Solar neutrino oscillations

The probability of u2 —> u, transition relevant for the solar neutrino oscillations in the Earth can be obtained immediately from the unitarily condition ... 

Neutrino oscillations in the weak matter effect regime have been discussed extensively before [1-13], in particular, for the solar and supemovae neutrinos propagating in the matter of the Earth. The previous work has been done mainly in the approximation of constant density profile which consists of several layers with constant density. 

The solution to the solar neutrino problem is that something is wrong with our ideas of the fundamental structure of matter, the so-called standard model. This difficulty takes the form of neutrino oscillations as the solution to the solar neutrino... 

Solar neutrinos, produced in the nuclear reactions that make the Sun shine, also show oscillations Ahmad et al.(2002),... 

Whatever the outcome, great repercussions on science resultfrom the solar neutrino problem. The implications may be for our Sun, or for the nature of neutrinos, or both. Recent evidence is convincing that the problem is in the nature of the neutrino itself namely, that during transit it spontaneously transforms (oscillates) to a neutrino of different flavor, and to which the detector is insensitive. This is possible because of the small rest mass of neutrinos. 

Detectors using gallium > 0.2 MeV), chlorine (Ej/ 0.8 MeV), and Cerenkov effect in water > 7 MeV) measure significantly lower neutrino rates than are predicted from solar models. The deficit in the solar neutrino flux compared with solar model calculations could be explained by oscillations with Am < 10 eV causing the disappearance of Pq. 

The results from the astroneutrino experiments in Tables V and VI are consistent with different numerical descriptions of neutrino oscillations. One finds solutions in which Am is of the order of 10 eV from two MSW solutions and 10 eV from the so-called solar neutrino vacuum oscillation solution, nominally representing a Ve -o- oscillation. A fourth solution yields 10 eV ... 

There is reason to believe that the above properties reflect the major neutrino oscillation channels, although only one of the three solar neutrino solutions will ultimately turn out to be valid. Neutrino searches for oscillations at nuclear reactors in France, in southern California in the United States, and in Japan, all past or near the data-taking stage, will ultimately help clarify the choice of solutions. More importantly, at least one of those experiments or the experiments discussed below may provide a conclusive demonstration that the astroneutrino data is correctly interpreted by the neutrino oscillation explanation. 

Abstract For the case of small matter effects V perturbation theory using e = 2V E/ Am2 as the expansion parameter. We derive simple and physically transparent formulas for the oscillation probabilities in the lowest order in e which are valid for an arbitrary density profile. They can be applied for the solar and supernova neutrinos propagating in matter of the Earth. Using these formulas we study features of averaging of the oscillation effects over the neutrino energy. Sensitivity of these effects to remote (from a detector), d > PE/AE, structures of the density profile is suppressed. 

For the LMA parameters the oscillations of solar and supernova (low energy) neutrinos inside the Earth occur in the vacuum (kinetic) energy dominating regime. This means that the matter potential V is much smaller than the kinetic energy of the neutrino system ... 

But quantitatively there is a disagreement between measurement and theory. The neutrinos actually caught in our traps are two or three times less numerous than the theory says they ought to be (Table 5.1). Naturally, this discrepancy is a challenge to the physicist. It does not seem to arise from any problem with the solar model itself, now that the Sun has been probed by its mechanical oscillations. 

The theoretical forecasts of the neutrino fluxes used to compare with experimental observations are those from the so-called standard solar model (SSM). This model relies on the values of the solar mass, radius, luminosity, and age (4.7 billion years) and on the best-considered values of the nuclear reaction cross sections. In addition, there are some special assumptions. It is presumed that the sun is not rotating, or differentially rotating, rapidly enough in its interior to affect its internal structure or dynamics. Processes that could mix the solar interior, such as diffusion or periodic hydrodynamic oscillation, are not taken into... 

---