This page is a convenience sample of physics papers suggesting causes for the values of the Standard Model of Particle Physics' experimentally measured constants, which I update from time to time. They are listed in order of publication from most recent to oldest. I do not render any opinion on the merits of these proposals.
Hajime Otsuka, Ryo Yokokura, "Non-Invertible Froggatt-Nielsen Symmetry" arXiv:2610.21688 (October 15, 2026).
I. Alikhanov, "Novel dependence between neutrino mass splittings strongly supported by initial JUNO results" arXiv:2610.06738 (October 5, 2026).
Rivero, A., "New Sum Rules of the Koide Type". Physics Letters B. 887 140510. arXiv:2606.10060. doi:10.1016/j.physletb.2026.140510 (2026).
Kirill Shulga, "Charged-Lepton Koide Geometry from a Green-Dressed Compact Family Cycle" arXiv:2605.10245 (May 11, 2026).
K. Hübner, "A minimization theorem for the Koide ratio and its Standard Model calibration" arXiv:2605.09651 (May 10, 2026)
Vernon Barger, "Quark Mixing from a Lattice Flavon Model: A Four-Magnitude Parameterization" arXiv:2603.00810v2 (August 24, 2026).
Mohammad Ful Hossain Seikh, "A geometrical approach to neutrino oscillation parameters" arXiv:2510.06526 (October 7, 2025).
Qiaofeng Liu, Ian Low, Zhewei Yin, "A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model" arXiv:2509.18251 (September 22, 2025)
Eckart Marsch, Yasuhito Narita, "On the Lagrangian and fermion mass of the unified SU(2) ⊗ SU(4) gauge field theory" arXiv:2508.15332 (August 21, 2025) (13 pages).
Rivero, A. (2024). "An interpretation of scalars in SO(32)". European Physical Journal C. 84 (10) 1058. arXiv:2407.05397. doi:10.1140/epjc/s10052-024-13368-3.
Boris Altshuler, "Quark mixing angles and weak CP-violating phase vs quark masses: potential approach" arXiv:2303.16568 (March 29, 2023) (substantial text overlap with arXiv:2210.09780).
Yuval Grossman, Ameen Ismail, Joshua T. Ruderman, Tien-Hsueh Tsai, "CKM substructure from the weak to the Planck scale" arXiv:2201.10561 (January 25, 2022).
Gustavo F. S. Alves, Enrico Bertuzzo, Gabriel M. Salla, "An on-shell perspective on neutrino oscillations and non-standard interactions" arXiv (March 30, 2021).
Y. Grossman and J. T. Ruderman, “CKM substructure,” JHEP 01, 143 arXiv:2007.12695 (2021)
Nobuhito Maru, Yoshiki Yatagai, "Fermion Mass Hierarchy in Grand Gauge-Higgs Unification" https://arxiv.org/abs/1903.08359
Van E. Mayes "All Fermion Masses and Mixings in an Intersecting D-brane World" https://arxiv.org/abs/1902.00983
Alexander Baur, Hans Peter Nilles, Andreas Trautner, Patrick K.S. Vaudrevange, "Unification of Flavor, CP, and Modular Symmetries" https://arxiv.org/abs/1901.03251
Andrea Wulzer, "Behind the Standard Model" https://arxiv.org/abs/1901.01017
Junu Jeong, Jihn E. Kim, Se-Jin Kim, "Flavor mixing inspired by flipped SU(5) GUT" https://arxiv.org/abs/1812.02556
Koide, Yoshio (2018). "What physics does the charged lepton mass relation tell us?". arXiv:1809.00425
Gauhar Abbas, "A new solution of the fermionic mass hierarchy of the standard model" https://arxiv.org/abs/1807.05683
Emiliano Molinaro, Francesco Sannino, Zhi-Wei Wang, "Safe Pati-Salam" https://arxiv.org/abs/1807.03669
J. T. Penedo, S. T. Petcov, "Lepton Masses and Mixing from Modular S4 Symmetry" https://arxiv.org/abs/1806.11040
Yoshio Koide, Hiroyuki Nishiura, "Parameter-Independent Quark Mass Relation in the U(3)×U(3)′ Model" https://arxiv.org/abs/1805.07334
T. K. Kuo, S. H. Chiu, "Flavor Mixing and the Permutation Symmetry among Generations" https://arxiv.org/abs/1805.05600
M. Novello, V. Antunes, "Connecting the Cabbibo-Kobayashi-Maskawa matrix to quark masses" https://arxiv.org/abs/1804.00572
Astrid Eichhorn, Aaron Held, "Mass difference for charged quarks from asymptotically safe quantum gravity" https://arxiv.org/abs/1803.04027
F.J. Himpsel, "Dynamical Symmetry Breaking by SU(2) Gauge Bosons", arXiv:1801.04604
Kevin Loch, "Emperically [sic] Derived Fermion Higgs Yukawa Couplings and Pole Masses"
http://vixra.org/abs/1711.0388 (note that links to vixra are to papers by non-professional physicists, some of which are contrary to accepted scientific findings and theories)
P. R. Silva, "About Neutrino Masses" https://vixra.org/abs/1702.0320 (February 26, 2017) (discussed by @dandb at Physics Stack Exchange on May 5, 2016 ).
Koide, Yoshio (2017). "Sumino model and my personal view". arXiv:1701.01921.
Rohit Verma, "Minimal Quark Mass Matrices from Physical Observables" (December 8, 2016).
Morimitsu Tanimoto and Tsutomu Yanagida, "Occam's razor in quark mass matrices", Prog. Theor. Exp. Phys (April 1, 2016)
S. Knapen and D. J. Robinson, “Disentangling Mass and Mixing Hierarchies,” Phys. Rev. Lett. 115 no. 16, (2015) 161803, arXiv:1507.00009
HM Chan, ST Tsou, "The Framed Standard Model (I) - A Physics Case for Framing the Yang-Mills Theory?" https://arxiv.org/abs/1505.05472
F. J. Himpsel, "A Higgs Boson Composed Of Gauge Bosons" arXiv:1502.06438 (January 6, 2015).
W. G. Hollik and U. J. Saldaña Salazar, “The double mass hierarchy pattern: simultaneously understanding quark and lepton mixing,” Nucl.Phys. B892 (2015) 364–389, arXiv:1411.3549
A. Gorsky, A. Mironov, A. Morozov, T.N. Tomaras, "Is the Standard Model saved asymptotically by conformal symmetry?" arXiv:1409.0492 (October 2, 2014) (published at ZhETF, 147 (2015) 399-409 (JETP, 120 (2015) 399-409)).
Stephen F. King "A model of quark and lepton mixing" https://arxiv.org/abs/1311.3295
J. Lemmon, "The origin of fermion families and the value of the fine structure constant" https://arxiv.org/abs/1307.2201
G. Lopez Castro, J. Pestieau, "Relation between masses of particles and the Fermi constant in the electroweak Standard Model" arXiv:1305.4208 (May 17, 2013).
Z.-z. Xing, “Model-independent access to the structure of quark flavor mixing,” Phys.Rev. D86 (2012) 113006, arXiv:1211.3890
Zenczykowski, Piotr (2012-12-26). "Remark on Koide's Z3-symmetric parametrization of quark masses". Physical Review D. 86 (11) 117303. arXiv:1210.4125. doi:10.1103/PhysRevD.86.117303.
Emilio Torrente-Lujan, "The Higgs mass coincidence problem: why is the Higgs mass m(H)^2 = m(Z)*m(t)?" Eur. Phys. J. C 74 (2014) 2744, arXiv:1209.0474 and also "The Higgs-top-
Z mass coincidence relation after NNLO matching" https://arxiv.org/abs/2605.21721 (revisiting this publication).
Cao, F. G. (2012). "Neutrino masses from lepton and quark mass relations and neutrino oscillations". Physical Review D. 85 (11) 113003. arXiv:1205.4068. doi:10.1103/PhysRevD.85.113003.
Motl, L. (16 January 2012). "Could the Koide formula be real?". blogspot.com (blog). The Reference Frame. Archived from the original on 2 August 2021. Retrieved 21 December 2023.
Rodejohann, W.; Zhang, H. (2011). "Extension of an empirical charged lepton mass relation to the neutrino sector". Physics Letters B. 698 (2): 152–156. arXiv:1101.5525. doi:10.1016/j.physletb.2011.03.007.
S. Morisi and E. Peinado, “An A(4) model for lepton masses and mixings,” Phys. Rev. D80 (2009) 113011, arXiv:0910.4389
Sumino, Y. (2009). "Family gauge symmetry as an origin of Koide's mass formula and charged lepton spectrum". Journal of High Energy Physics. 2009 (5): 75. arXiv:0812.2103. doi:10.1088/1126-6708/2009/05/075.
Goffinet, F. (2008). A bottom-up approach to fermion masses (PhD thesis). Louvain, FR: Université catholique de Louvain.
Rosen, G. (2007). "Heuristic development of a Dirac-Goldhaber model for lepton and quark structure". Modern Physics Letters A. 22 (4): 283–288. doi:10.1142/S0217732307022621.
Quadt, A., Top Quark Physics at Hadron Colliders (Berlin/Heidelberg: Springer, 2006), p. 147.
Brannen, Carl A. (2 May 2006). "The lepton masses" (PDF). Brannen's personal website.
J. Chkareuli, C. Froggatt, and H. Nielsen, “Minimal mixing of quarks and leptons in the SU(3) theory of flavor,” Nucl.Phys. B626 (2002) 307–343, arXiv:hep-ph/0109156
H. Fritzsch and Z.-z. Xing, “Mass and flavor mixing schemes of quarks and leptons,” Prog.Part.Nucl.Phys. 45 (2000) 1–81, arXiv:hep-ph/9912358
H. Fritzsch and Z.-z. Xing, “The Light quark sector, CP violation, and the unitarity triangle,” Nucl.Phys. B556 (1999) 49–75, arXiv:hep-ph/9904286
J. Chkareuli and C. Froggatt, “Where does flavor mixing come from?,” Phys.Lett. B450 (1999) 158–164, arXiv:hep-ph/9812499
A. Rasin, “Hierarchical quark mass matrices,” Phys.Rev. D58 (1998) 096012, arXiv:hep-ph/9802356
A. Rasin, “Diagonalization of quark mass matrices and the Cabibbo-Kobayashi-Maskawa matrix,” arXiv:hep-ph/9708216
Z.-z. Xing, “Implications of the quark mass hierarchy on flavor mixings,” J.Phys. G23 (1997) 1563–1578, arXiv:hep-ph/9609204
H. Lehmann, C. Newton, and T. T. Wu, “A New variant of symmetry breaking for quark mass matrices,” Phys. Lett. B384 (1996) 249–254.
Foot, R. (7 February 1994). "A note on Koide's lepton mass relation". arXiv:hep-ph/9402242.
L. J. Hall and A. Rasin, “On the generality of certain predictions for quark mixing,” Phys.Lett. B315 (1993) 164–169, arXiv:hep-ph/9303303
H. Fritzsch and J. Plankl, “Flavor Democracy and the Lepton - Quark Hierarchy,” Phys. Lett. B237 (1990) 451.
Koide, Yoshio (1990). "Charged lepton mass sum rule from U(3) family Higgs potential model". Modern Physics Letters A. 5 (28): 2319–2324. doi:10.1142/S0217732390002663.
L. Lavoura, “A Relationship Between the Democratic Family Mixing and the Fritzsch Schemes for the Mass Matrices,” Phys.Lett. B228 (1989) 245.
P. Kaus and S. Meshkov, “A BCS Quark Mass Matrix,” Mod.Phys.Lett. A3 (1988) 1251.
H. Fritzsch, “Hierarchical Chiral Symmetries and the Quark Mass Matrix,” Phys.Lett. B184 (1987) 391.
Koide, Y. (1983). "A fermion-boson composite model of quarks and leptons". Physics Letters B. 120 (1–3): 161–165. Bibcode:1983PhLB..120..161K. doi:10.1016/0370-2693(83)90644-5.
Koide, Y. (1981), Quark and lepton masses speculated from a subquark model
M. Veltman, "The Infrared Ultraviolet Connection" B12 Acta Phys. Polon. 437 (November 20, 1980).
Harari, Haim; Haut, Hervé; Weyers, Jacques (1978). "Quark masses and Cabibbo angles]" (PDF). Physics Letters B. 78 (4): 459–461. doi:10.1016/0370-2693(78)90485-9.
R. Gatto, G. Sartori, and M. Tonin, “Weak self-masses, Cabibbo angle, and broken SU(2)×SU(2),” Phys. Lett. B 28, 128 (1968). Full text (equations are handwritten and images of them are provided here) at https://cds.cern.ch/record/939987/files/CM-P00057857.pdf See also R. J. Oakes, “SU(2)×SU(2) breaking and the Cabibbo angle,” Phys. Lett. B 29, 683 (1969).
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