pith. sign in

arxiv: 2606.05291 · v1 · pith:HXIVY7MHnew · submitted 2026-06-03 · ✦ hep-ph · hep-ex

The Future of Lepton Flavor

Peter B. Denton , Julia Gehrlein , Henry Truelson This is my paper

Pith reviewed 2026-06-28 05:23 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords lepton flavorneutrino oscillationsflavor modelsmass sum rulestexture zerosmodular symmetriesCP violationneutrino mass ordering
0
0 comments X

The pith

Future neutrino measurements will sharply constrain and distinguish leptonic flavor models.

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

The paper maps how upcoming neutrino data on mass ordering, the theta_23 octant, the CP phase delta, improved theta_12 precision, and the absolute mass scale will interact with predictions from five classes of leptonic flavor models. It traces correlations and degeneracies within mass sum rules, one- and two-zero textures for Dirac and Majorana cases, charged-lepton corrections, modular symmetries, and constrained sequential dominance. A sympathetic reader cares because these measurements are expected to eliminate large regions of model space and begin separating the remaining possibilities, moving the field closer to an explanation of the observed lepton masses and mixings.

Core claim

The paper shows that the targeted experimental precisions on neutrino mass ordering, theta_23 octant, delta, absolute mass, and other oscillation parameters will be sufficient to dramatically reduce the number of viable leptonic flavor models, to disentangle the surviving classes, and to begin addressing the flavor puzzle by linking each model class's characteristic predictions to specific measurable quantities.

What carries the argument

Relations between the five model classes (mass sum rules, texture zeros, charged lepton corrections, modular symmetries, constrained sequential dominance) and the observables of mass ordering, theta_23 octant, delta, theta_12 precision, and absolute neutrino mass.

If this is right

  • Determination of the mass ordering will rule out entire classes of models that predict the opposite ordering.
  • Measurement of the theta_23 octant will resolve degeneracies in models that currently allow both octants.
  • Precision on delta will constrain or eliminate models whose CP phases fall outside the measured range.
  • Tighter bounds on absolute neutrino mass will further discriminate among the remaining model classes.
  • Improved theta_12 precision will tighten predictions in models that correlate this angle with other parameters.

Where Pith is reading between the lines

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

  • If the measurements eliminate most classes, experimental priority could shift toward observables that best separate the last survivors, such as neutrinoless double-beta decay rates.
  • The same mapping technique could be applied to test whether any surviving leptonic models are compatible with quark-sector data or grand-unified embeddings.
  • If modular symmetries survive while texture-zero models are ruled out, that would favor symmetry-based constructions over purely phenomenological texture assumptions.
  • The framework identifies which single observable has the highest model-discrimination power, allowing experiments to optimize run plans accordingly.

Load-bearing premise

The five model classes examined are representative of viable leptonic flavor models and that the listed experimental precisions will be reached without major unforeseen systematics.

What would settle it

A global fit after all listed measurements are completed that leaves multiple model classes with overlapping predictions still viable, or that leaves no model class consistent with the data.

read the original abstract

The flavor puzzle remains one of the biggest open questions in particle theory to date and upcoming results from neutrino experiments will have a large impact on its potential solution in the future. While some classes of leptonic flavor models are difficult to constrain with current data, this will change in the coming years as several yet unknown quantities, like the neutrino mass ordering and the octant of $\theta_{23}$, will be determined, and the CP-violating quantity $\delta$ will be measured with some precision. In addition, significant improvements in the precision of the other oscillation parameters, notably $\theta_{12}$, is also expected to impact our understanding of flavor. Together with anticipated improvements on the absolute neutrino mass scale determination from the combination of cosmological data sets or beta decay endpoint spectrum measurements, upcoming experiments will lead to a refined picture of our understanding of flavor in the lepton sector. In this paper, we show exactly how flavor model predictions relate to expected measurements. Five popular classes of leptonic flavor model predictions are considered: mass sum rules, one and two texture-zeros for both Dirac and Majorana neutrinos, charged lepton corrections, modular symmetries, and constrained sequential dominance. We discuss correlations, degeneracies, and discrimination capabilities in the context of the expected measurements from upcoming experiments. We also highlight how different flavor model predictions can be differentiated and the roles each upcoming observable has on flavor model predictions. We anticipate that the precision targeted in future measurements will be sufficient to dramatically reduce the number of viable leptonic flavor models, will allow us to disentangle them, and could hopefully begin to shed light on the answer to the flavor puzzle.

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

3 major / 2 minor

Summary. The manuscript reviews five classes of leptonic flavor models (mass sum rules, one- and two-texture zeros for Dirac and Majorana neutrinos, charged-lepton corrections, modular symmetries, and constrained sequential dominance) and maps their predictions onto anticipated future measurements of neutrino mass ordering, θ23 octant, CP phase δ, θ12 precision, and absolute mass scale. It argues that the targeted experimental precision will allow discrimination among these classes and thereby dramatically reduce the number of viable leptonic flavor models while beginning to address the flavor puzzle.

Significance. If the correlations and discrimination capabilities are quantitatively established, the work supplies a practical guide linking specific observables to model classes, which could usefully inform both experimental planning and model-building efforts in the lepton sector.

major comments (3)
  1. [Abstract] Abstract: the headline claim that future measurements 'will be sufficient to dramatically reduce the number of viable leptonic flavor models' presupposes that the five selected classes are representative of the broader landscape; the text describes them only as 'popular' and supplies no survey or argument showing that other constructions (additional discrete groups, alternative Froggatt-Nielsen charge assignments, or radiative models) would be comparably constrained by the same observables.
  2. [Model-class sections] Model-class sections (presumably §3–§7): the abstract states only qualitative expectations for model discrimination, with no visible derivations, quantitative forecasts, or error analyses demonstrating how the quoted experimental precisions translate into exclusion or separation of the five classes; without these, the discrimination claims cannot be assessed for robustness.
  3. [Introduction and conclusions] Discussion of representativeness: the central claim of broad reduction in viable models is load-bearing on the assumption that the examined classes exhaust or proxy the relevant model space, yet no explicit justification or exclusion of other frameworks is provided.
minor comments (2)
  1. [Figures] Figures comparing model predictions would benefit from explicit annotations indicating which observable drives each separation.
  2. [References] Ensure all cited experimental sensitivity projections reference the most recent official studies rather than older extrapolations.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim that future measurements 'will be sufficient to dramatically reduce the number of viable leptonic flavor models' presupposes that the five selected classes are representative of the broader landscape; the text describes them only as 'popular' and supplies no survey or argument showing that other constructions (additional discrete groups, alternative Froggatt-Nielsen charge assignments, or radiative models) would be comparably constrained by the same observables.

    Authors: We agree that the abstract phrasing could be read as implying a broader claim than intended. The manuscript explicitly selects five popular classes that are frequently studied in the literature and that yield testable predictions for the listed observables. We will revise the abstract, introduction, and conclusions to state that the anticipated reduction applies to the number of viable models within these classes, while noting that other frameworks lie outside the present scope. This clarifies the manuscript's focus without overstating generality. revision: yes

  2. Referee: [Model-class sections] Model-class sections (presumably §3–§7): the abstract states only qualitative expectations for model discrimination, with no visible derivations, quantitative forecasts, or error analyses demonstrating how the quoted experimental precisions translate into exclusion or separation of the five classes; without these, the discrimination claims cannot be assessed for robustness.

    Authors: Sections 3–7 discuss correlations, degeneracies, and discrimination capabilities for each class in the context of projected measurements. However, we acknowledge that more explicit quantitative illustrations would strengthen the presentation. We will add numerical examples, sensitivity plots, and brief error-propagation estimates showing how the targeted precisions on mass ordering, θ23 octant, δCP, θ12, and the absolute mass scale separate or exclude models within each class. revision: yes

  3. Referee: [Introduction and conclusions] Discussion of representativeness: the central claim of broad reduction in viable models is load-bearing on the assumption that the examined classes exhaust or proxy the relevant model space, yet no explicit justification or exclusion of other frameworks is provided.

    Authors: The five classes were chosen because they are among the most commonly employed constructions that make definite predictions for the observables under discussion. We will insert a short paragraph in the introduction stating the selection criteria (prevalence in the recent literature, coverage of both Majorana and Dirac cases, and direct link to the listed experimental targets) and reiterating that the work does not attempt an exhaustive classification of all possible flavor models. revision: yes

standing simulated objections not resolved
  • A comprehensive survey of every possible leptonic flavor construction (all discrete groups, all Froggatt-Nielsen assignments, all radiative mechanisms, etc.) and a quantitative assessment of their sensitivity to the same observables lies beyond the scope of any single focused review.

Circularity Check

0 steps flagged

No circularity: forward-looking constraints on external model classes

full rationale

The paper presents a discussion of how anticipated external experimental measurements (mass ordering, theta_23 octant, delta, absolute mass scale) will constrain five pre-existing classes of leptonic flavor models. No derivation chain reduces a claimed prediction to a fitted quantity or self-citation defined within the paper; the five classes are introduced as popular examples without any internal fitting or self-referential uniqueness theorem. The central claim is prospective and does not loop back to paper-internal inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The abstract invokes standard neutrino oscillation physics and five classes of flavor models but supplies no explicit list of free parameters, axioms, or invented entities; details would require the full text.

free parameters (1)
  • model-specific parameters in the five classes
    Each flavor model class (mass sum rules, texture zeros, etc.) typically introduces parameters fitted to oscillation data, but none are enumerated here.
axioms (1)
  • standard math Three active neutrino flavors with PMNS mixing matrix
    Standard assumption in leptonic flavor phenomenology invoked implicitly throughout.

pith-pipeline@v0.9.1-grok · 5820 in / 1041 out tokens · 21702 ms · 2026-06-28T05:23:56.647280+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

240 extracted references · 169 linked inside Pith

  1. [1]

    King and C

    S.F. King and C. Luhn,Neutrino Mass and Mixing with Discrete Symmetry,Rept. Prog. Phys.76(2013) 056201 [1301.1340]

    Pith/arXiv arXiv 2013

  2. [2]

    S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto,Neutrino Mass and Mixing: from Theory to Experiment,New J. Phys.16(2014) 045018 [1402.4271]

    Pith/arXiv arXiv 2014

  3. [3]

    Xing and Z.-h

    Z.-z. Xing and Z.-h. Zhao,A review ofµ-τflavor symmetry in neutrino physics,Rept. Prog. Phys.79(2016) 076201 [1512.04207]

    Pith/arXiv arXiv 2016

  4. [4]

    Petcov,Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation, Eur

    S.T. Petcov,Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation, Eur. Phys. J. C78(2018) 709 [1711.10806]

    Pith/arXiv arXiv 2018

  5. [5]

    Xing,Flavor structures of charged fermions and massive neutrinos,Phys

    Z.-z. Xing,Flavor structures of charged fermions and massive neutrinos,Phys. Rept.854 (2020) 1 [1909.09610]

    arXiv 2020

  6. [6]

    Gehrlein, S

    J. Gehrlein, S. Petcov, M. Spinrath and A. Titov,Testing neutrino flavor models, in2022 Snowmass Summer Study, 3, 2022 [2203.06219]

    arXiv 2022

  7. [7]

    Chauhan, P.S.B

    G. Chauhan, P.S.B. Dev, I. Dubovyk, B. Dziewit, W. Flieger, K. Grzanka et al., Phenomenology of lepton masses and mixing with discrete flavor symmetries,Prog. Part. Nucl. Phys.138(2024) 104126 [2310.20681]

    arXiv 2024

  8. [8]

    Altmannshofer and A

    W. Altmannshofer and A. Greljo,Recent Progress in Flavor Model Building,Ann. Rev. Nucl. Part. Sci.75(2025) 201 [2412.04549]

    arXiv 2025

  9. [9]

    Grinstein, M

    B. Grinstein, M. Redi and G. Villadoro,Low Scale Flavor Gauge Symmetries,JHEP11 (2010) 067 [1009.2049]

    Pith/arXiv arXiv 2010

  10. [10]

    Alonso, M.B

    R. Alonso, M.B. Gavela, G. Isidori and L. Maiani,Neutrino Mixing and Masses from a Minimum Principle,JHEP11(2013) 187 [1306.5927]

    Pith/arXiv arXiv 2013

  11. [11]

    Alonso, E

    R. Alonso, E. Fernandez Martinez, M.B. Gavela, B. Grinstein, L. Merlo and P. Quilez, Gauged Lepton Flavour,JHEP12(2016) 119 [1609.05902]

    Pith/arXiv arXiv 2016

  12. [12]

    Fern´ andez Navarro and S.F

    M. Fern´ andez Navarro and S.F. King,Tri-hypercharge: a separate gauged weak hypercharge for each fermion family as the origin of flavour,JHEP08(2023) 020 [2305.07690]

    arXiv 2023

  13. [13]

    Ibarra, A

    A. Ibarra, A. Kushwaha and S.K. Vempati,Clockwork for Neutrino Masses and Lepton Flavor Violation,Phys. Lett. B780(2018) 86 [1711.02070]

    Pith/arXiv arXiv 2018

  14. [14]

    Kitabayashi,Clockwork origin of neutrino mixings,Phys

    T. Kitabayashi,Clockwork origin of neutrino mixings,Phys. Rev. D100(2019) 035019 [1904.12516]

    arXiv 2019

  15. [15]

    S. Hong, G. Kurup and M. Perelstein,Clockwork Neutrinos,JHEP10(2019) 073 [1903.06191]

    arXiv 2019

  16. [16]

    Arkani-Hamed, C

    N. Arkani-Hamed, C. Figueiredo, L.J. Hall and C.A. Manzari,Generating the fermion mass hierarchy at the TeV scale,2602.17754. – 43 –

    arXiv

  17. [17]

    Barry and W

    J. Barry and W. Rodejohann,Neutrino Mass Sum-rules in Flavor Symmetry Models,Nucl. Phys. B842(2011) 33 [1007.5217]

    Pith/arXiv arXiv 2011

  18. [18]

    S.F. King, A. Merle and A.J. Stuart,The Power of Neutrino Mass Sum Rules for Neutrinoless Double Beta Decay Experiments,JHEP12(2013) 005 [1307.2901]

    Pith/arXiv arXiv 2013

  19. [19]

    Bergstrom, D

    J. Bergstrom, D. Meloni and L. Merlo,Bayesian comparison of U(1) lepton flavor models, Phys. Rev. D89(2014) 093021 [1403.4528]

    Pith/arXiv arXiv 2014

  20. [20]

    Ballett, S.F

    P. Ballett, S.F. King, C. Luhn, S. Pascoli and M.A. Schmidt,Testing atmospheric mixing sum rules at precision neutrino facilities,Phys. Rev. D89(2014) 016016 [1308.4314]

    Pith/arXiv arXiv 2014

  21. [21]

    Ballett, S.F

    P. Ballett, S.F. King, C. Luhn, S. Pascoli and M.A. Schmidt,Testing solar lepton mixing sum rules in neutrino oscillation experiments,JHEP12(2014) 122 [1410.7573]

    Pith/arXiv arXiv 2014

  22. [22]

    Girardi, S.T

    I. Girardi, S.T. Petcov and A.V. Titov,Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis,Eur. Phys. J. C75(2015) 345 [1504.00658]

    Pith/arXiv arXiv 2015

  23. [23]

    Agarwalla, S.S

    S.K. Agarwalla, S.S. Chatterjee, S.T. Petcov and A.V. Titov,Addressing Neutrino Mixing Models with DUNE and T2HK,Eur. Phys. J. C78(2018) 286 [1711.02107]

    Pith/arXiv arXiv 2018

  24. [24]

    Blennow, M

    M. Blennow, M. Ghosh, T. Ohlsson and A. Titov,Testing Lepton Flavor Models at ESSnuSB,JHEP07(2020) 014 [2004.00017]

    arXiv 2020

  25. [25]

    Blennow, M

    M. Blennow, M. Ghosh, T. Ohlsson and A. Titov,Probing Lepton Flavor Models at Future Neutrino Experiments,Phys. Rev. D102(2020) 115004 [2005.12277]

    arXiv 2020

  26. [26]

    Denton and J

    P.B. Denton and J. Gehrlein,Survey of neutrino flavor predictions and the neutrinoless double beta decay funnel,Phys. Rev. D109(2024) 055028 [2308.09737]

    arXiv 2024

  27. [27]

    Plentinger, G

    F. Plentinger, G. Seidl and W. Winter,Systematic parameter space search of extended quark-lepton complementarity,Nucl. Phys. B791(2008) 60 [hep-ph/0612169]

    Pith/arXiv arXiv 2008

  28. [28]

    Jenkins,Minimally Allowed beta beta 0 nu Rates From Approximate Flavor Symmetries, Phys

    J. Jenkins,Minimally Allowed beta beta 0 nu Rates From Approximate Flavor Symmetries, Phys. Rev. D79(2009) 113004 [0810.1263]

    Pith/arXiv arXiv 2009

  29. [29]

    Capozzi, E

    F. Capozzi, E. Lisi, F. Marcone, A. Marrone and A. Palazzo,Updated bounds on the (1,2) neutrino oscillation parameters after first JUNO results,2511.21650

    arXiv

  30. [30]

    Esteban, M.C

    I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J.P. Pinheiro and T. Schwetz,Lessons from the first JUNO results,2601.09791

    Pith/arXiv arXiv

  31. [31]

    Denton, M

    P.B. Denton, M. Friend, M.D. Messier, H.A. Tanaka, S. B¨ oser, J.A.B. Coelho et al., Snowmass Neutrino Frontier: NF01 Topical Group Report on Three-Flavor Neutrino Oscillations,2212.00809

    arXiv

  32. [32]

    Denton,Neutrino Oscillations in the Three Flavor Paradigm,2501.08374

    P.B. Denton,Neutrino Oscillations in the Three Flavor Paradigm,2501.08374. [36]DUNEcollaboration,Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report, Volume II: DUNE Physics,2002.03005. [37]JUNOcollaboration,JUNO physics and detector,Prog. Part. Nucl. Phys.123(2022) 103927 [2104.02565]. [38]Hyper-Kamiokandecollaboration,Hyper...

    arXiv 2002

  33. [33]

    Nunokawa, S.J

    H. Nunokawa, S.J. Parke and R. Zukanovich Funchal,Another possible way to determine the neutrino mass hierarchy,Phys. Rev. D72(2005) 013009 [hep-ph/0503283]. [42]IceCube-Gen2collaboration,Combined sensitivity to the neutrino mass ordering with JUNO, the IceCube Upgrade, and PINGU,Phys. Rev. D101(2020) 032006 [1911.06745]

    Pith/arXiv arXiv 2005

  34. [34]

    Parke and R

    S.J. Parke and R. Zukanovich-Funchal,Mass ordering sum rule for the neutrino disappearance channels in T2K, NOvA, and JUNO,Phys. Rev. D111(2025) 013008 [2404.08733]. [44]Planckcollaboration,Planck intermediate results. XVI. Profile likelihoods for cosmological parameters,Astron. Astrophys.566(2014) A54 [1311.1657]

    arXiv 2025

  35. [35]

    Couchot, S

    F. Couchot, S. Henrot-Versill´ e, O. Perdereau, S. Plaszczynski, B. Rouill´ e d’Orfeuil, M. Spinelli et al.,Cosmological constraints on the neutrino mass including systematic uncertainties,Astron. Astrophys.606(2017) A104 [1703.10829]. [46]eBOSScollaboration,Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from...

    Pith/arXiv arXiv 2017

  36. [36]

    E. Abdalla et al.,Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,JHEAp34(2022) 49 [2203.06142]

    Pith/arXiv arXiv 2022

  37. [37]

    Craig, D

    N. Craig, D. Green, J. Meyers and S. Rajendran,Noνs is Good News,JHEP09(2024) 097 [2405.00836]

    arXiv 2024

  38. [38]

    D. Wang, O. Mena, E. Di Valentino and S. Gariazzo,Updating neutrino mass constraints with background measurements,Phys. Rev. D110(2024) 103536 [2405.03368]

    arXiv 2024

  39. [39]

    Allali and A

    I.J. Allali and A. Notari,Neutrino mass bounds from DESI 2024 are relaxed by Planck PR4 and cosmological supernovae,JCAP12(2024) 020 [2406.14554]

    arXiv 2024

  40. [40]

    Yadav, S

    A. Yadav, S. Kumar, C. Kibris and O. Akarsu, Λ sCDM cosmology: alleviating major cosmological tensions by predicting standard neutrino properties,JCAP01(2025) 042 [2406.18496]

    arXiv 2025

  41. [41]

    Green and J

    D. Green and J. Meyers,Cosmological preference for a negative neutrino mass,Phys. Rev. D111(2025) 083507 [2407.07878]

    arXiv 2025

  42. [42]

    Elbers, C.S

    W. Elbers, C.S. Frenk, A. Jenkins, B. Li and S. Pascoli,Negative neutrino masses as a mirage of dark energy,Phys. Rev. D111(2025) 063534 [2407.10965]

    arXiv 2025

  43. [43]

    Naredo-Tuero, M

    D. Naredo-Tuero, M. Escudero, E. Fern´ andez-Mart´ ınez, X. Marcano and V. Poulin,Critical look at the cosmological neutrino mass bound,Phys. Rev. D110(2024) 123537 [2407.13831]

    arXiv 2024

  44. [44]

    Jiang, W

    J.-Q. Jiang, W. Giar` e, S. Gariazzo, M.G. Dainotti, E. Di Valentino, O. Mena et al., Neutrino cosmology after DESI: tightest mass upper limits, preference for the normal ordering, and tension with terrestrial observations,JCAP01(2025) 153 [2407.18047]

    arXiv 2025

  45. [45]

    Bert´ olez-Mart´ ınez, I

    T. Bert´ olez-Mart´ ınez, I. Esteban, R. Hajjar, O. Mena and J. Salvado,Origin of cosmological neutrino mass bounds: background versus perturbations,JCAP06(2025) 058 [2411.14524]. – 45 –

    arXiv 2025

  46. [46]

    Lynch and L

    G.P. Lynch and L. Knox,What’s the matter withΣmν?,Phys. Rev. D112(2025) 083543 [2503.14470]. [58]CosmoVerse Networkcollaboration,The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics,Phys. Dark Univ.49(2025) 101965 [2504.01669]

    arXiv 2025

  47. [47]

    Sailer, G.S

    N. Sailer, G.S. Farren, S. Ferraro and M. White,Addressing Tensions inΛCDM Cosmology by an Increase in the Optical Depth to Reionization,Phys. Rev. Lett.136(2026) 081002 [2504.16932]

    arXiv 2026

  48. [48]

    Cozzumbo, M

    A. Cozzumbo, M. Atzori Corona, R. Murgia, M. Archidiacono and M. Cadeddu,A short blanket for cosmology: the CMB lensing anomaly behind the preference for a negative neutrino mass,2511.01967. [61]KATRINcollaboration,Direct neutrino-mass measurement based on 259 days of KATRIN data,Science388(2025) adq9592 [2406.13516]

    arXiv 2025

  49. [49]

    Gastaldo et al.,The electron capture in 163Ho experiment – ECHo,Eur

    L. Gastaldo et al.,The electron capture in 163Ho experiment – ECHo,Eur. Phys. J. ST226 (2017) 1623. [63]Project 8collaboration,Determining the neutrino mass with cyclotron radiation emission spectroscopy—Project 8,J. Phys. G44(2017) 054004 [1703.02037]

    Pith/arXiv arXiv 2017

  50. [50]

    Direct neutrino mass measurements at katrin and beyond

    A. Gavin, “Direct neutrino mass measurements at katrin and beyond.” https://indico.sanfordlab.org/event/68/contributions/1539/attachments/781/ 1994/CoSSURF_KATRINplus_2024.pdf. [65]PTOLEMYcollaboration,Neutrino physics with the PTOLEMY project: active neutrino properties and the light sterile case,JCAP07(2019) 047 [1902.05508]

    arXiv 1994

  51. [51]

    Font-Ribera, P

    A. Font-Ribera, P. McDonald, N. Mostek, B.A. Reid, H.-J. Seo and A. Slosar,DESI and other dark energy experiments in the era of neutrino mass measurements,JCAP05(2014) 023 [1308.4164]. [67]Simons Observatorycollaboration,The Simons Observatory: Science goals and forecasts, JCAP02(2019) 056 [1808.07445]. [68]CMB-S4collaboration,CMB-S4 Science Book, First E...

    Pith/arXiv arXiv 2014

  52. [52]

    Brinckmann, D.C

    T. Brinckmann, D.C. Hooper, M. Archidiacono, J. Lesgourgues and T. Sprenger,The promising future of a robust cosmological neutrino mass measurement,JCAP01(2019) 059 [1808.05955]

    Pith/arXiv arXiv 2019

  53. [53]

    Wolfenstein,CP Properties of Majorana Neutrinos and Double beta Decay,Phys

    L. Wolfenstein,CP Properties of Majorana Neutrinos and Double beta Decay,Phys. Lett. B 107(1981) 77

    1981

  54. [54]

    Kayser,CPT, CP, and C Phases and their Effects in Majorana Particle Processes,Phys

    B. Kayser,CPT, CP, and C Phases and their Effects in Majorana Particle Processes,Phys. Rev. D30(1984) 1023

    1984

  55. [55]

    Bilenky, N.P

    S.M. Bilenky, N.P. Nedelcheva and S.T. Petcov,Some Implications of the CP Invariance for Mixing of Majorana Neutrinos,Nucl. Phys. B247(1984) 61

    1984

  56. [56]

    Branco, L

    G.C. Branco, L. Lavoura and M.N. Rebelo,Majorana Neutrinos and CP Violation in the Leptonic Sector,Phys. Lett. B180(1986) 264

    1986

  57. [57]

    Feruglio, C

    F. Feruglio, C. Hagedorn and R. Ziegler,Lepton Mixing Parameters from Discrete and CP Symmetries,JHEP07(2013) 027 [1211.5560]. – 46 –

    Pith/arXiv arXiv 2013

  58. [58]

    Holthausen, M

    M. Holthausen, M. Lindner and M.A. Schmidt,CP and Discrete Flavour Symmetries, JHEP04(2013) 122 [1211.6953]

    Pith/arXiv arXiv 2013

  59. [59]

    Ding and Y.-L

    G.-J. Ding and Y.-L. Zhou,Predicting lepton flavor mixing from∆(48) and generalizedCP symmetries,Chin. Phys. C39(2015) 021001 [1312.5222]

    Pith/arXiv arXiv 2015

  60. [60]

    Ding and Y.-L

    G.-J. Ding and Y.-L. Zhou,Lepton mixing parameters from∆(48)family symmetry and generalised CP,JHEP06(2014) 023 [1404.0592]

    Pith/arXiv arXiv 2014

  61. [61]

    King and T

    S.F. King and T. Neder,Lepton mixing predictions including Majorana phases from∆(6n 2) flavour symmetry and generalised CP,Phys. Lett. B736(2014) 308 [1403.1758]

    Pith/arXiv arXiv 2014

  62. [62]

    Ding and S.F

    G.-J. Ding and S.F. King,GeneralizedCPand∆(96)family symmetry,Phys. Rev. D89 (2014) 093020 [1403.5846]

    Pith/arXiv arXiv 2014

  63. [63]

    Hagedorn, A

    C. Hagedorn, A. Meroni and E. Molinaro,Lepton mixing from∆(3n 2) and∆(6n 2) and CP, Nucl. Phys. B891(2015) 499 [1408.7118]

    Pith/arXiv arXiv 2015

  64. [64]

    Ding, S.F

    G.-J. Ding, S.F. King and T. Neder,Generalised CP and∆(6n 2)family symmetry in semi-direct models of leptons,JHEP12(2014) 007 [1409.8005]

    Pith/arXiv arXiv 2014

  65. [65]

    Ding and S.F

    G.-J. Ding and S.F. King,Generalized CP and∆(3n 2)Family Symmetry for Semi-Direct Predictions of the PMNS Matrix,Phys. Rev. D93(2016) 025013 [1510.03188]

    Pith/arXiv arXiv 2016

  66. [66]

    L.J. Hall, H. Murayama and N. Weiner,Neutrino mass anarchy,Phys. Rev. Lett.84(2000) 2572 [hep-ph/9911341]

    Pith/arXiv arXiv 2000

  67. [67]

    Haba and H

    N. Haba and H. Murayama,Anarchy and hierarchy,Phys. Rev. D63(2001) 053010 [hep-ph/0009174]

    Pith/arXiv arXiv 2001

  68. [68]

    Jenkins,Minimally Allowed beta beta 0 nu Rates Within an Anarchical Framework,Phys

    J. Jenkins,Minimally Allowed beta beta 0 nu Rates Within an Anarchical Framework,Phys. Rev. D79(2009) 113003 [0808.1702]

    Pith/arXiv arXiv 2009

  69. [69]

    de Gouvea and H

    A. de Gouvea and H. Murayama,Neutrino Mixing Anarchy: Alive and Kicking,Phys. Lett. B747(2015) 479 [1204.1249]

    Pith/arXiv arXiv 2015

  70. [70]

    Froggatt and H.B

    C.D. Froggatt and H.B. Nielsen,Hierarchy of Quark Masses, Cabibbo Angles and CP Violation,Nucl. Phys. B147(1979) 277

    1979

  71. [71]

    Leurer, Y

    M. Leurer, Y. Nir and N. Seiberg,Mass matrix models,Nucl. Phys. B398(1993) 319 [hep-ph/9212278]

    Pith/arXiv arXiv 1993

  72. [72]

    Leurer, Y

    M. Leurer, Y. Nir and N. Seiberg,Mass matrix models: The Sequel,Nucl. Phys. B420 (1994) 468 [hep-ph/9310320]

    Pith/arXiv arXiv 1994

  73. [73]

    Cornella, D

    C. Cornella, D. Curtin, G. Krnjaic and M. Mellors,Testing the Froggatt-Nielsen mechanism with lepton flavor and number violating processes,Phys. Rev. D112(2025) 115010 [2501.00629]

    arXiv 2025

  74. [74]

    M. Ibe, S. Shirai and K. Watanabe,Comprehensive Bayesian exploration of Froggatt-Nielsen mechanism,JHEP03(2025) 150 [2412.19484]

    arXiv 2025

  75. [75]

    King and G.G

    S.F. King and G.G. Ross,Fermion masses and mixing angles from SU (3) family symmetry and unification,Phys. Lett. B574(2003) 239 [hep-ph/0307190]

    Pith/arXiv arXiv 2003

  76. [76]

    D’Agnolo and D.M

    R.T. D’Agnolo and D.M. Straub,Gauged flavour symmetry for the light generations,JHEP 05(2012) 034 [1202.4759]

    Pith/arXiv arXiv 2012

  77. [77]

    Greljo, A.E

    A. Greljo, A.E. Thomsen and H. Tiblom,Flavor hierarchies from SU(2) flavor and quark-lepton unification,JHEP08(2024) 143 [2406.02687]. – 47 –

    arXiv 2024

  78. [78]

    Greljo and A.E

    A. Greljo and A.E. Thomsen,Rising through the ranks: flavor hierarchies from a gauged SU(2) symmetry,Eur. Phys. J. C84(2024) 213 [2309.11547]

    arXiv 2024

  79. [79]

    Li and E

    X. Li and E. Ma,Gauge Model of Generation Nonuniversality,Phys. Rev. Lett.47(1981) 1788

    1981

  80. [80]

    Bordone, C

    M. Bordone, C. Cornella, J. Fuentes-Martin and G. Isidori,A three-site gauge model for flavor hierarchies and flavor anomalies,Phys. Lett. B779(2018) 317 [1712.01368]

    Pith/arXiv arXiv 2018

Showing first 80 references.