Nuclear Physics B231 (1984) 493-505 '~ North-Holland Publishing Company THE MAJORON AND LEFT-HANDED NEUTRINO MASSES IN SU(5) Franco BUCCELLA Istituto di Fisica Teorica, Napoli, Italy, Istituto Nazionale di Fisica Nucleareo Napoli, Italy Graciela B. GELMINI* International Centre of Theoretical Physics, Trieste, Italy Antonio MASIERO* and Marco RONCADELLI** Max Planck-lnstitut fiJr Physik und Astrophysik, Werner Heisenberg-lnstitut fi~r Physik, D-8000 Munich 40, Fed. Rep. of Germany Received 13 May 1982 (Revised 22 August 1983) We consider the spontaneous breaking of B-L in SU(5) in connection with left-handed neutrino masses. We show that the ensuing Goldstone boson, "the majoron," is harmless. The low-energy predictions are the same as in the SU(2)t x U(1) majoron model which, in particular, predicts the existence of doubly and singly charged scalars, with masses < 250 GeV and with a mass ratio of ¢'2. Going to SU(5), one would expect these scalars to escape to the grand unified mass. This does not happen and, surprisingly, even the ratio ¢'2- is preserved. 1. Introduction One of the greatest challenges facing theory and experiments in particle physics concerns neutrino masses. Various hints point, if not conclusively, in favour of massive neutrinos. Even more interestingly, all these suggestions present the exciting coincidence of the eV range for these masses [1]. An incomplete list of these indications includes tritium beta decay [2], neutrino-less double beta decay [3], and neutrino oscillations [4]. From the theoretical point of view, the big question is why neutrino masses are much smaller than charged lepton masses. This can find a natural explanation only in terms of Majorana masses for neutrinos [5]. As is well-known, such mass terms * Present address: Theory Division, CERN, CH-1211 Geneva 23, Switzerland. ** Address after 1 November 1983: Dipartimento di Fisica Nucleare e Teorica, Universit~tdi Pavia, Pavia, Italy. Associato INFN, Pavia, Italy. 493