Volume 146B, number 1,2 PHYSICS LETTERS 4 October 1984 DOES COSMOLOGY IMPLY A DIRAC NEUTRINO MASS? Daniele FARGION Physics Department "G. Marconi", Rome University "La Sapienza ", Piazzale Aldo Moro, 2, 00185 - Rome, Italy and Michael G. SHEPKIN Institute of Theoretical and Experimental Physics, Moscow, USSR Received 9 May 1984 Present bounds on double beta decay and tritium decay together with cosmological bounds on early nucleosynthesis lead to stringent limits on both left-handed (mL) and right-handed (mR) Majorana masses: (m L + mR) ~ 2 × 10-1° eV. Therefore right-handed neutrinos of masses of a few keV are no longer a plausible candidate for galaxy formation processes. Introduction. If the neutrino has a mass it may be either of Dirac nature, as for all known fermions, or of Majorana nature, with a consequent lepton number violation. In the most general case the neutrino may be a combination of both Dirac and Majorana fields [1]. From an aesthetic point of view particle physicists preferred a Majorana term because of the small neu- trino mass with respect to all remaining quark-lepton masses [2]. Nevertheless our understanding of the mass spectrum of basic Dirac fermions is far from be- ing satisfactory. Moreover a Majorana mass should manifest itself in a neutrinoless double beta decay. Recent evidence of the absence of such decays [3] im- plies an upper limit on the left-handed Majorana mass of the neutrino re: mve L <~ 10 eV. This result is no longer compatible with the pio- neering ITEP experiments [4] on the/3 spectrum in tritium which has yielded a lower limit for the Ve mass: rove >~ 20 eV. As a consequence of this conflicting analysis one is forced to assume a ruling Dirac mass term: m ~ 10 eV, (la) VD with a possible smaller (left-handed) Majorana compo- nent : m ~ 10 eV. (lb) VM Motivated by these experimental results different authors considered recently a possible mechanism to generate a light Dirac neutrino mass in the framework of unified [5] or of supergrand unified [6] theories. Nevertheless the most general phenomenological neutrino mass to be considered, consistent with all present laboratory data, may contain a Dirac and a smaller Majorana term [1]. Early and late cosmology are strongly related to the tiny neutrino mass, flavours and also to its possible Dirac-Majorana nature; consequently known limits on cosmological parameters lead to corresponding bounds on the neutrino parameters. Here we show that these bounds almost suppress the Majorana mass term of light neutrinos (mv < O~eV)). Neutrinos in the early universe. The high number of cosmological neutrinos may rule the present cosmo- logical expansion as well as the age and the structure of the universe * a Moreover the total number of neutrino flavours and helicity states are strongly bounded by the theory on cosmological nucleosynthesis [8] : no more than 4 half- helicity neutrino flavours N u are admitted in thermal equilibrium in the early universe: (T ~Mzo). ,1 For a review see ref. [7]. 46