptance in the current form.","major_comments":[{"comment":"The BAU result is internally inconsistent with the stated parameter choices. With v_R=v'=10 TeV, Re[q_i]=Im[q_i] in [0.01,0.1] (so |q_i|≤0.141), |Y_i|≤1.092 from Table V, and g1=g2 in [10,50] keV, every entry of M_R and M_N in Eqs. (3.7) and (3.9) is at most about 4.5 TeV, while M_S entries are at most about 0.1 MeV. Consequently the 6×6 matrix in Eq. (6.1) has all eigenvalues bounded by a few TeV, for example by the Frobenius norm or Gershgorin disk theorem. Section VII.E's claim that successful BAU requires heavy neutrino masses between 200 TeV and 2000 TeV (Fig. 8c,d) therefore cannot be realized at any point in the stated parameter space, so the central leptogenesis claim fails.","section":"VII.E, Eqs. (3.7), (3.9), (6.1)"},{"comment":"The claimed 'predictions' of the neutrino mixing angles are circular. Section VII.A states that the Yukawa couplings are calculated using the 3σ values of the neutrino oscillation parameters from Table I, and then the resulting mixing angles are compared with the same experimental ranges. Since the oscillation parameters are used as input to determine the model parameters, the agreement of the mixing angles is a fit, not a prediction. The abstract's statement that the model 'successfully predicts' the mixing angles and the conclusion's emphasis on 'strong predictive power' are therefore overstated. The sum of neutrino masses may still be a prediction, but the mixing angles cannot be claimed as such without a parameter-count analysis showing that the model has fewer free parameters than the observables it reproduces.","section":"VII.A and Abstract"},{"comment":"The 0νββ results are not reproducible because the inputs M_WR, g_R/g_L, tan ζ, and |p| are never specified. The effective mass shown in Figure 5 depends sensitively on these quantities through the factors (M_WL/M_WR)^2(g_R/g_L)^3 and |p|, so without their values the plot cannot be verified. Moreover, in Eq. (4.1) the heavy right-handed neutrino contribution m_{N,ee}^λ has denominator M_Si^2, which is the sterile neutrino mass; this appears to be a typo for M_Ni^2. The same issue appears in Eq. (4.2). The authors should provide the numerical inputs and correct the denominators.","section":"Section IV, Eqs. (4.1)-(4.2)"},{"comment":"The entire model rests on the assertion that Y_{3,1}^{(0)}, Y_{3,2}^{(0)}, Y_{3,3}^{(0)} are weight-zero polyharmonic Maass forms for Γ(3) transforming as an A4 triplet, but no derivation or explicit source is given. The q-expansions in Eq. (A7) are simply stated. If these functions are not the correct weight-zero polyharmonic Maass forms, all mass matrices in Eqs. (3.5)-(3.11) change and the subsequent phenomenology follows only by accident. The authors should either derive these expansions or cite the exact reference (including level, weight, and A4 decomposition) and verify the modular transformation property. There is also a typographical error in the third term of Y_{3,1}^{(0)} ('−−12πy'), which makes the expansion ambiguous.","section":"Appendix A, Eq. (A7)"}],"minor_comments":[{"comment":"In the last row, second column of the second matrix, 'q5−g4Y_{3,1}^{(0)}' should read 'q5−q4Y_{3,1}^{(0)}'.","section":"Eq. (3.7)"},{"comment":"The text states that 'q9 and q10 are taken in the keV range,' but q9 and q10 never appear in the Lagrangian or in the mass matrices (Eqs. (3.2)-(3.11)). Presumably the keV-scale parameters are g1 and g2; please clarify or remove q9 and q10.","section":"Section III, after Eq. (3.11)"},{"comment":"The dilution factor is said to be determined 'using equation (4.1)', but Eq. (4.1) is the 0νββ effective-mass formula; the dilution factor is given in Eq. (6.9).","section":"Section VII.E"},{"comment":"There is a spurious minus sign in the first line, '−d≈ ...'; the dilution factor should be positive.","section":"Eq. (6.9)"},{"comment":"The text after Eq. (5.2) says 'M_W represents the mass of the right-handed gauge boson respectively,' but the formula uses M_WL (the left-handed W mass); the text should read 'left-handed' or define the notation.","section":"Section V, Eq. (5.2)"},{"comment":"There are numerous typographical errors (e.g., 'RESONENT LEPTOGENSIS' in the Section VI heading, 'Maaβ' spelling inconsistencies, and incomplete figure captions). A careful proofread is needed.","section":"General"}],"recommendation":"reject","confidential_remarks":"The paper presents an interesting framework, but the numerical results are not trustworthy as written. The BAU inconsistency is sufficient for rejection: the stated 10 TeV VEVs and O(0.1) couplings cannot produce heavy neutrino masses of 200–2000 TeV. Even if that were fixed, the circularity of the neutrino 'predictions' and the unspecified 0νββ inputs would require a major re-analysis. I would encourage the authors to resubmit after addressing these issues, particularly the heavy-neutrino mass scale and the derivation of the polyharmonic Maass forms."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper takes a real idea—non-holomorphic Yukawas from weight-zero polyharmonic Maass forms—and slots it into a non-SUSY left-right asymmetric inverse seesaw. That combination is new. The neutrino mass matrices and the LFV formulas are standard, and the authors do try to face constraints from 0νββ and BAU simultaneously. Credit where due: the Γ(3) implementation with A4 triplets is worked out in detail, and the paper is explicit about its parameter ranges.\n\nBut there are two problems that currently sink the main claims.\n\nFirst, the BAU result cannot come from the stated parameter space. With v_R = v' = 10 TeV, |q_i| ≤ 0.14, |Y_i| ≤ 1.1, and g1, g2 in the 10–50 keV range, every entry of the 6×6 heavy-neutrino mass matrix in Eq. (6.1) is at most a few TeV. The eigenvalues are bounded by that scale. Section VII.E, however, says the baryon asymmetry is produced for heavy masses between 200 and 2000 TeV (NH). Those masses are unreachable. This is an internal contradiction, independent of any worry about the q-expansions. Either the scans used different parameters than reported, or the diagonalization is wrong. The leptogenesis plots therefore don't validate the model.\n\nSecond, the neutrino sector is circular. Section VII.A states that the Yukawa couplings are calculated from the 3σ oscillation data, and then the mixing angles and Σmν are exhibited as predictions. That's fitting, not predicting. The density plots show allowed regions, not independent outputs. The abstract's 'successfully predicts' overstates what was done.\n\nThere are also smaller issues: Eq. (4.1) puts M_Si in the denominator for the heavy RH contribution, 'g4' appears instead of 'q4' in Eq. (3.7), and q9/q10 are mentioned but never defined or used. The 0νββ calculation omits M_WR, g_R/g_L, tan ζ, and |p|, so it cannot be reproduced. The q-expansions in Appendix A are quoted without derivation or reference; some terms (the e^{-4πy} structure) look non-standard and need checking.\n\nThe core idea—using polyharmonic Maass forms in a non-supersymmetric flavor model—is worth exploring, and the paper might be salvageable after major revision. A serious referee should see it because the topic is current and the flaws are concrete and fixable. But as written, the BAU claim is unsupported and the predictive language is misleading. I would send it out for review, with the clear expectation of major revision. Not desk-reject; also not accept.","headline":"Interesting application of polyharmonic Maass forms to a non-SUSY left-right model, but the BAU claim is internally inconsistent with the stated parameters and the neutrino 'predictions' are circular fits.","tokens_in":17165,"tokens_out":4398,"would_cite":false,"duration_ms":41630,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A non-supersymmetric modular model using polyharmonic Maass forms and an extended inverse seesaw fits neutrino oscillation data within 3σ and keeps neutrinoless double beta decay, lepton flavor violation, and the baryon asymmetry inside…","keywords":["neutrino masses and mixing","modular flavor symmetry","polyharmonic Maass forms","left-right asymmetric model","extended inverse seesaw","neutrinoless double beta decay","lepton flavor violation","resonant leptogenesis"],"falsifier":"Evaluate the hyperbolic Laplacian $\\Delta_0$ acting on each of the three expansions in Eq. (A7); if any function is not annihilated by $\\Delta_0$, or if the triplet $(Y_{3,1}^{(0)}, Y_{3,2}^{(0)}, Y_{3,3}^{(0)})$ fails to transform as an $A_4$ triplet under the modular generators $S$ and $T$, the claimed Yukawa structure and all derived predictions collapse. This check can be done directly from the published expansions.","tokens_in":15980,"feed_emoji":"⚛️","tokens_out":26905,"duration_ms":237818,"temperature":0.7,"pith_summary":"This paper argues that a non-supersymmetric extension of the Standard Model built on polyharmonic Maass forms—modular functions that need not be holomorphic in the modulus $\\tau$—can explain neutrino masses and mixing without auxiliary scalar fields (flavons) to break the flavour symmetry. The authors construct a left-right asymmetric gauge model, in which the left- and right-handed gauge couplings are not equal, and generate neutrino masses through an extended inverse seesaw mechanism, taking three weight-zero polyharmonic Maass forms, $Y_{3,1}^{(0)}, Y_{3,2}^{(0)}, Y_{3,3}^{(0)}$, as an $A_4$ triplet of Yukawa couplings. They report that the model reproduces the neutrino mixing angles within $3\\sigma$ and predicts a sum of neutrino masses below the current cosmological bound. Using the same parameter space, they compute the effective Majorana mass for $0\\nu\\beta\\beta$ decay, the branching ratios for $\\mu\\to e\\gamma$, $\\tau\\to\\mu\\gamma$, and $\\tau\\to e\\gamma$, and the baryon asymmetry from resonant leptogenesis; the LFV rates and baryon asymmetry are consistent with current limits, and the effective Majorana mass is predominantly below the experimental bound. The model therefore demonstrates that modular flavour symmetry can operate without supersymmetry and produces testable lepton-number-violating signatures.","feed_headline":"Fits neutrino data and satisfies rare-decay and double-beta bounds","feed_subtitle":"A modular Maass-form model reproduces neutrino mixing and stays inside current rare-decay and double-beta limits.","key_machinery":"The load-bearing object is the weight-zero polyharmonic Maass form: a modular function of the modulus $\\tau$ that satisfies the hyperbolic Laplacian condition $\\Delta_k Y=0$ rather than holomorphicity, so it may carry both holomorphic and non-holomorphic components and may have zero or negative modular weight. The paper takes the three forms in Eq. (A7) as an $A_4$ triplet and inserts them into the Dirac, Majorana, $N$–$S$ mixing, and sterile mass matrices of an extended inverse seesaw, so that the flavour structure is fixed by the modulus $\\tau$ together with a set of complex couplings. The companion mechanism is resonant leptogenesis: among the six heavy neutral fermions, a nearly degenerate quasi-Dirac pair has mass splitting comparable to its decay width, enhancing the CP asymmetry through the $f_{ik}$ factors in Eq. (6.5), and the resulting baryon asymmetry is obtained after applying a dilution factor.","core_discovery":"The paper's central claim is that the three functions $Y_{3,1}^{(0)}, Y_{3,2}^{(0)}, Y_{3,3}^{(0)}$ in Eq. (A7)—asserted to be weight-zero polyharmonic Maass forms for the level-3 principal congruence subgroup $\\Gamma(3)$, forming a triplet of the finite modular group $A_4$—can serve as the complete Yukawa sector of a non-supersymmetric left-right asymmetric model. With these couplings, the active neutrino mass matrix takes the extended inverse seesaw form $m_\\nu = M_D M_N^{-1} M_S (M_D M_N^{-1})^T$, where the smallness of neutrino mass is set by the keV-scale sterile mass $M_S$ rather than by an extremely heavy right-handed scale. Scanning the three Yukawa couplings and the modulus $\\tau$, the authors find regions of parameter space where the mixing angles and mass splittings fall inside the $3\\sigma$ ranges for both normal and inverted ordering, and where the sum of neutrino masses satisfies the current cosmological bound. Over the same region, the model gives $\\lambda$-diagram contributions to $0\\nu\\beta\\beta$ decay mostly below the experimental limit, LFV branching ratios below current bounds, and a resonant-leptogenesis CP asymmetry large enough to reproduce the observed baryon asymmetry, with viable heavy-neutrino masses of roughly 200 TeV to 2000 TeV for normal ordering and 50 TeV to 100 TeV for inverted ordering.","pith_inferences":["An immediate check the authors leave implicit: because the expansions in Eq. (A7) are supplied without derivation, one can verify by direct computation whether they satisfy $\\Delta_0 Y=0$ and the $A_4$ triplet transformation law; that verification would either cement or invalidate the numerical results that follow.","The framework's permission of zero and negative modular weights is not used to its fullest here; applying the same construction to quark-sector mass matrices or to other finite modular groups would test whether the non-holomorphic mechanism can reproduce fermion hierarchies as well as neutrino angles.","The distinct LFV pattern—$\\tau\\to\\mu\\gamma$ and $\\tau\\to e\\gamma$ near present limits with $\\mu\\to e\\gamma$ far below—means a future observation of tau LFV without muon LFV would single out this kind of inverse-seesaw modular model.","The paper's inverted-ordering leptogenesis region is sparse; if future data were to exclude normal ordering, this construction would face tension in explaining the baryon asymmetry even though its oscillation fit would survive."],"forward_implications":["The model gives a concrete non-supersymmetric realization in which the same three Yukawa couplings and one modulus control neutrino masses, $0\\nu\\beta\\beta$ decay, LFV, and the baryon asymmetry, so a measurement in any one channel constrains the others.","The leptogenesis mechanism fixes the heavy neutrino masses to a specific window—roughly 200 TeV to 2000 TeV for normal ordering and 50 TeV to 100 TeV for inverted ordering—so the scale at which new physics must appear is a prediction of the neutrino fit.","The predicted branching ratios for $\\tau\\to\\mu\\gamma$ and $\\tau\\to e\\gamma$ can lie just below present limits (about $10^{-8}$ to $10^{-11}$), while $\\mu\\to e\\gamma$ is predicted to be far below them ($10^{-15}$ to $10^{-18}$), giving a distinctive pattern for next-generation LFV searches.","The effective Majorana mass for $0\\nu\\beta\\beta$ decay is dominated by right-handed neutrino exchange, with values mostly between about $10^{-6}$ eV and $10^{-1}$ eV, so experiments closing in on that range can confirm or exclude the model."],"supporting_citations":[{"why":"Provides the non-holomorphic modular flavor-symmetry framework where Yukawa couplings satisfy a Laplacian condition instead of holomorphicity.","marker":"[18]"},{"why":"Supplies the automorphic-form construction that yields the polyharmonic Maass forms used as the model's Yukawa couplings.","marker":"[19]"},{"why":"Establishes the modular-symmetry approach in which the modulus τ replaces flavon fields to break flavour symmetry.","marker":"[15]"},{"why":"Provides the asymmetric left-right model and the extended inverse seesaw structure from which the 9×9 neutral mass matrix is built.","marker":"[23]"},{"why":"Supplies the left-right model formalism and mixing matrices used to derive light, sterile, and heavy neutrino masses.","marker":"[24]"},{"why":"Gives the 3σ neutrino oscillation ranges that the model's predictions for mixing angles and mass splittings are tested against.","marker":"[26]"},{"why":"Provides the formula for charged-lepton flavor-violating branching ratios in the inverse seesaw mechanism.","marker":"[28]"},{"why":"Gives the CP-asymmetry formula used to compute the baryon asymmetry from heavy neutrino decays.","marker":"[34]"},{"why":"Supplies the experimental upper bound on the muon radiative decay μ→eγ used to validate the model's LFV predictions.","marker":"[30]"},{"why":"Supplies the experimental upper bounds on the tau radiative decays τ→eγ and τ→μγ used to validate the model's LFV predictions.","marker":"[29]"}],"fun_headline_variants":["Modular Maass forms fit neutrino data and enable leptogenesis","Non-supersymmetric modular model fits neutrino mixing and rare decays","Maass-form Yukawa sector passes double-beta and LFV bounds","Polyharmonic Maass forms unify neutrino masses and baryogenesis"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the three functions $Y_{3,1}^{(0)}, Y_{3,2}^{(0)}, Y_{3,3}^{(0)}$ written down in Eq. (A7) of Appendix A are genuinely weight-zero polyharmonic Maass forms for $\\Gamma(3)$ transforming as an $A_4$ triplet; the paper gives these expansions without derivation, and if they are wrong every mass matrix and every numerical result built on them changes.","fun_headline_variants_meta":{"raw":{"variants":["Modular Maass forms fit neutrino data and enable leptogenesis","Non-supersymmetric modular model fits neutrino mixing and rare decays","Maass-form Yukawa sector passes double-beta and LFV bounds","Polyharmonic Maass forms unify neutrino masses and baryogenesis"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001238,"raw_usage":{"total_tokens":5153,"prompt_tokens":1084,"completion_tokens":4069,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":700,"completion_tokens_details":{"reasoning_tokens":3996}},"tokens_in":700,"tokens_out":4069,"duration_ms":28187,"temperature":1.0,"reasoning_tokens":3996,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:56:05.249839+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the hyperbolic Laplacian $\\Delta_0$ acting on each of the three expansions in Eq. (A7); if any function is not annihilated by $\\Delta_0$, or if the triplet $(Y_{3,1}^{(0)}, Y_{3,2}^{(0)}, Y_{3,3}^{(0)})$ fails to transform as an $A_4$ triplet under the modular generators $S$ and $T$, the claimed Yukawa structure and all derived predictions collapse. This check can be done directly from the published expansions.","supporting_citations":[{"cited_title":"Are neutrino masses modular forms? , pages 227–266","cited_arxiv_id":null,"evidence_quote":"Provides the non-holomorphic modular flavor-symmetry framework where Yukawa couplings satisfy a Laplacian condition instead of holomorphicity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the automorphic-form construction that yields the polyharmonic Maass forms used as the model's Yukawa couplings."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the modular-symmetry approach in which the modulus τ replaces flavon fields to break flavour symmetry."},{"cited_title":"Chang, R","cited_arxiv_id":null,"evidence_quote":"Provides the asymmetric left-right model and the extended inverse seesaw structure from which the 9×9 neutral mass matrix is built."},{"cited_title":"Rizzo and Goran Senjanovic","cited_arxiv_id":null,"evidence_quote":"Supplies the left-right model formalism and mixing matrices used to derive light, sterile, and heavy neutrino masses."},{"cited_title":"A comparative study of 0νββ decay in symmetric and asymmetric left-right model","cited_arxiv_id":null,"evidence_quote":"Gives the 3σ neutrino oscillation ranges that the model's predictions for mixing angles and mass splittings are tested against."},{"cited_title":"Grimus and L","cited_arxiv_id":null,"evidence_quote":"Provides the formula for charged-lepton flavor-violating branching ratios in the inverse seesaw mechanism."},{"cited_title":"Resonant leptogenesis in (2,2) inverse see-saw realisation","cited_arxiv_id":null,"evidence_quote":"Gives the CP-asymmetry formula used to compute the baryon asymmetry from heavy neutrino decays."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the experimental upper bound on the muon radiative decay μ→eγ used to validate the model's LFV predictions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the experimental upper bounds on the tau radiative decays τ→eγ and τ→μγ used to validate the model's LFV predictions."}],"review_version":1}