Determining fermion masses and resolving the problem of generations: A clue to incorporate Gravity into the Standard Model

K Tennakone


Inspired by the Poincare model of the electron, elementary fermions are assumed to be bubble like structures with negative internal pressure and a size corresponding to a radius or equivalently an ultraviolet cut-off. Negative pressure, self-interaction of gauge fields up to the cut-off energy and gravity contribute to the self-energy. All corrections are considered to be proportional to the observed mass of the fermion in order to preserve chiral symmetry in the limit of vanishing fermion mass. Fermion self-energy is thus constituted of terms; inverse cubic, logarithmic (as in qed self-energy of the electron), linear and quadratic in the cut-off parameter and defines coupling coefficients. The latter two terms originating from gravity are fixed on basis of dimensional considerations. The condition of extremization of total energy to determine equilibrium states, leads to a quantic equations with three real roots, giving three values for the fermion mass, for each set of coupling coefficients. The model represents observed quark – lepton mass ratios explaining generation problem and suggest possible numerical values for neutrino masses in agreement with the oscillation data in an inverted order. As a result of incorporation of gravity, Planck energy sets as the natural physically meaningful scale, deriving other scales corresponding to sizes of elementary fermions ranging from Planck length to few thousand times this unit. The model interprets, the physical quality distinguishing a generation as the phase of the false vacuum ‘inside’ the elementary bubble. The unconventional approach behind the model may also have implications on unifications of couplings, incorporation of gravity into the standard model and issue of divergences in quantum field theories.

Full Text:



S. Weinberg, Essay: Half a Century of the Standard Model. Phys. Rev. Lett., 121, 220001 (2018)

H. Murayama, Supersymmetry Phenomenology, ICTP Series in Theoretical Physics-V16, Proc. 1999 Summer School in Particle Physics, pp 298-302 (1999).

S.L. Glashow, Symmetries of Weak Interaction, Nucl. Phys., 127, 965-970 (1961).

J. Goldstone, A.Salam, Weinberg, Broken Symmetries, Phys. Rev., 127, 965-970 (1962).

P.W.Higgs, Broken symmetries and masses of gauge bosons, Phys. Rev. Lett. 13,508-509 (1964).

F. Englert, R.Brout, Broken symmetry and mass of gauge vector mesons, Phys. Rev. Lett.13, 321-323 (1964).

J.A.Casa, Some aspects of Physics beyond the Standard Model, J. Phys. Conference Series, 485, 012006 (2014)

J. Barranco, Some Model Problems and Possible solutions, J. Phys. Conference Series, 761 (2016) 012007.

S.Troitsky, Unsolved Problems in Particle Physics, arXiv: 1112.451 v1 [hep-ph] 19 Dec 2011 pp 1-49

Z. Xing, Quark mass hierarchy and flavor mixing puzzles, Int. J. Mod. Phys. A29, 1430067 (2014).

M. Yu.Khlopov, On problem of quark lepton families, [12] arXiv.1306.470v2 [hep-ph] 29 June 2013.

T. Kajita, Atmospheric neutrinos and discovery of neutrino oscillations, Proc. Jpn. Acad. Ser. B Phys. Biol.Sci. 86, 303-321 (2010).

S. Bilenky, Neutrino Oscillations: From a historical perspective, Nucl. Phys., B 908, 2-13 (2016).

G’t Hooft and M.Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B44, 189-213 (1972).

M. Abraham, Principium der Dynamik des Electrons, Ann. Phys., 10, 105 -179 (1903).

H.A. Lorentz, The Theory of Electrons (New York, Dover 1952).

M.H. Poincare On dynamics of the electron, Rendiconti del Matematico di Palermo, 21, 129-176 (1906).

K.Tennakone, A Semiclassical Model of Leptons, J.Appl.Found. Phys. 5,225-230 (2018).

R.P Feynman, On space-time approach to quantum electrodynamics, Phys.Rev.76, 769-789 (1949).

J.L. Jimenez and I. Campos, Models of the classical electron after a century, Found. Phys. Lett. 12, 127-146 (1999).

R.N Tiwari , J.R. Rao and R.R Kanakamedala , Electromagnetic mass models in general relativity, Phys. Rev. D30 ,489 -491(1984).

R. Gautreau, Gravitational models of a Lorentz extended electron, Phys. Rev. D 31, 1860-1863 (1985).

C.A. Lopez, Extended model of the electron in general relativity, Phys. Rev. D, 30 313 (1984).

F.Rahaman, Jamil and K. Chakraborty, Revisiting the classical electron in general relativity, Astrophys. Space. Sci, 331,191-197 (2011)

O. Grön, A charged generalization of Florides interior Schwarzschild Solution, Gen. Rel.Grav. 18 591-596 (1986).

S. K. Maurya, Y.K. Gupta, S. Ray and S. R. Chowdhury, Spherically symmetric charged compact stars, Eur. Phys. J. C 75, 389-401 (2015).

S. Ray and S.Bhadra, Classical electron models with negative energy density in Einstein-Cartan Theory of Gravitation, Int. J. Mod. Phys. D13 1555-1566 (2004).

G.Rosen, Quantum theory of gravitation and mass of the electron. Phys.Rev.D4, 275 (1971)

A. Burinskii, Gravity versus Quantum theory: Is electron point like, arXiv: 1104.057v1 [hep-ph]

L. N. Chang, C.Soo, Standard model with gravity couplings, Phys. Rev. D53, 5652 (1996)

I. Chakraborty, I. Kundu, Naturalness Problem: Off the beaten track, Pramana J. Phys. (2016) 87, 38-49 (2016).

M.Rosen, Niels Hendrik Abel and the equation of fifth degree, Amer. Math. Monthly, 102, 495-505 (1995).

The CMS Collaboration , Search for flavor changing neutral current interactions of the top quark and Higgs boson into pair of b quarks √s = 13 TeV., arXiv.1712.02399 v2 [hep-ex] 29June 2018.

R.Jeremy, P.Alexander, Stability of Inverted Pendulum and Heisenberg Uncertainty Principle , American Physical Society, Annual Meeting of the Four Corners Section October 2010, Abstract id H4.004

S. Roy, N. N. Singh, Quasi- degenerate neutrino mass models and their significance, Nucl. Phys. B 887, 321-342 (2013).

A. S. Joshipura, K. M. Patel., Quasi-degenerate neutrinos in SO (10), Phys. Rev., D82, 031701, (2010)

B.G.Sidharth ,C.R.Dasm, C.D. Froggatt, H.B.Nielson, L. Laperashvilli, Degenerate vacua of the Universe and What Beyond Standard Model, arXiv.1801.06979 v2 [hep-ph] 29 Jan 2018.

C.D.Froggatt, H.B. Nielson, Standard Model Criticality Prediction: Top quark mass 173 +/-GeV and Higgs mass 135+/-9 GeV, Phys. Lett B368, 96-102 (1996).

M. Chabab, M. Peyranere, L.Rahili, Probing the Higgs sector of Y = 0 Higgs triplet model at LHC. Euro. Phys. J. C, 78, 873 (2018).

D. Gosh, R. S. Gupta, G. Perez. Is Higgs mechanism of fermion mass generation a fact? A Yukawa-less first two generation model, Phys. Lett. B735, 504-508 (2016)

T. Alanne, T Frandsen, D.B. Franzosi, Testing a dynamical origin of standard model fermions, Phys. Rev.D 94, 074071703 (2010)

D. Bolmatov, E. T. Musaev, K.Trachenko. Symmetry breaking gives rise to energy spectra of three states of matter. Scientific Reports 2794 (2013).

P. F. de Salas, S. Gariazzo. O. Mena, C.A.Ternes M.Tortola, Neutrino mass ordering from oscillations and beyond, in Frontiers in Astronomy and space science, Oct.2018, Ed. A. Salvio (CERN, Switzerland).

Iteration and use of the facility Quantic Equation Calculator, Brian JavaScript Utilities, available

http// equation calculator.htm.

S. Hossenfelder, Minimal length scale scenarios for quantum gravity. Living Rev. Relativity 16, 2 (2013)


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

ISSN: 2394-3688

© Science Front Publishers