Implications of neutrino data circa 2005
Introduction
The most plausible extension of the Standard Model that allows to interpret a wealth of neutrino data [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] consists in adding a Majorana mass term for neutrinos, For normal mass hierarchy we order the neutrino masses as , whereas for inverted mass hierarchy we choose . The neutrino mixing matrix is A similar result holds in the case of Dirac masses, with the difference that the number of physical parameters decreases from 9 to 7: the Majorana phases α and β can be reabsorbed by field redefinitions.
Data on neutrino oscillations fix and where . As discussed later (Sections 2 Oscillations with solar frequency, 3 Oscillations with atmospheric frequency) our present knowledge of oscillation parameters is approximatively summarized in the upper rows of Table 1. The uncertainties are almost Gaussian in the chosen variables; Fig. 1 shows the full functions. Correlations among parameters are ignored because negligible, with the exception that the upper bound on that depends on (and mildly on , see Section 2.3). While is rather precisely measured, the other 2 mixing angles have large uncertainties. Planned long-baseline oscillation experiments can strongly improve on and (if ) measure , the phase ϕ, and determine which type of mass hierarchy is realized in nature.
Oscillation experiments, however, are insensitive to the absolute neutrino mass scale (say, the mass of the lightest neutrino) and to the 2 Majorana phases α and β. Other types of experiments can study some of these quantities and the nature of neutrino masses. They are: β-decay experiments, that in good approximation probe ; neutrino-less double-beta decay () experiments, that probe the absolute value of the Majorana mass ; cosmological observations (large scale structures and anisotropies in the cosmic microwave background), that in good approximation probe . Only neutrinoless double beta decay () probes the Majorana nature of the mass. The values are unknown, but can be partially inferred from oscillation data. Table 1 shows our results, discussed in Section 4, in the limit where the mass of the lightest neutrino is negligible. In the opposite limit neutrinos are quasi-degenerate and can be arbitrarily large.
From the point of view of 3 massive neutrinos, it is natural to divide in three parts a discussion of the present situation and of the perspectives of improvements, namely:
- 1.
Oscillations with ‘solar’ frequency, that tell and and give a sub-dominant constraint on . In Section 2 we discuss solar and reactor neutrino experiments, showing that the program of measurement of parameters is well under way (if not accomplished), and discussing other interesting related goals.
- 2.
Oscillations with ‘atmospheric’ frequency, that tell , and , are discussed in Section 3.
- 3.
Non-oscillation experiments, that can tell the absolute neutrino mass. In Section 4 we discuss the present status and assess the implications of the existing information on neutrino oscillations for these experiments, particularly for . We conclude by commenting on the recent claim of evidence for this transition [13], [14].
Section snippets
Oscillations with solar frequency
A few years ago the solar anomaly rested on global fits that combined solar model predictions with a few measurements of solar neutrino rates. In recent times, the situation changed. As prospected in [16] (written a few years ago, while sub-MeV solar experiments were discussed as a tool for discriminating LMA from LOW, SMA, QVO, …), SNO, KamLAND, Borexino had in any case the capability to identify the true solution of the solar anomaly and make precision measurements of the oscillation
Oscillations with atmospheric frequency
Present data do not precisely determine nor (see Table 1 or Fig. 1), give an upper bound on and do not determine the sign of (i.e., if neutrinos have ‘normal’ or ‘inverted’ mass hierarchy). Several experimental programs using long-baseline and reactor neutrinos plan to confirm the SK evidence and to improve on , and , possibly measuring a non-zero value of the latter angle. From the point of view of the 3 neutrino framework these experimental programs seem
Non-oscillation experiments
In this section we discuss non-oscillation experiments and consider the 3 non-oscillation parameters mentioned in the introduction. Making reference to experimental sensitivities, the 3 probes should be ordered as follows: cosmology, and finally β decay. Ordering them according to reliability would presumably result into the reverse list: cosmological results are based on untested assumptions, and suffers from severe uncertainties in the nuclear matrix elements. Even more, there is an
Conclusions
Assuming oscillations of three active massive neutrinos we updated the determination of the oscillations parameters, at the light of latest experimental data. Results are shown in Table 1 and in Fig. 1. We notice that the parameters are now dominantly determined by simple and robust sub-sets of data, such that simple arguments give the same final result as global analyses. Pieces of data that play a sub-dominant role in parameter determination allow to test our assumptions: e.g.,
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