2 v 1 2 9 M ar 1 99 8 On mixing angles and magnetic moment of heavy tau

If the magnetic moment of unstable tau neutrinos with the mass of O(MeV) is in the region of 10 −8 µ B µ ντ 10 −6 µ B , it is compatible with the present experimental and cosmological bounds. It is pointed out here, that if the tau neutrino has such a large magnetic moment and can oscillate into a neutrino of another flavour the results from νe scattering experiment at LAMPF constrain the tau neutrino mixing angles to sin 2 2θ eτ 2 × 10 −6 − 2 × 10 −2 and sin 2 2θ µτ 10 −6 − 10 −2 depending on the magnetic moment value in the allowed region. In many extensions of the standard model the neutrino acquire a nonzero mass and a magnetic moment (for review see e.g. [1]). Usually large magnetic moment imply large masses. In the simplest extension, for example, neutrino masses and magnetic moment are proportional [2, 3]. A nonzero mass of the neutrino is also required for Cosmology to solve the problem of dark matter in the Universe. It is generally assumed that massive tau neutrinos are natural candidates for the hot component of the dark matter of the Universe, see e.g. ref. [4]. But they cannot provide an explanation for a cold dark matter, because of constraints from relic abundance. However, as was proposed by Giudice [5], a stable (or quasi-stable in cosmological times) tau neutrino with a mass in the range from ≃1 MeV up to the present experimental upper limit of 25 MeV and a magnetic moment µ ντ as large as ≃ 10 −6 Bohr magneton (µ B = e/2m e) could be a possible candidate for a cold dark matter particle. Experimental limit from BEBC (CERN), µ ντ < 5.4 × 10 −7 µ B [6], and revised calculations of the evolution and freeze-out of the tau neutrino number density, ref. [7], definitely rule out Giudice's hypothesis. However, it was pointed out, that if the tau neutrino is an unstable particle with the lifetime exceeding one second, a band of magnetic moment values 10 −8 µ B µ ντ 10 −6 µ B (1) remains compatible with experimental and cosmological bounds [7]. In this case, if the magnetic moment of ν τ exists, massive tau neutrinos could manifest themselves in terrestrial experiments through the effect of ν µ (ν e) → ν τ