X iv : h ep - p h / 02 02 09 7 v 1 1 1 Fe b 20 02 Can radiative correction cause large neutrino mixing ?

We investigate whether radiative corrections can be responsible for the generation of large mixing in a pair of degenerate neutrino with same CP parity. We find that this mechanism is fine tuned and doesn’t work for arbitrary mixing at the high scale. The data from the solar neutrino and the atmospheric neutrino experiments can be explained through flavor oscillations of massive neutrinos. The favoured solution of both these problems are a pair of neutrinos with very small mass squared difference and large mixing [1,2]. The mass square difference required for the solar neutrino oscillation is less than 10eV 2 while for the atmospheric neutrinos it is 10eV . If neutrinos form the hot Dark Matter then the masses of all the neutrinos have to be of the order of 1eV. This, along with the very small mass square differences suggests that neutrino mass spectrum is almost degenerate. If neutrinos have Majorana mass, then one can have a pair of degenerate neutrinos with opposite CP parities. These are called Pseudo Dirac neutrinos. The mixing between such pairs can be shown to be maximal [3]. The smallness of neutrino mass can be obtained through the seesaw mechanism [4] in which neutrinos can have both Dirac and Majorana masses. Even in this mechanism Pseudo Dirac neutrinos with maximal mixing are possible for a suitable choice of the structure of right handed Majorana mass matrix [5]. While these models can generate only one maximal mixing in 3 generation scenario, the solar neutrino problem and the atmospheric neutrino problem requires two pairs with maximal mixing. Another problem is that for degenerate Majorana neutrinos, large mixing may not be stable under small radiative corrections. A pair of Majorana neutrinos with opposite CP parities is stable but for a pair with same CP parity large mixing collapse to 0 due to radiative correction [6]. Some authors [7–9] suggested that the same instability can cause large mixing at the low scale from an arbitrary mixing at the high scale. This mechanism is similar to the MSW mechanism where the mixing angle gets enhanced at the resonance. As this requires the present scale of the universe to be at the ‘resonance’ as far as neutrino mixing is concerned, this is a fine tuned solution. This is because 0 mixing is a fixed point of the renormalisation group evolution of neutrino masses and mixing whereas maximal mixing is not [10]. We investigate whether such a mechanism can be at work to