Nucleosynthesis Bounds on Small Dirac Neutrino Masses due to Chiral Symmetry Breaking

A Higgs doublet which has a positive mass squared term and Yukawa couplings to the quarks will acquire a vacuum expectation value typically of the order of 10eV or less, as a result of chiral symmetry breaking. We consider nucleosynthesis constraints on models which use this fact as a basis for understanding very small Dirac neutrino masses without requiring very small Yukawa couplings. The simplest such model requires the introduction of a second Higgs doublet plus right-handed neutrinos together with a global horizontal symmetry U(1)H which ensures that the neutrinos are naturally massless in the chiral symmetric limit. We show that present big-bang nucleosynthesis constraints impose a well-defined upper bound of 0.1eV on the neutrino masses. This bound may become several orders of magnitude more stringent in the future as our understanding of the observational constraints on nucleosynthesis improves. We discuss the phenomenological implications for neutrino dark matter, the solar neutrino problem and the atmospheric neutrino deficit.