Neutrino condensation from a new Higgs-like interaction
In this work, we revisit the scenario of having a new interaction between neutrinos and a Higgs-like scalar suggested by short-baseline neutrino anomalies. We find that there are two possible attractive channels in the resulting effective 4-Fermi theory which lead to a neutrino condensation in cosmic neutrinos and the creation of a neutrino superfluid at low temperatures and finite chemical potential. We find that at the minimum of the effective potential V the condensates are mostly made up of pairs of left-left + right-right composites, with a tiny admixture of left-right + right-left composites which differs from the scenario of Kapusta which focused on the energetically unfavored left-right + right-left scenario. We obtain an approximate equation for the gap Δ 2 = 4 m H ( μ - m ) Exp [ - π 2 G eff μ μ 2 - m 2 ] , where m H is the mass of the Higgs scalar, and G eff is the effective (renormalized) 4- Fermi interaction. Recent constraints on cosmological neutrinos suggest the possibility that log 10 ( G eff MeV 2 ) = - 1.72 which would lead to an exponentially small gap.