Neutrinos and Theories of Particles

In the Standard Model of Particle Physics, neutrinos are elementary particles in the family of leptons (same family as the electron), thus not sensitive to strong interaction, and with no electric charge, thus not sensitive to electromagnetic interaction.

The study of neutrino properties, from the measurement of its helicity to the long-awaited discovery of oscillations, had an important impact on particle theory. The early experimental data (or its theoretical interpretation) seemed to suggest that neutrinos, unlike other fermions, were massless. Indeed, the Goldhaber experiment showed in 1958 that the neutrino helicity is negative [Gol58] ; because of this, the founders of the Standard Model (S.L. Glashow, S. Weinberg and A. Salam) did not include right-handed neutrinos in their theory [Gla61,Wei67,Sal68]. Neutrinos are therefore massless in the Standard Model.

This did not prevent theorists like Pontecorvo, to consider the possibility of neutrino flavour oscillations [Pon67]. Oscillations, which require neutrinos to be massive, seem to be in contradiction with the Standard Model.  But the Standard Model itself could be the low-energy limit of a more fundamental theory[1], such as one of the Grand Unified Theories developed in the 1970s by Georgi, Glashow and other theorists. In this case, the Standard Model would be supplemented by additional interaction terms  (so-called higher-dimensional operators) suppressed by powers of a scale Λ characteristic of the high-energy theory. Weinberg noticed that the interaction term llHH/Λ (known as the Weinberg operator) [Wei79], which involves two lepton and two Higgs doublets and violates lepton number, generates a mass mν~M2W/Λ for the Standard Model neutrinos, which are then promoted to Majorana neutrinos. For mν~0.05 eV, this gives Λ~1014 GeV, close to the Grand Unification scale MGUT ~1016 GeV.

Roughly at the same time, several theorists realized that Grand Unified Theories based on the SO(10) gauge group contain all the ingredients needed to generate light neutrino masses [Gel79,Gla79,Moh80]. These theories predict the existence of heavy Majorana neutrinos, whose coupling to the lepton and Higgs fields induce the Weinberg operator via the so-called “seesaw mechanism” [Min77,Yan79]. The masses of these heavy neutrinos lie typically a few orders of magnitude below MGUT, yielding masses in the eV or sub-eV range for the Standard Model neutrinos. The existence of light Majorana neutrinos can therefore be viewed as a prediction of the seesaw mechanism and of Grand Unified Theories, even though alternative mechanisms could be at the origin of neutrino masses. It is, unfortunately, very hard to test this appealing idea. A first step – necessary but not sufficient – would be to prove, through the observation of neutrinoless double beta decay, that neutrinos are Majorana fermions. If, in addition, proton decay were observed, this would strongly support the Grand Unification hypothesis and give some credit to the seesaw mechanism.

[1] It is also possible that neutrino masses arise from some low-energy physics that would complement the Standard Model. The simplest option is to add right-handed neutrinos to the Standard Model and to impose lepton number conservation, in which case neutrinos are Dirac fermions, but there is no natural explanation for the smallness of their masses.

Further information

During the conference on the History of the Neutrino (Sept. 5-7, 2018 in Paris) the subject of Neutrinos and Particle Physics Models was reviewed by Pierre Ramond (University of Florida, USA) : here the slides and the video of his talk.


Fey58R.P. Feynman and M. Gell-MannTheory of the Fermi interactionPhys. Rev. 109 (1958) 193
Gel79M. Gell-Mann, P. Ramond and R. Slansky Complex Spinors and Unified Theories Supergravity, ed. by D. Freedman and P. van Nieuwenhuizen, North-Holland (1979) p. 315, retro-print arXiv:1306.4669 & Talk by P. Ramond "The family group and Grand Unified Theories" at the 19th Sanibel Symposium, February 1979, retro-print arXiv:hep-ph/9809459
Gla61S.L. GlashowPartial symmetries of weak interactionsNucl. Phys. 22 (1961) 579
Gla79S.L. GlashowThe future of elementary particle physicsCargèse lectures, July 1979, in Quarks and Leptons, Plenum, 1980
Gol58M. Goldhaber, L. Grodzins, A. Sunyar Helicity of neutrinos Phys. Rev. 109 (1958) 1015
Gro58L. GrodzinsLifetime of a 1 - level in 152 SmPhys. Rev. 109 (1958) 1015
Min77P. Minkowskim → e g at a rate of one out of 1 billion muon decaysPhys. Lett. B67 (1977) 421
Moh80R.N. Mohapatra and G. SenjanovicNeutrino mass and spontaneous parity nonconservationPhys. Rev. Lett. 44 (1980) 912
Pon67B. Pontecorvo Neutrino experiments and the question of leptonic-charge conservationZETF 53 (1967) 1717 – Soviet Physics JETP 26 (1968) 984
Sal68A. SalamWeak and electromagnetic interactionsProceedings of the 8th Nobel Symposium, Conf. Proc.C 680519 (1968) 367
Wei67S. Weinberg A model of leptonsPhys. Rev. Lett. 19 (1967) 1264
Wei79S. Weinberg Baryon and lepton non conserving processesPhys. Rev. Lett. 43 (1979) 1566

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