Vacuum oscillations of solar neutrinos: correlation between spectrum distortion and seasonal variations

Long length vacuum oscillations solution of the solar neutrino problem is discussed. We show that there is a strict correlation between a distortion of the neutrino energy spectrum and an amplitude of seasonal variations of the neutrino flux. The slope parameter which characterizes a distortion of the recoil electron energy spectrum in the Super-Kamiokande experiment and the seasonal asymmetry of the flux have been calculated in a wide range of oscillation parameters. The correlation of the slope and asymmetry gives crucial criteria for identification or exclusion of this solution. Long length vacuum oscillations of neutrinos on the way from the Sun to the Earth [1, 2, 3, 4, 5] allow one to solve the solar neutrino problem (see [6, 7, 8] for latest analysis) . There are two key signatures of this solution. (i). Distortion of the neutrino energy spectrum [5]: A variety of distortions of the boron neutrino spectrum is expected depending on values of the neutrino mass squared difference ∆m ≡ m22 −m 2 1 and mixing angle θ. (ii). Seasonal variations of the fluxes: Due to ellipticity of the Earth’s orbit the variations are expected both due to the geometrical factor, 1/R, and due to change of the probability [3, 5]. Depending on values of oscillation parameters ∆m ≡ m22 −m 2 1 and sin 2 2θ one may get an enhancement or damping of the geometrical effect [10] or even more complicated variations of signals. In this Letter we point out that there is a strict correlation between a distortion of the boron neutrino energy spectrum and seasonal variations of the boron neutrino flux. This gives crucial criteria for identification or discrimination of vacuum oscillations solution. The flux of neutrinos at the Earth, F , can be written as F = F0 ( L0 L )2 · P (L,E), (1) where F0 is the flux at the astronomical unit L0, L is the distance between the Sun and the Earth at a given moment t: L ≈ L0 ( 1 + ǫ cos 2πt T −1 , (2) ǫ = 0.00167 is the eccentricity, T ≡ 1 year, P is the oscillation survival probability: P = 1− sin 2θ sin (