Electron-neutrino survival probability from solar-neutrino data

With SNO data on electron-neutrino flux from the sun, it is possible to derive the $\nu_e$ survival probability $P_{ee}(E)$ from existing experimental data of Super-Kamiokande, gallium experiments and Homestake. The combined data of SNO and Super-Kamiokande provide boron $\nu_e$ flux and the total flux of all active boron neutrinos, giving thus $P_{ee}(E)$ for boron neutrinos. The Homestake detector, after subtraction of the signal from boron neutrinos, gives the flux of Be+CNO neutrinos, and $P_{ee}$ for the corresponding energy interval, if the produced flux is taken from the Standard Solar Model (SSM). Gallium detectors, GALLEX, SAGE and GNO, detect additionally pp-neutrinos. The pp-flux can be calculated subtracting from the gallium signal the rate due to boron, beryllium and CNO neutrinos. The ratio of the measured $pp$-neutrino flux to that predicted by the SSM gives the survival probability for $pp$-neutrinos. Comparison with theoretical survival probabilities shows that the best (among known models) fit is given by LMA and LOW solutions.


1
The recent measurement of boron ν e flux by SNO [1], combined with Super-Kamiokande data [2], gives strong evidence for neutrino oscillations [1]. It is based on the fact that the ν e flux measured by SNO through the charged current (CC) interaction ν e +d → e+p+p induces in the Super-Kamiokande detector less electrons than observed. The excess of the electrons can be produced only by active neutrinos of other flavors: ν µ and ν τ . This flux of active neutrinos is thus determined and found to be 3.3σ above the zero value. Such analysis was suggested earlier in Ref. [3], and recently it was further developed in Ref. [4] (for other recent analysis of SNO data see [5,6]).
In this Letter we shall demonstrate that the new results obtained by SNO allow us to derive the survival probability for boron, beryllium and pp electron neutrinos (for general analysis see [7] and for calculation of survival probability for boron neutrinos [4]).
The probability of electron neutrinos to survive on the way from the production point inside the Sun to the detection site on the Earth is referred to as survival probability, P ee . In case of oscillations, 1 − P ee is the probability of electron-neutrino conversion into neutrinos of other flavors.
Note that this derivation of P ee does not depend on the SSM flux. The partial oscillation to sterile neutrinos, ν e → ν s , diminishes further P ee . This possibility is somewhat disfavored by the observation that Φ tot is close to prediction of the SSM [1].
The error in the value of P ee indicated above is calculated by adding all errors in quadrature and it needs further discussion. The uncertainties of Φ νe and Φ tot are correlated 2 and therefore the usual interpretation of the indicated error is allowed only in the limit Φ νe ≪ Φ tot . In fact, the 2σ-and 3σ-equivalent intervals are asymmetric and greater than 1σ error 0.065 multiplied by factor of 2 and 3, respectively. In particular it can be shown that 1 − P ee interval has real 3.3σ deflection from zero value.
The value of P ee is plotted in Figs. 1-3. The calculated value refers to the whole energy interval of boron neutrinos measured in Super-Kamiokande: in Figs.1-3 the horizontal error bars show the width of this interval. The value of P ee is plotted in the middle of this interval and looks asymmetric in logarithmic scale. As already mentioned above, one should not interpret the many standard deviations which separates P ee from unity in the usual way: the probability that P ee = 1 corresponds to about 3.3σ and not to ≈ 10σ as it might appear from the figure.
The Homestake detector is sensitive to the boron, beryllium and CNO ν e -neutrinos.
Subtracting the contribution of the measured flux of boron ν e -neutrinos with the standard spectrum to the chlorine detector, we determine the contribution of Be+CNO neutrinos to the signal. For the production fluxes we use that of the SSM [8]: note that the prediction for the Be neutrino flux is reliable and the contribution of CNO neutrinos is small. In  MeV) is valid also for the lower part of the boron-neutrino spectrum. Since in both cases only electron neutrinos produce the signal, the extracted survival probability is not affected by oscillation to sterile neutrinos.
In Fig. 1 the observed survival probabilities are compared with the predictions of the LMA MSW, LOW MSW and Gribov-Pontecorvo (GP) [9] solutions. For LMA we use one of the best fit solutions from Ref. [10]: ∆m 2 = 3.7 × 10 −5 eV 2 and sin 2 2θ = 0.79; for LOW: ∆m 2 = 1.0 × 10 −7 eV 2 , and sin 2 2θ = 0.97 [10], and for the Gribov-Pontecorvo solution [9] sin 2 2θ = 1. The LMA and LOW survival probabilities shown are not averaged over the production points in the sun. The LOW curve is practically independent of the production point. The LMA solid curve is shown for a production point in the boron/beryllium production zone and the dashed curve shows the survival probability for a neutrino produced at the peak of the pp region. Averaging over the production region gives a curve close to the solid one for boron and beryllium neutrinos, and a curve between the solid and dashed one for pp neutrinos (in fact there is little difference between these curves in the energy region of pp neutrinos).
Only for illustration, we present χ 2 /d.o.f. values for the fits of the data by different oscillation solutions: they are 4/3, 5/3 and 10/3 for the LMA, LOW and GP solutions, respectively.
In fact, this χ 2 analysis could be misleading because when the survival probability is used as a variable, the probability distribution is not Gaussian.
In Fig. 2  In principle the survival probabilities for boron neutrinos can be given for several energy bins. Since the observed spectrum is well described by the SSM spectrum, the energy bin analysis will further decrease the probability of SMA MSW, which produces a significant spectrum distortion in the boron energy window, and will favour the solutions with a flat suppression of boron neutrino spectrum, such as the GP, LMA and LOW solutions. Daynight dependence will not change the analysis in a significant way, since these solutions have little day-night dependence in the boron high-energy window. In