Leptonic Photon and Light Element Abundancies

In the framework of a model, in which a single leptonic photon γl has the same coupling to the doublets μνμ and τ̄ ν̄τ , there is no cosmological bound on the strength of this coupling. A few papers devoted to hypothetical leptonic photons have appeared recently [1, 2, 3, 4] (for the first discussion of leptonic photons see ref. [5] for that of baryonic photons – ref. [6]). In particular in ref. [1] an anomaly-free model was suggested in which a single leptonic photon γl had the same coupling to the doublets μνμ and ν̄τ τ̄ and was decoupled from eνe. In this note we will consider this model from the point o f view of cosmology. The cosmological limit set by the theory of nucleosynthesis and the present data on abundancies of light elements allows the existence in equilibrium at T ∼ 1 MeV of only one new light particle with two degrees of freedom [7, 8, 9] in addition to three left-handed neutrinos (νe, νμ, ντ ), their right-handed antineutrinos and the ordinary photon (for the first estimates see [10, 11]). In the framework of our model the Dirac masses of mu onic and tauonic neutrinos are forbidden if the leptonic photon coupling is strong enough (αμ ≡ ατ ≡ αe > 10 ). This follows from considerations of ref. [4]. Due to strict conservation of muonic and tauonic charges the right-handed νμ and ντ and the left-handed ν̄μ and ν̄τ must have the same strength of the coupling with γl, as the ordinary left-handed νμ and ντ and right-handed ν̄μ and ν̄τ . As a result all these neutrinos would be in thermal equilibrium at the moment of nucleosynthesis and there would exist 3 extra particles with two degrees of freedom each, while the cosmological limit allows only one such particle. Thus the νμ and ντ must be either two-component and hence massless or have a common non-diagonal Majorana mass of ZKM type [12, 13]. In the former case the theory would be plagued by infrared divergence s, which however are not so damaging, as to make it non-viable. In the latter case a τ lepton may be produced by an originally clean νμ-beam, but the probability of such event would be negligibly small for small values of the mass. If further progress in understanding the nucleosynthesis excludes the existence of any extra light particle in equilibrium at T ∼ 1 MeV, then the leptonic photon γl is allowed to come into equilibrium with other light particles only at T < 1 MeV. This would set an upper limit on the leptonic fine structure constant αl ≡ ατ ≡ αμ. By comparing the rate of reactions νμν̄μ ↔ γlγl, ντ ν̄τ ↔ γlγl, proportional to α 2 l T , with the Hubble expansion rate, proportional to T /Mpl, at T < 1 MeV, as was done in ref. [4], one would get, αl < ∼ 10 . But with the present data on the abundancies of light elements there is no cosmological limit on αl in the framework of the model under discussion. As already mentioned elsewhere [1, 5], the present experimental upper limit on αμ is 10 α. It may be improved by an order of magnitude [14] by analyzing the data of high energy neutrino experiments. Note that if the model under discussion is correct, there should be no νμ