Texture of a Four–Neutrino Mass Matrix

We propose a simple texture of the neutrino mass matrix with one sterile neutrino along with the three standard ones. It gives maximal mixing angles for νe → νS and νμ → ντ oscillations or vice versa. Thus with only four parameters, this mass matrix can explain the solar neutrino anomaly, atmospheric neutrino anomaly, LSND result and the hot dark matter of the universe, while satisfying all other Laboratory constraints. Depending on the choice of parameters, one can get the vacuum oscillation or the large angle MSW solution of the solar neutrino anomaly. Recently the super-Kamiokande experiment has confirmed the atmospheric neutrino oscillation result, suggesting nearly maximal mixing of νμ with another species of neutrino [1]. The same experiment has also confirmed the solar neutrino oscillation result, which suggests mixing of νe with another species of neutrino [2]. Moreover, the energy spectrum of the recoil electron seems to favour the large mixing-angle vacuum oscillation of νe over the MSW solutions [2], although this may have limited statistical significance in the global fit to the solar neutrino data [3, 4]. They have led to a flurry of phenomenological models for neutrino mass and mixing which can account for these oscillations [5-8], most of which are focussed on the bi-maximal mixing angles for the atmospheric and the solar neutrinos. However, almost all of these works are based on the three-neutrino formalism, involving the standard left handed neutrinos νe, νμ and ντ [5]. On the other hand the inclusion of the LSND neutrino oscillation result [9] is known to require a fourth neutrino, which has to be a sterile one (νS) for consistency with the observed Z–width [10]. Moreover it requires either νμ or νe to oscillate into νS for explaining the atmospheric and solar neutrino anomalies, while requiring νμ → νe oscillation for the LSND result. Thus the three-neutrino models for atmospheric and solar neutrino anomalies, based on a νe−νμ−ντ mixing, are in direct conflict with the LSND result. While the LSND result has not been corroborated by the preliminary KARMEN data [11], the statistical significance of the latter is limited by its lower sensitivity in the relevant region of parameter space. Indeed, with the standard statistical method the 90 % c.l. limit of KARMEN excludes only half the parameter space of the LSND data in the ∆m ≤ 2eV 2 region [12]. Hopefully, this issue will be resolved by the proposed mini-BOONE experiment at Fermilab along with more data from KARMEN. It seems to us premature, however, to rule out the LSND result at present. Therefore we have tried to construct a four-neutrino mass matrix, which can account for the present solar and atmospheric neutrino data along with the LSND result. It can also account for the hot dark matter content of the universe [13], while satisfying all laboratory and astrophysical constraints [14, 15, 16]. Table 1 summarises the experimental constraints on neutrino mass and mixing parameters, which are relevant for our model. The large angle MSW and the vacuum oscillation solutions to the solar neutrino data [2, 17, 18] are taken from a recent fit to the νe suppression rates along with the recoil electron spectrum by Bahcall, Krastev and Smirnov [3]. For both the solutions the fit favours the oscillation of νe into a doublet neutrino over νe → νS. The reason is that in the former case the NC scattering of this doublet neutrino