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Solar neutrinos [70]

The Solar neutrinos gave the first convincing evidence for neutrino mass and mixing. Bahcall reviewed [71] the status of the standard solar model (SSM), emphasizing that ``Solar model predictions have been robust for 30 years.''

Ferrari [74] described the results of Run I of the Gallium Neutrino Observatory (GNO). They obtain a rate of $65.8^{+10.2+3.4}_{-\ 9.6-3.6}$ SNU, consistent with the earlier GALLEX and SAGE results, and about half of the SSM prediction.

Suzuki [35] presented new solar neutrino results for Superkamiokande:

Suzuki presented the SuperK oscillation analysis (including the rates from other experiments). He argued that there is no smoking gun for one solution over another. However, the data favors the LMA solution; the SMA solution is disfavored but not excluded; vacuum solutions are disfavored; and the pure $\nu_e \mbox{$\rightarrow$}\nu_s$ is disfavored at 95%, by a combination of day-night, spectrum, and rate information. (A significant admixture of $\nu_s$ is still allowed in 3$\nu$ fits [36], especially for small mixing angles.)

Smirnov [24] discussed the various solar neutrino solutions, commenting that ``Nature selects the most ambiguous solution'', i.e., no solution is strongly excluded or preferred, and hints are at the level of systematics. He argued that the LMA is favored, but SMA may be back. Smirnov described that the SuperK zenith spectrum has a small excess in the first night-time bin, contrary to any of the solutions (LMA is flat at night, LOW may yield an excess in the second bin, and SMA may imply an excess in the last (core) bin), adding to the confusion. He argued the importance of studying the correlations between various observables (e.g., charged current rate vs. day-night) for distinguishing solutions in the future.

A number of global analyses of the solar data were presented at the conference or in the recent literature [18,24,35,36], allowing mixing between 2, 3, or 4 neutrinos, including sterile. The 2$\nu$ solutions are shown schematically in Figure [*]. The small mixing angle (SMA) solution, with $\mbox{$\Delta m^2$}\mathrel{\mathpalette\lower2.pt\vbox{\baselineskip0pt \lines...
...
\ialign{$\mathsurround=0pt ;\hfil ... eV$^2$ and $10^{-3} < \mbox{$\sin^2 2 \theta$}< 10^{-2}$, is most analogous to the (small) quark mixings. The large mixing angle (LMA) and low mass (LOW) solutions, with $\mbox{$\Delta m^2$}\sim (10^{-5}-10^{-4})$ and $10^{-7}$ eV$^2$, respectively, are close to the vacuum solutions ( $\mbox{$\sin^2 2 \theta$}= 1$). Regeneration in the earth is important in these solutions. The original vacuum (VAC) solutions with $\mbox{$\Delta m^2$}\sim 10^{-10}$ eV$^2$ involved an accidental coincidence between the Earth-Sun distance and the vacuum oscillation length, and therefore predicted large energy and seasonal variations that are now mainly excluded. Matter effects are starting to be relevant in the transition or quasi-vacuum region [75], ( $10^{-10} - 10^{-7}$ eV$^2$). There is a SMA solution for transitions to sterile neutrinos, but no viable analogs of the other regions. The major difference compared with active neutrinos is the absence of a neutral current component to $\nu_e e \mbox{$\rightarrow$}\mbox{$\nu_e$}e$ in Kamiokande and Superkamiokande. There is a smaller effect from the small neutron density in the Sun.

All of the analyses, which had slightly different inputs, favor the LMA solution, with the SMA, LOW, vacuum, and pure sterile (with parameters in the SMA range) solutions disfavored to various extents, depending on the analysis. One of the differences was in the simultaneous application of the SuperK spectrum and zenith angle distributions. The full two-dimensional distribution with correlations has never been presented, so each analysis has either used separate distributions (which double counts the same data), or ignored some of the data. Another problem or source of ambiguity is the statistical treatment of non-Gaussian effects, such as the allowed regions of parameters when there are multiple minima.

Many of the recent studies have used $\tan^2 \theta$ rather than $\sin^2 2 \theta$ as the mixing parameter. Allowing $\tan^2 \theta > 1$ includes the second octant $\pi/4 < \theta \le \pi/2$. This ``dark side'' [76] was usually ignored in past studies, which assumed implicitly that $0 \le \theta \le \pi/4$ and $\Delta m^2$$>$ 0. (The second octant solutions correspond to exchanging $\nu_e$ and the second neutrino, i.e., they are equivalent to restricting $\theta \le \pi/4$ but allowing $\Delta m^2$$<0$.) The effect is mainly important for the LOW solutions, which extend well into the dark side [36]. However, LMA does also at high confidence level. Vacuum solutions do not depend on the sign of $\Delta m^2$, so they are mirror-symmetric.

There are many future experiments underway or proposed:

The theoretical and experimental situation for the solar neutrinos has become very mature. Refined and multiple experiments are needed to simultaneously determine the neutrino solutions (especially if nature chooses a complicated scenario, e.g., with 3 relevant neutrinos) and constrain the astrophysics. As we enter into a ``precision'' phase with several high statistics experiments with multiple observables, it is important that the data be presented and analyzed in a manner that allows us to extract the maximum and most reliable conclusions. In particular, it is important for each group to publish all of their data with fully correlated errors (e.g., the spectral and zenith data should be presented as a two-dimensional distribution). Similarly, to ensure an optimal treatment of common sytematics and theory uncertainties, it would be useful for the experiments to perform combined analyses, analogous to the highly successful LEP Electroweak Working Group.


next up previous
Next: Atmospheric neutrinos [,] Up: LOW ENERGY NEUTRINOS Previous: LOW ENERGY NEUTRINOS
Paul Langacker 2001-09-27