Elsevier

Nuclear Physics B

Volume 726, Issues 1–2, 17 October 2005, Pages 294-316
Nuclear Physics B

Implications of neutrino data circa 2005

https://doi.org/10.1016/j.nuclphysb.2005.07.031Get rights and content

Abstract

Adopting the 3 neutrino framework, we present an updated determination of the oscillation parameters. We perform a global analysis and offer simple arguments that give essentially the same result. We also discuss determinations of solar neutrino fluxes, capabilities of future experiments, tests of CPT, implications for neutrino-less double-β decay, β decay, cosmology.

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, L=LSM+12(νmν+h.c.),m=Vdiag(m1,m2e2iα,m3e2iβ)V. For normal mass hierarchy we order the neutrino masses m1,2,30 as m1<m2<m3, whereas for inverted mass hierarchy we choose m3<m1<m2. The neutrino mixing matrix is V=R23(θ23)diag(1,eiϕ,1)R13(θ13)R12(θ12). 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 θ12,θ23,Δm122 and |Δm232| where Δmij2mj2mi2. 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 χ2 functions. Correlations among parameters are ignored because negligible, with the exception that the upper bound on θ13 that depends on |Δm232| (and mildly on θ12, see Section 2.3). While θ12 is rather precisely measured, the other 2 mixing angles have large uncertainties. Planned long-baseline oscillation experiments can strongly improve on Δm232 and (if θ131°) measure θ13, 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 mνe2(mm)ee=i|Vei2|mi2; neutrino-less double-beta decay (0ν2β) experiments, that probe the absolute value of the Majorana mass meeiVei2mi; cosmological observations (large scale structures and anisotropies in the cosmic microwave background), that in good approximation probe mcosmoΩνh2(93.5eV)=imi. Only neutrinoless double beta decay (0ν2β) probes the Majorana nature of the mass. The values |mee|,mνe,mcosmo 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 |mee|,mνe,mcosmo 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 Δm122 and θ12 and give a sub-dominant constraint on θ13. 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 Δm232, θ23 and θ13, 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 0ν2β. We conclude by commenting on the recent claim of evidence for this transition [13], [14].

We assume the 3 neutrino framework because it is plausible, well defined, restrictive and compatible with data. However it is just an assumption, and before proceeding we recall some alternatives. The most plausible one is the presence of extra light fermions (‘sterile neutrinos’) or bosons, which can manifest in many ways. Going to rather exotic scenarios, Lorentz or CPT invariance (here studied in Fig. 3) might be violated in neutrinos, that might have anomalous interactions (gauge couplings, or magnetic moments, or else), might not obey the Pauli principle, etc. Present solar and atmospheric data cannot be explained by these alternatives, which however might be present as sub-leading effects on top of oscillations among active neutrinos, such that our determinations of active oscillation parameters would need model-dependent modifications. The present data do not give any clear indication for extra effects, but contain some anomalous hints. Most notably, the LSND anomaly [15] is not compatible with the 3 neutrino context we assume.

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 |Δm232| nor θ23 (see Table 1 or Fig. 1), give an upper bound on θ13 and do not determine the sign of Δm232 (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 Δm232, θ23 and θ13, 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, 0ν2β and finally β decay. Ordering them according to reliability would presumably result into the reverse list: cosmological results are based on untested assumptions, and 0ν2β 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 Δm122,θ12,θ23 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.,

References (50)

  • Phys. Rev. D

    (2001)
  • S. Goswami et al.

    Nucl. Phys. B (Proc. Suppl.)

    (2005)
    B.S. Koranga et al.G.L. Fogli

    Phys. Rev. D

    (2002)
  • J.N. Bahcall et al.

    Phys. Rev. Lett.

    (2003)
  • F. Feruglio et al.

    Nucl. Phys. B

    (2002)
    F. Feruglio et al.

    Nucl. Phys. B

    (2003)
  • C.L. BennettD.N. SpergelA. Lewis et al.

    Phys. Rev. D

    (2002)
    S. Hannestad

    JCAP

    (2003)
    S.W. Allen et al.

    Mon. Not. R. Astron. Soc.

    (2003)
    M. Tegmark

    Phys. Rev. D

    (2004)
    V. Barger

    Phys. Lett. B

    (2004)
    P. Crotty et al.

    Phys. Rev. D

    (2004)
    U. SeljakG.L. Fogli

    Phys. Rev. D

    (2004)
  • Phys. Lett. B

    (1999)
    The latest results have been presented in a talk by V. Lobashev at the XI International Workshop on Neutrino...
  • E. Caurier

    Phys. Rev. Lett.

    (1996)
  • V.A. Rodin

    Phys. Rev. C

    (2003)
  • J. Engel

    Phys. Rev. C

    (1988)
  • C.E. Aalseth

    Mod. Phys. Lett. A

    (2002)
  • B.T. Cleveland

    Astrophys. J.

    (1998)
  • Phys. Lett. B

    (1999)
  • J. Exp. Theor. Phys.

    (2002)
  • Phys. Lett. B

    (2003)
  • K. Scholberg, Talk at the WIN05 Conference, Delphi,...
  • H.V. Klapdor-Kleingrothaus et al.

    Mod. Phys. Lett. A

    (2001)
  • H.V. Klapdor-Kleingrothaus et al.

    Nucl. Instrum. Methods A

    (2004)
  • A. Strumia et al.

    JHEP

    (2001)
  • Cited by (136)

    • Double beta decay experiments: Past and present achievements

      2011, Nuclear Physics B - Proceedings Supplements
    • Neutrino-less double beta decay and particle physics

      2011, International Journal of Modern Physics E
    View all citing articles on Scopus
    View full text