%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    INSTITUTE OF PHYSICS PUBLISHING                                   %
%                                                                      %
%   `Preparing an article for publication in an Institute of Physics   %
%    Publishing journal using LaTeX'                                   %
%                                                                      %
%    LaTeX source code `ioplau2e.tex' used to generate `author         %
%    guidelines', the documentation explaining and demonstrating use   %
%    of the Institute of Physics Publishing LaTeX preprint files       %
%    `iopart.cls, iopart12.clo and iopart10.clo'.                      %
%                                                                      %
%    `ioplau2e.tex' itself uses LaTeX with `iopart.cls'                %
%                                                                      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% First we have a character check
%
% ! exclamation mark    " double quote  
% # hash                ` opening quote (grave)
% & ampersand           ' closing quote (acute)
% $ dollar              % percent       
% ( open parenthesis    ) close paren.  
% - hyphen              = equals sign
% | vertical bar        ~ tilde         
% @ at sign             _ underscore
% { open curly brace    } close curly   
% [ open square         ] close square bracket
% + plus sign           ; semi-colon    
% * asterisk            : colon
% < open angle bracket  > close angle   
% , comma               . full stop
% ? question mark       / forward slash 
% \ backslash           ^ circumflex
%
% ABCDEFGHIJKLMNOPQRSTUVWXYZ 
% abcdefghijklmnopqrstuvwxyz 
% 1234567890
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\documentclass{iopart}
\usepackage{epsf,epsfig,graphicx}
%\usepackage[square,comma,sort&compress]{natbib}
% if you have landscape tables
%\usepackage[figuresright]{rotating}
% put your own definitions here:
\usepackage{array}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\def\simlt{\buildrel < \over {_{\sim}}}
\def\simgt{\buildrel > \over {_{\sim}}}
%
\DeclareMathAlphabet{\mathsc}{OT1}{cmr}{m}{sc}
%
\newcommand{\ttbs}{\char'134}
\newcommand{\AmS}{{\protect\the\textfont2
  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
\newcommand{\lesssim}{\raisebox{0.3mm}{\em $\, <$} 
\hspace{-3.3mm} \raisebox{-1.8mm}{\em $\sim \,$}}
\newcommand{\gtrsim}{\raisebox{0.3mm}{\em $\, >$} 
\hspace{-3.3mm} \raisebox{-1.8mm}{\em $\sim \,$}}
% Uncomment next line if AMS fonts required
%\usepackage{iopams}  
\newcommand{\CL}   {C.L.}
\newcommand{\dof}  {d.o.f.}
\newcommand{\EtAl} {{\it et al.\/}}
\newcommand{\eVq}  {\rm{eV}^2}
\newcommand{\Sol}  {\mathsc{sol}}
\newcommand{\Atm}  {\mathsc{atm}}
\newcommand{\JSQ}  {{Just-So$^2$}}

\newcommand{\Dcq}  {\Delta\chi^2}
\newcommand{\Dms}  {\Delta m^2_\Sol}
\newcommand{\Dma}  {\Delta m^2_\Atm}
\newcommand{\Eps}  {\varepsilon}
\newcommand{\Epp}  {\varepsilon'}
%
\newcommand{\AHEP}{Instituto de F\'{\i}sica Corpuscular \\
  C.S.I.C./Universitat de Val{\`e}ncia \\
  Edificio Institutos de Paterna, Apt 22085\\
  E--46071 Val{\`e}ncia, Spain\\}
%
\newcommand{\snocc}{SNO$_\mathrm{CC}^\mathrm{rate}$ }
\newcommand{\snotot}{SNO$_\mathrm{CC,NC}^\mathrm{SP,DN}$ }
%
\def\lsim{\raise0.3ex\hbox{$\;<$\kern-0.75em\raise-1.1ex\hbox{$\sim\;$}}}
\def\gsim{\raise0.3ex\hbox{$\;>$\kern-0.75em\raise-1.1ex\hbox{$\sim\;$}}}
%
\def\e6{$E(6)$}
\def\10{$SO(10)$}
\def\21{$SU(2) \otimes U(1) $}
\def\lr{$SU(2)_L \otimes SU(2)_R \otimes U(1)$}
\def\422{$SU(4) \otimes SU(2) \otimes SU(2)$}
\def\321{$SU(3) \otimes SU(2) \otimes U(1)$}
%
\def\ne{\hbox{$\nu_e$ }}
\def\nm{\hbox{$\nu_\mu$ }}
\def\bne{\hbox{$\bar\nu_e$ }}
\def\bnm{\hbox{$\bar\nu_\mu$ }}
\def\nt{\hbox{$\nu_\tau$ }}
\def\ns{\hbox{$\nu_{s}$ }}
\def\nr{\hbox{$\nu_R$}}
\def\O{\hbox{$\cal O$ }}
\def\L{\hbox{$\cal L$ }}
\def\ed{\end{document}}
\def \nbb {$\beta\beta_{0\nu}$ }
\def\Eb{E_{\rm b}}
\def\Ee{\langle E_{\bar\nu_{\rm e}}\rangle}
\def\Eh{\langle E_{\bar\nu_{\rm h}}\rangle}
\def\VEV#1{\left\langle #1\right\rangle}
\let\vev\VEV
%

% add words to TeX's hyphenation exception list
\hyphenation{author another created financial paper re-commend-ed Post-Script}



\begin{document}

%\title{Probing standard and non-standard neutrino oscillations }
\title{Standard and non-standard neutrino oscillations }

\author{J.~W.~F. Valle\address{\AHEP}}
       %

\begin{abstract}
  I describe recent determination of neutrino oscillation parameters
  from solar and atmospheric data, comparing the results of different
  analyses.  Non-oscillation phenomena such as neutrinoless double
  beta decay in addition to probing the absolute scale of neutrino
  mass, may also reveal its Majorana nature.  I also discuss
  non-oscillation solutions to the solar neutrino problem in terms of
  spin-flavor precession and non-standard neutrino interactions, which
  will be crucially tested at KamLAND.  \vspace{1pc}
\end{abstract}

% typeset front matter (including abstract)
%\maketitle

\section{SOLAR NEUTRINOS}

Solar neutrinos have now been detected with the geochemical method via
the \ne + ${}^{37}$Cl $\to {}^{37}$Ar + $e^-$ reaction at Homestake,
and via the \ne + ${}^{71}$Ga $\to ^{71}$Ge + $e^-$ reaction at the
Gallex, Sage and GNO experiments, as well as directly with Cherenkov
techniques using $\nu_e e$ scattering on water at Super-K, and heavy
water at SNO~\cite{nu2002}. The latter have given a robust
confirmation that the number of solar neutrinos detected in
underground experiments is less than expected from theories of energy
generation in the sun.
%
Altogether these experiments provide a solid evidence for solar
neutrino conversions and, as a result, imply that an extension of the
Standard Model of particle physics in the lepton sector is needed.

Although not yet unique, the most popular explanation of solar
neutrino experiments is provided by the neutrino oscillations
hypothesis.  Present data indicate that the mixing angle is
large~\cite{Maltoni:2002ni}, the best description being given by the
LMA MSW-type~\cite{Wolfenstein:1977ue} solution, already hinted
previously from the flat Super-K recoil electron
spectra~\cite{Gonzalez-Garcia:1999aj,Gonzalez-Garcia:2000sq}.
%
The absence of a clear hint for day-night or seasonal variation
in the solar neutrino signal places important restrictions on neutrino
parameters.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
In ref.~\cite{Maltoni:2002ni} the solar neutrino data, including the
latest 1496--day data and the SNO neutral current (NC) result have
been analysed in the general framework of mixed active-sterile
neutrino oscillations, where the electron neutrino produced in the sun
converts to $\nu_x$ (a combination of $\nu_\mu$ and $\nu_\tau$) and a
sterile neutrino $\nu_s \:$: $ \nu_e \to \sqrt{1-\eta_s}\, \nu_x +
\sqrt{\eta_s}\, \nu_s$.
%
The setting for such scenarios are four-neutrino mass
schemes~\cite{Peltoniemi:1992ss} which try to accommodate the solar
and atmospheric mass-splittings with the hint for short baseline
oscillations from LSND~\cite{LSND} indicating a large $\Delta m^2$.
%
The parameter $\eta_s$ with $0\le \eta_s \le 1$ describes the fraction
of sterile neutrinos taking part in the solar oscillations.

In Fig.~\ref{fig:sol-osc-par} we display the regions of solar neutrino
oscillation parameters for 3 \dof\ with respect to the global
minimum, for the standard case of active oscillations, $\eta_s = 0$,
as well as for $\eta_s = 0.2$ and $\eta_s = 0.5$.
%
The first thing to notice is the impact of the SNO NC, spectral, and
day/night data in improving the determination of the oscillation
parameters: the shaded regions after their inclusion are much smaller
than the hollow regions delimited by the corresponding \snocc\ 
confidence contours. Especially important is the full \snotot\ 
information in closing the LMA region from above: values of $\Dms >
10^{-3}~\eVq$ appear only at $3\sigma$. Previously solar data on their
own could not close the LMA region, only the inclusion of reactor
data~\cite{CHOOZ} probed the upper part of the LMA
region~\cite{Gonzalez-Garcia:2000sq}. Furthermore, the complete
\snotot\ information is important for excluding \texttt{maximal} solar
mixing in the LMA region.  At $3\sigma$ we find (1 \dof):
%
\begin{equation}
\label{t12bound}
    \rm{LMA}\,:\quad 0.26 \le \tan^2\theta_\Sol \le 0.85 \,.
\end{equation}
%
showing that in the LMA region $\tan^2\theta_\Sol$ is significantly
below maximal.

%%%%%%%%%%%%

As discussed in ref.~\cite{Maltoni:2002ni} all groups find that the
best fit lies in the LMA region, although there are quantitative
differences even for this preferred solution, with the GOF of the
best-fit LMA solution, ranging from 53\% to 97\%.

Generally speaking, one expects the differences in the statistical
treatment of the data to have little impact close to the global best
fit point, located in the LMA region.  These differences typically
become more visible as one departs from the best fit region towards
more disfavored solutions. Aware of this, ref.~\cite{Maltoni:2002ni}
took special care to details such as the dependence of the theoretical
errors on the oscillation parameters, which enter in the covariance
matrix characterizing the Super-K and SNO electron recoil spectra.
This way results reliable in the full oscillation parameter space were
obtained.

Despite differences in the various solar neutrino data analyzes there
is relatively good agreement on the best fit LMA active oscillation
parameters: the obtained best fit values for $\tan^2\theta_\Sol$ are
in the range $0.34- 0.47$ and for $\Dms$ they lie in the interval
$(5.0 - 7.9)\times 10^{-5}$ eV$^2$. There is also good agreement on
the allowed ranges of the oscillation parameters.
%
There is remarkable agreement on the rejection of the LOW solution
with respect to LMA with a $\Delta\chi^2_{\rm{LOW, active}} \approx
10$. The result for the vacuum solution in \cite{Maltoni:2002ni}
$\Delta\chi^2_{\rm{VAC, active}} = 8.9$ is in good agreement with the
values obtained by the Super-K collaboration, as well as Bahcall et
al, de Holanda \& Smirnov and Fogli et al, whereas Bandyopadhyay et
al, Barger et al and Creminelli etal obtain higher values.  Our result
for the SMA solution of $\Delta\chi^2_{\rm SMA, active} = 23.2$ is in
good agreement with the values obtained in Bahcall et al, Creminelli
et al and Fogli et al; while Bandyopadhyay et al and de
Holanda \& Smirnov, and especially Barger et al obtain higher values.

All in all, taking into account the vast input data, variations in the
analysis (such as the construction of the $\chi^2$ function or the
treatment of errors and their correlations) and the complexity of the
codes involved it seems encouraging that there is reasonable agreement
amongst different analyzes. Scrutinizing the origin of the differences
which are found is not an easy task.  Typically the results of a given
analysis away from the best fit region serve as an indicator of its
quality.

%%%%%%%%%%

Note that in order to compare the allowed regions in
Fig.~\ref{fig:sol-osc-par} with others, one must note that our \CL\ 
regions correspond to the 3 \dof\ corresponding to
$\tan^2\theta_\Sol$, $\Dms$ and $\eta_s$.  Therefore at a given \CL\ 
our regions are larger than the usual regions for 2 \dof, because we
also constrain the parameter $\eta_s$.
%
\begin{figure*}[thbp] 
    \includegraphics[height=6cm,width=0.96\linewidth]{Sol-region.eps}
%\vspace*{-8mm}
      \caption{\label{fig:sol-osc-par}%
        Allowed $\tan^2\theta_\Sol$ and $\Dms$ regions for $\eta_s =
        0$ (active oscillations), $\eta_s = 0.2$ and $\eta_s = 0.5$.
        The lines and shaded regions correspond to the \snocc\ and
        \snotot analyses, respectively, as defined in
        Ref.~\cite{Maltoni:2002ni}.  The 90\%, 95\%, 99\% C.L. and
        3$\sigma$ contours are for 3 \dof.}
\vspace*{-2mm}
\end{figure*}
%
Our global best fit point occurs for active oscillations with 
%
\begin{equation}
\label{t12d12}
    \tan^2\theta_\Sol = 0.46\,, \quad
    \Dms = 6.6\times 10^{-5}~\eVq
\end{equation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

A concise way to illustrate the above results is displayed in
Fig.~\ref{fig:chi-sol}. We give the profiles of $\Delta\chi^2_\Sol$ as
a function of $\Dms$ (left) as well as $\tan^2\theta_\Sol$ (right), by
minimizing with respect to the undisplayed oscillation parameters, for
the fixed values of $\eta_s=0$, $0.5$, $1$.
%
\begin{figure*}[thbp] \centering
\includegraphics[height=7cm,width=0.96\textwidth]{sol-chisq.eps}
%\vspace*{-8mm}
  \caption{ \label{fig:chi-sol}%
    $\Delta\chi^2_\Sol$ as a function of $\Dms$ and
    $\tan^2\theta_\Sol$, for pure active ($\eta_s = 0$), pure sterile
    ($\eta_s = 1$) and mixed neutrino oscillations ($\eta_s = 0.5$).
    Upper and lower panels correspond to the \snocc\ and \snotot\ 
    samples defined in Ref.~\cite{Maltoni:2002ni}.}
\vspace*{-2mm}
\end{figure*}
%
By comparing top and bottom panels one can clearly see the impact of1
the full \snotot\ sample in leading to the relative worsening of all
non-LMA solutions with respect to the preferred active LMA solution.
%
One sees also how the preferred LMA status survives in the presence of
a small sterile admixture characterized by $\eta_s$ (also seen in
Figs.~\ref{fig:sol-osc-par} and \ref{fig:sol02.etas}). Increasing
$\eta_s$ leads to a deterioration of all oscillation solutions.


It is also instructive to display the profile of $\Delta\chi^2_\Sol$
as a function of $0 \leq \eta_s \leq 1$, irrespective of the detailed
values of the solar neutrino oscillation parameters $\Dms$ and
$\theta_\Sol$, as shown in Fig.~\ref{fig:sol02.etas}.
%
\begin{figure*}[htbp] \centering
  \includegraphics[height=5cm,width=0.96 \textwidth]{sol-etas.eps}
%\vspace*{-4mm}
  \caption{ \label{fig:sol02.etas}%
    $\Delta\chi^2_\Sol$ displayed as a function of $\eta_s$ with
    respect to favored active LMA solution, for the \snocc\ (left
    panel) and the \snotot\ (right panel) analysis, as defined in
    Ref.~\cite{Maltoni:2002ni}.}  
\vspace*{-2mm}
\end{figure*}
%
One can see that there is a crossing between the LMA and
quasi--vacuum--oscillations (QVO) solutions. This implies that the
best pure--sterile description lies in the QVO regime. However, in the
global analysis pure sterile oscillations with $\eta_s=1$ are highly
disfavored. We find a $\chi^2$-difference between pure active and
sterile of $\Delta\chi^2_\mathrm{s-a} = 32.9$ if we restrict to the
LMA solution, or $\Delta\chi^2_\mathrm{s-a} = 22.9$ if we allow also
for QVO. For 3 \dof\ the $\Delta\chi^2_\mathrm{s-a} = 22.9$ implies
that pure sterile oscillations are ruled out at 99.996\% \CL\ compared
to the active case. From the figure we obtain the bound
%
\begin{equation}
    \label{eq:etasSol}
    \rm{solar \: data:}\quad \eta_s \leq 0.44 \, \rm{(boron-fixed),}\:
                    \quad \eta_s \leq 0.61 \,.  \rm{(boron-free)}.    
\end{equation}
%
at 99\% \CL\ for 1 \dof. A complete table of best fit values of $\Dms$
and $\theta_\Sol$ with the corresponding $\chi^2_\Sol$ and GOF values
for pure active, pure sterile, and mixed neutrino oscillations is
given in \cite{Maltoni:2002ni}, both for the \snocc\ ($48-2$ \dof) and
the \snotot\ analysis ($81-2$ \dof).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{ATMOSPHERIC NEUTRINOS}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Here I summarize the analysis of atmospheric data given in
Ref.~\cite{Maltoni:2002ni}, in a generalized oscillation scheme in
which a light sterile neutrino takes part in the oscillations, under
the approximation $\Dms\ll\Dma$ (for earlier pure active descriptions
see, for example, ref.~\cite{Fornengo:2000sr} and references therein).
In order to comply with the strong constraints from reactor
experiments~\cite{CHOOZ} we completely decouple the electron neutrino
from atmospheric oscillations.
%
In contrast with the case of solar oscillations, the constraints on
the $\nu_\mu$--content in atmospheric oscillations are not so
stringent.  Thus the description of atmospheric neutrino oscillations
in this general framework requires \texttt{two new parameters} besides
the standard 2-neutrino oscillation parameters $\theta_\Atm$ and
$\Dma$.  We will use the parameters $d_\mu$ and $d_s$ already
introduced in Ref.~\cite{Maltoni:2001bc}, and defined in such a way
that $1-d_\mu$ ($1-d_s$) corresponds to the fraction of $\nu_\mu$
($\nu_s$) participating in oscillations with $\Dma$. Hence, pure
active atmospheric oscillations with $\Dma$ are recovered when
$d_\mu=0$ and $d_s=1$. In four-neutrino models there is a
mass-scheme-dependent relationship between $d_s$ and the solar
parameter $\eta_s$. For details see Ref.~\cite{Maltoni:2001bc}.

To get a feeling on the physical meaning of these two parameters, note
that for $d_\mu=0$ we obtain that the $\nu_\mu$ oscillates with $\Dma$
to a linear combination of $\nu_\tau$ and $\nu_s$ given as
%
$ \nu_\mu \to \sqrt{d_s} \,\nu_\tau + \sqrt{1-d_s} \,\nu_s \,.$

Our global best fit point occurs at 
%
\begin{equation}
    \sin^2\theta_\Atm = 0.49 \,,\quad \Dma = 2.1 \times
    10^{-3}~\eVq 
\end{equation}
%
and has $d_s=0.92,\: d_\mu=0.04$. We see that atmospheric data prefers
a small sterile neutrino admixture. However, this effect is not
statistically significant, since the pure active case ($d_s=1,
d_\mu=0$) also gives an excellent fit: the difference in $\chi^2$ with
respect to the best fit point is only $\Dcq_\mathrm{act-best} = 3.3$.
For the pure active best fit point we obtain,
%
\begin{equation}
\label{t23d23}
    \sin^2\theta_\Atm = 0.5 \,,\: \Dma = 2.5 \times
    10^{-3}~\eVq \: 
\end{equation}
%
with the 3$\sigma$ ranges (1 \dof)
%
\begin{eqnarray} 
    0.3 \le \sin^2\theta_\Atm \le 0.7 \\ 
    1.2 \times 10^{-3}~\eVq \le \Dma  \le 4.8 \times
    10^{-3}~\eVq \,. 
\end{eqnarray}
%
The determination of the parameters $\theta_\Atm$ and $\Dma$ is
summarized in Figs.~\ref{fig:atm-osc-par} and \ref{fig:chi-atm}.  
%
\begin{figure*}[t] \centering
  \includegraphics[width=0.96\textwidth,height=7cm]{Atm-region.eps}
%\vspace*{-4mm}
  \caption{ \label{fig:atm-osc-par}%
    Allowed regions of $\sin^2\theta_\Atm$ and $\Dma$ at 90\%, 95\%,
    99\% and 3$\sigma$ for 4 \dof\ and different assumptions on the
    parameters $d_s$ and $d_\mu$, from~\cite{Maltoni:2002ni}. The
    lines (shaded regions) correspond to 1289 (1489) days of Super-K
    data. }  \vspace*{-2mm}
\end{figure*}
%
Note that Fig.~\ref{fig:chi-atm} considers several cases: arbitrary
$d_s$ and $d_\mu$, best--fit $d_s$ and $d_\mu$, and pure active and
mixed active--sterile neutrino oscillations, as indicated.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

At a given \CL\ we cut the $\chi^2_\Atm$ at a $\Dcq$ determined by 4
\dof\ to obtain 4-dimensional volumes in the parameter space of
($\theta_\Atm, \Dma, d_\mu,d_s$).  In the upper panels we show
sections of these volumes at values of $d_s=1$ and $d_\mu=0$
corresponding to the pure active case (left) and the best fit point
(right). Again we observe that moving from pure active to the best fit
does not change the fit significantly.  In the lower right panel we
project away both $d_\mu$ and $d_s$, whereas in the lower left panel
we fix $d_s=0.5$ and eliminate only $d_\mu$.
%
Comparing the regions resulting from 1489 days Super-K data (shaded
regions) with the one from the 1289 days Super-K sample (hollow
regions) we note that the new data leads to a slightly better
determination of $\theta_\Atm$ and $\Dma$. However, more importantly,
from the lower left panel we see, that the new data shows a much
stronger rejection against a sterile admixture: for $d_s=0.5$ no
allowed region appears at 3$\sigma$ for 4 \dof.
%
\begin{figure*}[bthp] \centering
  \includegraphics[width=0.96\textwidth,height=3.5cm]{Atm-chisq.eps}
%  \vspace*{-5mm}
\caption{\label{fig:chi-atm}%
  $\Dcq_\Atm$ as a function of $\Dma$, $\sin^2\theta_\Atm$, $d_s$ and
  $d_\mu$. In each panel the undisplayed parameters are integrated
  out. The ``Mixed'' and ``Restricted'' cases correspond to $d_s =
  0.5$ and $d_\mu = 0$, respectively~\cite{Maltoni:2002ni}.}
\vspace*{-2mm} 
\end{figure*}

\section{NEUTRINO PARAMETERS}

The basic structure of the neutrino sector required to account for
present solar and atmospheric data has been developed in the early
eighties, motivated mainly by
theory~\cite{Weinberg:uk,seesaw,seesaw2,seesaw3}.  In a gauge theory
of the weak interaction the \texttt{simplest} lepton mixing matrix is
characterized by 3 angles and 3 CP violating
phases~\cite{Schechter:1980gr}:
\begin{itemize}
\item the solar angle $\theta_{12}$
\item the atmospheric angle $\theta_{23}$
\item the reactor angle $\theta_{13}$
\item one Kobayashi-Maskawa-like CP phase 
\item 2 extra (Majorana-type) CP phases
\end{itemize}
%
The structure of leptonic weak interactions is more complex in
theories containing \21 singlet leptons, especially if, for some
symmetry reason, they happen to be light.  In such case the charged
current mixing matrix is rectangular and the neutral current is
non-trivial, with yet new angles and phases present
(see~\cite{Schechter:1980gr} for a detailed discussion and
parametrization).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

As seen above, current solar and atmospheric data fit very well with
oscillations among the three active neutrinos, provided that
$\theta_{12}$ is large as seen in Eq.~(\ref{t12d12}), but non-maximal,
given in Eq.~(\ref{t12bound}), while $\theta_{23}$ must be nearly
maximal, from Eq.~(\ref{t23d23}). As mentioned, $\theta_{13}$ must be
rather small~\cite{Gonzalez-Garcia:2000sq}.  Note from
Eqs.~(\ref{t12d12}) and~(\ref{t23d23}) that $\Dma \gg \Dms$.
Depending on the sign of $\Delta m_{32}^2$ there are two possible
neutrino mass schemes: normal and inverse-hierarchical neutrino
masses.

If solar and atmospheric data are combined with short baseline data
including the LSND hint, then one needs, in the framework of the
oscillation hypothesis, the existence of a light sterile
neutrino~\cite{Peltoniemi:1992ss} taking part in the
oscillations~\cite{Maltoni:2001bc}. 

With the latest data one finds that, even though 4-neutrino models can
not be ruled out as such, the resulting global fit of all current
oscillation data is extremely poor~\cite{Maltoni:2002xd}.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vv


It should be clear that neutrino oscillations are sensitive only to
mass splittings, not to the absolute scale of neutrino mass, nor to
whether neutrinos are Dirac or Majorana particles.  The main process
relevant to decide this fundamental issue is \nbb decay
\cite{Morales:1998hu}.  The \texttt{black-box theorem} states that, in
a ``natural'' gauge theory, irrespective of how \nbb is engendered, it
implies a Majorana neutrino mass, and vice-versa, as illustrated by
Fig.  \ref{fig:bbox}.
%
\begin{figure}[htbp] \centering
\includegraphics[width=0.4\textwidth,height=3cm]{blackbox.eps}  
% \vspace*{-8mm}
 \caption{The black-box \nbb argument \cite{Schechter:1981bd}.}
 \label{fig:bbox} 
\vspace*{-2mm}
\end{figure}
%
One may quantify the implications of the black-box argument once a
particular model is specified. The strength of
neutrino-exchange-induced \nbb is characterized by an ``effective''
neutrino mass parameter $M_{ee}$ which takes into account possible
cancellations among individual neutrino
amplitudes~\cite{pseudo,Valle:1982yw}.  As seen in
Fig.~\ref{fig:bbmass} this is directly correlated~\cite{Barger:2002xm}
with the neutrino mass scales probed in tritium beta
decays~\cite{katrin} and cosmology~\cite{Elgaroy:2002bi}. It is
therefore important to probe \nbb in a more sensitive experiment, such
as GENIUS \cite{Klapdor-Kleingrothaus:1999hk}.
%
\begin{figure}[htbp] \centering
\includegraphics[width=0.4\textwidth,height=3.5cm]{barger2.eps}
% \vspace*{-8mm}
 \caption{\nbb and the scale of neutrino mass.}
 \label{fig:bbmass} 
 \vspace*{-2mm}
\end{figure}
%
Moreover $\Delta L=2$ processes, such as \nbb decay, are sensitive to
the ``Majorana-type'' phases~\cite{Schechter:1980gr,Doi:1985dx} which
drop out from ordinary ($\Delta L=0$) neutrino oscillations.  Given
present uncertainties these phases can not be reliably extracted from
\nbb alone.
%
Direct tests of leptonic (``Dirac'') CP violation in oscillation
experiments, such as neutrino factories, will be a tough challenge,
due to the hierarchical neutrino mass splittings and the smallness of
$\theta_{13}$ indicated by reactors (the CP violation disappears as
two neutrinos become degenerate \cite{Schechter:1979bn} and as
$\theta_{13} \to 0$~\cite{CHOOZ}).
%
Fortunately the LMA solution helps, so with good luck, neutrino
factories may probe leptonic CP violating effects, through the
measurement of CP asymmetries.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{NON-STANDARD NEUTRINOS}

Non-standard neutrinos interactions (NSI) are expected in most
neutrino mass models~\cite{Schechter:1980gr,Valle:1990pk} and can be
of two types: flavour-changing (FC) and non-universal (NU). They may
arise from a nontrivial structure of CC and NC weak interactions
characterized a non-unitary lepton mixing matrix and a correspondingly
non-trivial NC matrix~\cite{Schechter:1980gr}.  Such
\texttt{gauge-induced} NSI may lead to flavor and CP violation, even
with degenerate massless neutrinos \cite{NSImodels2}. In radiative
models of neutrino mass \cite{Zee:1980ai} and supersymmetric models
with broken R parity \cite{rpmnu-spo,rpmnu-exp} FC-NSI can also be
\texttt{Yukawa-induced}, from the exchange of spinless bosons.
%
In supersymmetric unified models, they may be calculable
as renormalization effects~\cite{NSImodels3}.

\subsection{NSI solutions to the solar neutrino problem}

At the moment one can not yet pin down the exact profile of the \ne
survival probability and, as a result, the underlying mechanism of
solar neutrino conversion remains unknown.  Alternatives to
oscillations have been suggested since the eighties, including
non-standard neutrino matter interactions (NSI)~\cite{Valle:gv} and
spin-flavor precession (SFP)~\cite{Akhmedov:uk,Schechter:1981hw}. The
former may be represented as effective dimension-6 terms of the type
$\varepsilon G_F$, as illustrated in Fig.~\ref{fig:nuNSI}, where
$\varepsilon$ specifies their sub-weak strength.
%
\begin{figure}[htbp]
  \centering
\includegraphics[scale=.24]{fc.ps}  
% \vspace*{-6mm}
 \caption{Effective  NSI operator.}
  \label{fig:nuNSI}
  \vspace*{-2mm}
\end{figure}

Analyses of solar neutrino data in terms of NSI~\cite{Guzzo:2001mi}
and SFP~\cite{Barranco:2002te,Miranda:2001hv,Miranda:2001bi} have been
given recently.  SFP solutions exist both in the resonant
(RSFP)~\cite{Miranda:2001bi} and non-resonant regimes
(NRSFP)~\cite{Miranda:2001hv}.  The NSI solar neutrino energy spectrum
is undistorted, in agreement with data. On the other hand
Fig.~\ref{chi2sfp} shows the predicted modification of the solar
neutrino spectra for the ``best'' LMA solution, and for the ``best''
SFP solutions \cite{Barranco:2002te}, from latest solar data. Clearly
the spectra in the high energy region are nearly undistorted in all 3
cases, in agreement with observations.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[tbh] 
\includegraphics[width=0.48\textwidth,height=3cm]{probs.eps}
\includegraphics[width=0.48\textwidth,,height=3cm]{chi84.eps}
%\vspace*{-8mm}
\caption{Best LMA and SFP \ne survival probabilities 
  (left) and $\Delta\chi^2_\Sol$ versus $\tan^2\theta_\Sol$, for RSFP,
  LMA (central minima) and NRSFP solutions, from two different
  analyses described in Ref.~\cite{Barranco:2002te}.}
 \label{chi2sfp}
 \vspace*{-2mm}
 \end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Although LMA oscillations are clearly favored over other
\texttt{oscillation} solutions~\cite{Maltoni:2002ni}, present solar
neutrino data \texttt{can be equally well-described by SFP and NSI
  solutions}. Fig.~\ref{chi2sfp} shows how this happens in the
SFP-oscillation case, the resulting parameter regions is given in
\cite{Barranco:2002te}.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 Apart from the fact that the two SFP solutions lie slightly lower
 than the LMA minimum, the 3 solutions are statistically equivalent.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
 Ways to distinguish LMA from the NRSFP solution and the simplest RSFP
 solution at Borexino have been considered in
 Refs.~\cite{Barranco:2002te,Akhmedov:2002ti}.
 %
 On the other hand, if the LMA solution is finally confirmed by
 KamLAND, such alternative mechanisms of solar neutrino conversion
 will still be interesting for study since their sub-leading admixture
 will be testable, as discussed in~\cite{Barranco:2002te}.
%
 For example, if KamLAND confirms the LMA solution, one can place a
 constraint on $\mu B_\perp$, which are sensitive to how good is the
 KamLAND determination of the LMA oscillation
 parameters~\cite{KamLAND} and also to the ultimate central $\Dms$
 value indicated by this experiment.

Last, but not least, solar neutrino data to derive stringent bounds on
Majorana neutrino transition moments~\cite{Schechter:1981hw} when
LMA-MSW oscillations account for the solar neutrino data, as discussed
in ref.  \cite{Grimus:2002vb}. Should such TMs be present, they would
contribute to the neutrino--electron scattering cross section and
hence affect the signal observed in Super-Kamiokande. Assuming that
LMA-MSW is the solution of the solar neutrino problem ref.
\cite{Grimus:2002vb} constrains neutrino TMs by using the latest
global solar neutrino data.  One finds that \texttt{all} elements of
the TM matrix can be bounded at the same time.  Moreover, ref.
\cite{Grimus:2002vb} shown how reactor data play a complementary role
to the solar neutrino data.  The resulting combined solar + reactor
bound on TMs is $2 \times 10^{-10} \mu_B$ at the 90\% C.L. The
sensitivity of the upcoming Borexino experiment and is about an order
of magnitude better, thanks to its lower energy.

%%%%%%%%%%%%%%%%%%%%%%%

Let me now turn to the possibility of non-standard neutrino matter
interactions (NSI). These may also affect the propagation of neutrinos
in a variety of astrophysical environments~\cite{Nunokawa:1996tg} and
also provide an excellent description of present solar neutrino data.
The allowed regions for the NSI mechanism of solar neutrino conversion
are shown in Fig.~\ref{fig:hybparam}. The required NSI values
indicated by the solar data analysis are fully acceptable also for the
atmospheric data.
%
\begin{figure*}[t]
  \centering
\includegraphics[width=0.96\textwidth,height=6cm]{Nsi-solar-U.eps}  
%\vspace*{-8mm}
  \caption{Parameters of NSI solution to the solar neutrino anomaly, 
from \cite{Guzzo:2001mi}.}
  \label{fig:hybparam}
\vspace*{-2mm}
\end{figure*}
Such NSI description of solar data was also shown~\cite{Guzzo:2001mi}
to be slightly better than that of the LMA oscillation solution.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Probing NSI with Atmospheric neutrinos}


FC-NSI interactions in the \nm-\nt channel without neutrino mass nor
mixing have been shown to account for the zenith--angle--dependent
deficit of atmospheric neutrinos observed in \texttt{contained}
Super-K events \cite{Gonzalez-Garcia:1998hj,Fornengo:1999zp}.  However
such NSI explanation fails to reconcile these with Super-K and MACRO
\texttt{up-going muons}, due to the lack of energy dependence
intrinsic of NSI conversions. As a result, a pure NSI conversion in
the atmospheric channel is ruled out at 99\% \CL
~\cite{Fornengo:2001pm}. Thus, unlike the case of solar neutrinos, the
oscillation interpretation of atmospheric data is robust, NSI being
allowed only at a sub-leading level.
%


%
The most recent global analysis of the atmospheric neutrino anomaly in
terms of NSI shows that a pure NSI mechanism is now ruled out, while
the standard \nm $\to$ \nt oscillations provide a remarkably good
description of the anomaly \cite{Fornengo:2001pm}.
%
The robustness of the atmospheric \nm $\to$ \nt oscillation hypothesis
was shown to provide the most stringent and model-independent limits
on flavour-changing (FC) and non-universal (NU) neutrino interactions,
as illustrated in Fig.~\ref{fig:atmnsibds}.
\begin{figure}[tbh]
\centering
%\includegraphics[width=0.47\textwidth,height=5cm]{fig.chi2_eps.eps}  
\includegraphics[width=0.47\textwidth,height=4cm]{Nsi-atmos-D.eps}  
%\vspace*{-8mm}
  \caption{Atmospheric bounds on NSI, from Ref.~\cite{Fornengo:2001pm}.}
  \label{fig:atmnsibds}
  \vspace*{-2mm}
\end{figure}
These limits are for the case of NSI off-down-type quarks. They are
rather model-independent, as they are obtained from pure
neutrino-physics processes.


%%%%%%%%%% start new %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
These limits are model independent as they are obtained from pure
neutrino-physics processes. The stability of the neutrino oscillation
solution to the atmospheric neutrino anomaly against the presence of
non-standard neutrino interactions illustrates the robustness of the
near-maximal atmospheric mixing and massive-neutrino hypothesis.


\subsection{Probing NSI in Neutrino Factories~\cite{Huber:2001zw,Huber:2001de}}
\label{sec:nufact}

As we have seen at this conference how future neutrino factories aim
at probing the lepton mixing angle $\theta_{13}$ with much better
sensitivity than possible today by combining reactor and atmospheric
data \cite{Fornengo:2001pm}. Given the LMA solution of the solar
neutrino problem, it follows that there is a chance that indeed
neutrino factories (Nufact, for short) will also probe the concurrent
leptonic CP violating effects (for example, through the measurement of
CP asymmetries).

The potential of such a generic Nufact in probing non-standard
neutrino-matter interactions has been determined in ref.
\cite{Huber:2001zw}.  It has been found that the sensitivity to
flavour-changing (FC) NSI can be substantially improved with respect
to present atmospheric neutrino data, especially at energies higher
than approximately 50 GeV, where the effect of the tau mass is small,
as illustrated in Fig. \ref{fig:nufacnsibds}.  For example, a 100 GeV
Nufact can probe FC neutrino interactions at the level of few
$|\epsilon| < {\rm few} \times 10^{-4}$ at 99 \% C.L.
%
\begin{figure}[htbp]
  \centering
\includegraphics[scale=.65,height=3.5cm]{sensMTlow.eps}
  \caption{Nufact sensitivities to non-standard neutrino 
    interactions, from \cite{Huber:2001zw}.}
  \label{fig:nufacnsibds}
\end{figure}

%%%%%%%%%%%% end new %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Note also that in such hybrid solution to the neutrino anomalies, with
FC-NSI explaining the solar data, and oscillations accounting for the
atmospheric data, the two sectors are connected not only by the
neutrino mixing angle $\theta_{13}$, but also by the \ne-\nt FC-NSI
parameters. As a result NSI and oscillations may be confused, as shown
in~\cite{Huber:2001de}.  This implies that information on
$\theta_{13}$ can only be obtained if bounds on NSI are available.
Taking into account the existing bounds on FC interactions, one finds
a drastic loss in \texttt{Nufact} sensitivities on $\theta_{13}$, of
at least two orders of magnitude. A near--detector offers the
possibility to obtain stringent bounds on some NSI parameters and
therefore constitutes a crucial necessary step towards the
determination of $\theta_{13}$ and subsequent study of leptonic CP
violation.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

This work was supported by Spanish grant BFM2002-00345, by the
European Commission RTN network HPRN-CT-2000-00148, by the European
Science Foundation network grant N.~86.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section*{References}
\begin{thebibliography}{99}
  
\bibitem{nu2002} Proceedings of Neutrino 2002,
  http://neutrino2002.ph.tum.de/pages/transparencies2.html

\bibitem{Maltoni:2002ni}
M.~Maltoni, T.~Schwetz, M.~A.~Tortola and J.~W.~Valle,
%``Constraining neutrino oscillation parameters with current solar and  atmospheric data,''
arXiv:hep-ph/0207227 (Phys. Rev. D, in press) and references therein
%%CITATION = HEP-PH 0207227;%%

\bibitem{Wolfenstein:1977ue}
L.~Wolfenstein,
%``Neutrino Oscillations In Matter,''
Phys.\ Rev.\ D {\bf 17}, 2369 (1978);
%%CITATION = PHRVA,D17,2369;%%
S.~P.~Mikheev and A.~Y.~Smirnov,
%``Resonance Enhancement Of Oscillations In Matter And Solar Neutrino  Spectroscopy,''
Sov.\ J.\ Nucl.\ Phys.\  {\bf 42} (1985) 913
%%CITATION = SJNCA,42,913;%%

\bibitem{Gonzalez-Garcia:1999aj}
M.~C.~Gonzalez-Garcia, P.~C.~de Holanda, C.~Pena-Garay and J.~W.~Valle,
%``Status of the MSW solutions of the solar neutrino problem,''
Nucl.\ Phys.\ B {\bf 573}, 3 (2000) 
%%CITATION = HEP-PH 9906469;%%

\bibitem{Gonzalez-Garcia:2000sq}
M.~C.~Gonzalez-Garcia, M.~Maltoni, C.~Pena-Garay and J.~W.~Valle,
%``Global three-neutrino oscillation analysis of neutrino data,''
Phys.\ Rev.\ D {\bf 63}, 033005 (2001)
%%CITATION = HEP-PH 0009350;%%

\bibitem{Peltoniemi:1992ss}
J.~T.~Peltoniemi, D.~Tommasini and J.~W.~Valle,
%``Reconciling dark matter and solar neutrinos,''
Phys.\ Lett.\ B {\bf 298}, 383 (1993).
%%CITATION = PHLTA,B298,383;%%
J.~T.~Peltoniemi and J.~W.~Valle,
%``Reconciling dark matter, solar and atmospheric neutrinos,''
Nucl.\ Phys.\ B {\bf 406}, 409 (1993);
%%CITATION = HEP-PH 9302316;%%
D.~O.~Caldwell and R.~N.~Mohapatra,
%``Neutrino Mass Explanations Of Solar And Atmospheric Neutrino Deficits  And Hot Dark Matter,''
Phys.\ Rev.\ D {\bf 48} (1993) 325; additional references in Giunti
and Lavader's excellent web--page
http://www.to.infn.it/~giunti/neutrino/

\bibitem{LSND}
Talk by G. Drexlin, at Neutrino 2002

\bibitem{CHOOZ} 
M. Apollonio et al, CHOOZ Coll., Phys. Lett.
  B \textbf{466} (1999) 415; F.~Boehm et al, Palo Verde Coll.,
  %``Final results from the Palo Verde neutrino oscillation experiment,''
  Phys.\ Rev.\ D {\bf 64} (2001) 112001
  %%CITATION = HEP-EX 0107009;%%
  
\bibitem{Fornengo:2000sr}
N.~Fornengo, M.~C.~Gonzalez-Garcia and J.~W.~Valle,
%``Updated global analysis of the atmospheric neutrino data in terms of  neutrino oscillations,''
Nucl.\ Phys.\ B {\bf 580} (2000) 58 [arXiv:hep-ph/0002147].
%%CITATION = HEP-PH 0002147;%%

\bibitem{Maltoni:2001bc}
M.~Maltoni, T.~Schwetz and J.~W.~Valle,
%``Status of four-neutrino mass schemes: A global and unified approach to  current neutrino oscillation data,''
Phys.\ Rev.\ D {\bf 65}, 093004 (2002);
%%CITATION = HEP-PH 0112103;%%
%``Cornering (3+1) sterile neutrino schemes,''
Phys.\ Lett.\ B {\bf 518} (2001) 252 
%%CITATION = HEP-PH 0107150;%%

\bibitem{Weinberg:uk} S.~Weinberg, Proceedings of \texttt{Neutrinos
    78}, p,~1-21; R.~Barbieri, J.~R.~Ellis and M.~K.~Gaillard,
%``Neutrino Masses And Oscillations In SU(5),''
Phys.\ Lett.\ B {\bf 90}, 249 (1980).
%%CITATION = PHLTA,B90,249;%%

\bibitem{seesaw} M. Gell-Mann, P. Ramond and R. Slansky in {\it
    Supergravity} (North Holland, Amsterdam 1979); T. Yanagida in {\it
    Proc. of the Workshop on Unified Theory and Baryon Number of the
    Universe}, KEK, Japan, 1979.

\bibitem{seesaw2}
R.~N.~Mohapatra and G.~Senjanovic,
%``Neutrino Mass And Spontaneous Parity Nonconservation,''
Phys.\ Rev.\ Lett.\  {\bf 44} (1980) 912;
%%CITATION = PRLTA,44,912;%%
J.~Schechter and J.~W.~Valle,
%``Neutrino Masses In SU(2) X U(1) Theories,''
Phys.\ Rev.\ D {\bf 22}, 2227 (1980);
%%CITATION = PHRVA,D22,2227;%%
C.~Wetterich,
%``Neutrino Masses And The Scale Of B-L Violation,''
Nucl.\ Phys.\ B {\bf 187} (1981) 343.
%%CITATION = NUPHA,B187,343;%%

\bibitem{seesaw3}
Y.~Chikashige, R.~N.~Mohapatra and R.~D.~Peccei,
%``Are There Real Goldstone Bosons Associated With Broken Lepton Number?,''
Phys.\ Lett.\ B {\bf 98} (1981) 265;
%%CITATION = PHLTA,B98,265;%%
J.~Schechter and J.~W.~Valle,
%``Neutrino Decay And Spontaneous Violation Of Lepton Number,''
Phys.\ Rev.\ D {\bf 25} (1982) 774;
%%CITATION = PHRVA,D25,774;%%
G.~B.~Gelmini and J.~W.~Valle,
%``Fast Invisible Neutrino Decays,''
Phys.\ Lett.\ B {\bf 142}, 181 (1984).
%%CITATION = PHLTA,B142,181;%%

\bibitem{Schechter:1980gr}
J.~Schechter and J.~W.~Valle,
%``Neutrino Masses In SU(2) X U(1) Theories,''
Phys.\ Rev.\ D {\bf 22}, 2227 (1980);
%%CITATION = PHRVA,D22,2227;%%
%``Neutrino Oscillation Thought Experiment,''
Phys.\ Rev.\ D {\bf 23}, 1666 (1981).
%%CITATION = PHRVA,D23,1666;%%

\bibitem{Maltoni:2002xd}
M.~Maltoni, T.~Schwetz, M.~A.~Tortola and J.~W.~Valle,
%``Ruling out four-neutrino oscillation interpretations of the LSND  anomaly?,''
Nucl.\ Phys.\ B {\bf 643} (2002) 321 [arXiv:hep-ph/0207157]
%%CITATION = HEP-PH 0207157;%%

\bibitem{Morales:1998hu}
A.~Morales,
%``Review on double beta decay experiments and comparison with theory,''
Nucl. Phys.\ Proc.\ Suppl.\ {\bf 77}, 335 (1999);
%%CITATION = HEP-PH 9809540;%%
A.~Faessler and F.~Simkovic,
%``Nuclear Structure And The Double Beta Decay,''
Prog.\ Part.\ Nucl.\ Phys.\  {\bf 46} (2001) 233.
%%CITATION = PPNPD,46,233;%%

\bibitem{Schechter:1981bd}
J.~Schechter and J.~W.~Valle,
%``Neutrinoless Double-Beta Decay In SU(2) X U(1) Theories,''
Phys.\ Rev.\ D {\bf 25}, 2951 (1982).
%%CITATION = PHRVA,D25,2951;%%

\bibitem{pseudo}
L.~Wolfenstein,
%``Different Varieties Of Massive Dirac Neutrinos,''
Nucl.\ Phys.\ B {\bf 186} (1981) 147.
%%CITATION = NUPHA,B186,147;%%
J.~W.~Valle and M.~Singer,
%``Lepton Number Violation With Quasi Dirac Neutrinos,''
Phys.\ Rev.\ D {\bf 28}, 540 (1983).
%%CITATION = PHRVA,D28,540;%%

\bibitem{Valle:1982yw}
J.~W.~Valle,
%``Neutrinoless Double-Beta Decay With Quasi-Dirac Neutrinos,''
Phys.\ Rev.\ D {\bf 27}, 1672 (1983).
%%CITATION = PHRVA,D27,1672;%%

\bibitem{Barger:2002xm}
V.~Barger et al, %%%S.~L.~Glashow, D.~Marfatia and K.~Whisnant,
%``Neutrinoless double beta decay can constrain neutrino dark matter,''
Phys.\ Lett.\ B {\bf 532} (2002) 15.
%%CITATION = HEP-PH 0201262;%%
F.~Feruglio, A.~Strumia and F.~Vissani, arXiv:hep-ph/0201291;
%%CITATION = HEP-PH 0201291;%%
H.~Minakata and H.~Sugiyama,
%``Constraints on neutrino mixing parameters by observation of  neutrinoless double beta decay,''
Phys.\ Lett.\ B {\bf 532}, 275 (2002) 
%%CITATION = HEP-PH 0202003;%%

\bibitem{katrin}
Talk by Ch. Weinheimer, at Neutrino 2002

\bibitem{Elgaroy:2002bi}
O.~Elgaroy et al,
%``A new limit on the total neutrino mass from the 2dF galaxy redshift survey,''
 arXiv:astro-ph/0204152.
%%CITATION = ASTRO-PH 0204152;%%

\bibitem{Klapdor-Kleingrothaus:1999hk}
H.~V.~Klapdor-Kleingrothaus et al,  [GENIUS Collaboration],
%``GENIUS: A supersensitive germanium detector system for rare events,''
arXiv:hep-ph/9910205.
%%CITATION = HEP-PH 9910205;%%

\bibitem{Doi:1985dx}
M.~Doi, T.~Kotani and E.~Takasugi,
%``Double Beta Decay And Majorana Neutrino,''
Prog.\ Theor.\ Phys.\ Suppl.\  {\bf 83}, 1 (1985).
%%CITATION = PTPSA,83,1;%%

\bibitem{Schechter:1979bn}
J.~Schechter and J.~W.~Valle,
%``Comment On The Lepton Mixing Matrix,''
Phys.\ Rev.\ D {\bf 21}, 309 (1980).
%%CITATION = PHRVA,D21,309;%%

\bibitem{Valle:1990pk}  J.~W.~Valle,
%``Gauge Theories And The Physics Of Neutrino Mass,''
Prog.\ Part.\ Nucl.\ Phys.\  {\bf 26}, 91 (1991).
%%CITATION = PPNPD,26,91;%%

\bibitem{NSImodels2}
R.~N.~Mohapatra and J.~W.~F.~Valle,
%``Neutrino Mass And Baryon-Number Nonconservation In Superstring Models,''
Phys.\ Rev.\ D {\bf 34} (1986) 1642.
%%CITATION = PHRVA,D34,1642;%%
D.~Wyler and L.~Wolfenstein,
%``Massless Neutrinos In Left-Right Symmetric Models,''
Nucl.\ Phys.\ B {\bf 218} (1983) 205.
%%CITATION = NUPHA,B218,205;%%

\bibitem{Zee:1980ai}
A.~Zee,
%``A Theory Of Lepton Number Violation, Neutrino Majorana Mass, And Oscillation,''
Phys.\ Lett.\ B {\bf 93} (1980) 389 [Err-ibid.\ B {\bf 95} (1980) 461].
%%CITATION = PHLTA,B93,389;%%
K.~S.~Babu,
%``Model Of 'Calculable' Majorana Neutrino Masses,''
Phys.\ Lett.\ B {\bf 203} (1988) 132.
%%CITATION = PHLTA,B203,132;%%

\bibitem{rpmnu-spo} 
C.~S.~Aulakh and R.~N.~Mohapatra,
%``Neutrino As The Supersymmetric Partner Of The Majoron,''
Phys.\ Lett.\ B {\bf 119}  (1982) 13;
G.~G.~Ross and J.~W.~F.~Valle,
%``Supersymmetric Models Without R Parity,''
Phys.\ Lett.\ B {\bf 151} (1985) 375;
%%CITATION = PHLTA,B151,375;%%
J.~R.~Ellis et al, 
%``Phenomenology Of Supersymmetry With Broken R Parity,''
Phys.\ Lett.\ B {\bf 150} (1985) 142;
%%CITATION = PHLTA,B150,142;%%
A.~Santamaria and J.~W.~F.~Valle,
%``Spontaneous R Parity Violation In Supersymmetry: A Model For Solar Neutrino Oscillations,''
Phys.\ Lett.\ B {\bf 195}, 423 (1987);
%%CITATION = PHLTA,B195,423;%%
%
%``Supersymmetric Majoron Signatures And Solar Neutrino Oscillations,''
Phys.\ Rev.\ Lett.\  {\bf 60}, 397 (1988);
%%CITATION = PRLTA,60,397;%%
%
%``Solar Neutrino Oscillation Parameters And The Broken R Parity Majoron,''
Phys.\ Rev.\ D {\bf 39}, 1780 (1989).
%%CITATION = PHRVA,D39,1780;%%

\bibitem{rpmnu-exp} 
L.~J.~Hall and M.~Suzuki,
%``Explicit R Parity Breaking In Supersymmetric Models,''
Nucl.\ Phys.\ B {\bf 231} (1984) 419,
%%CITATION = NUPHA,B231,419;%%
see also \cite{Allanach:1999bf} and papers therein.

\bibitem{NSImodels3}
  L.\ J.\ Hall, V.\ A.\ Kostelecky and S.\ Raby,
  Nucl.\ Phys.\ B {\bf 267} (1986) 415
  %%CITATION = NUPHA,B267,415;%%
R.~Barbieri, L.~J.~Hall and A.~Strumia,
%``Violations of lepton flavor and CP in supersymmetric unified theories,''
Nucl.\ Phys.\ B {\bf 445}, 219 (1995) 
%%CITATION = HEP-PH 9501334;%%
  F.~Gabbiani et al, 
%``A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model,''
Nucl.\ Phys.\ B {\bf 477}, 321 (1996) 
%%CITATION = HEP-PH 9604387;%%

\bibitem{Valle:gv}
J.~W.~Valle,
%``Resonant Oscillations Of Massless Neutrinos In Matter,''
Phys.\ Lett.\ B {\bf 199}, 432 (1987).
%%CITATION = PHLTA,B199,432;%%

\bibitem{Akhmedov:uk}
E.~K.~Akhmedov,
%``Resonant Amplification Of Neutrino Spin Rotation In Matter And The  Solar-Neutrino Problem,''
Phys.\ Lett.\ B {\bf 213} (1988) 64.
%%CITATION = PHLTA,B213,64;%%
C.~S.~Lim and W.~J.~Marciano,
%``Resonant Spin-Flavor Precession Of Solar And Supernova Neutrinos,''
Phys.\ Rev.\ D {\bf 37} (1988) 1368.
%%CITATION = PHRVA,D37,1368;%%

\bibitem{Schechter:1981hw}
J.~Schechter and J.~W.~Valle,
%``Majorana Neutrinos And Magnetic Fields,''
Phys.\ Rev.\ D {\bf 24}, 1883 (1981)
[Err.-ibid.\ D {\bf 25}, 283 (1982)].
%%CITATION = PHRVA,D24,1883;%%

\bibitem{Guzzo:2001mi}
M.~Guzzo et al, 
%``Status of a hybrid three-neutrino interpretation of neutrino data,''
Nucl.\ Phys.\ B {\bf 629}, 479 (2002)
%%CITATION = HEP-PH 0112310;%%

\bibitem{Barranco:2002te}
J.~Barranco et al, 
%``Confronting spin flavor solutions of the solar neutrino problem with  current and future solar neutrino data,''
arXiv:hep-ph/0207326, Phys.\ Rev.\ D, in press
%%CITATION = HEP-PH 0207326;%%

\bibitem{Miranda:2001hv}
O.~G.~Miranda et al, 
%``A non-resonant dark-side solution to the solar neutrino problem,''
Phys.\ Lett.\ B {\bf 521}, 299 (2001) 
%%CITATION = HEP-PH 0108145;%%

\bibitem{Miranda:2001bi}
O.~G.~Miranda et al, 
%``The simplest resonant spin-flavour solution to the solar neutrino  problem,''
Nucl.\ Phys.\ B {\bf 595}, 360 (2001) 
%%CITATION = HEP-PH 0005259;%%

\bibitem{Akhmedov:2002ti}
E.~K.~Akhmedov and J.~Pulido,
%``Distinguishing magnetic moment from oscillation solutions of the solar  neutrino problem with Borexino,''
Phys.\ Lett.\ B {\bf 529}, 193 (2002) 
%%CITATION = HEP-PH 0201089;%%

\bibitem{KamLAND}
Talk by J. Shirai, at Neutrino 2002

\bibitem{Grimus:2002vb}
W.~Grimus et al, 
%``Constraining Majorana neutrino electromagnetic properties from the  LMA-MSW solution of the solar neutrino problem,''
arXiv:hep-ph/0208132, Nucl. Phys. B, in press;
%%CITATION = HEP-PH 0208132;%%
J.~F.~Beacom and P.~Vogel,
%``Neutrino magnetic moments, flavor mixing, and the superKamiokande solar  data,''
Phys.\ Rev.\ Lett.\  {\bf 83}, 5222 (1999)

\bibitem{Nunokawa:1996tg}
H.~Nunokawa et al, 
%``Resonant conversion of massless neutrinos in supernovae,''
Phys.\ Rev.\ D {\bf 54}, 4356 (1996); 
%%CITATION = HEP-PH 9605301;%%
H.~Nunokawa et al,
%``Supernova bounds on supersymmetric R-parity violating interactions,''
Nucl.\ Phys.\ B {\bf 482}, 481 (1996);
%%CITATION = HEP-PH 9606445;%%
D.~Grasso et al,
%``Pulsar velocities without neutrino mass,''
Phys.\ Rev.\ Lett.\ {\bf 81}, 2412 (1998);
%%CITATION = ASTRO-PH 9803002;%%
G.~L.~Fogli et al, 
%``Revisiting nonstandard interaction effects on supernova neutrino flavor  oscillations,''
Phys.\ Rev.\ D {\bf 66}, 013009 (2002) 
%%CITATION = HEP-PH 0202269;%%

\bibitem{Gonzalez-Garcia:1998hj}
M.~C.~Gonzalez-Garcia et al,
%``Atmospheric neutrino observations and flavor changing interactions,''
Phys.\ Rev.\ Lett.\ {\bf 82}, 3202 (1999) 
%%CITATION = HEP-PH 9809531;%%

\bibitem{Fornengo:1999zp}
N.~Fornengo et al,
%``On the interpretation of the atmospheric neutrino data in terms of  flavor changing neutrino interactions,''
JHEP {\bf 0007}, 006 (2000) 
%%CITATION = HEP-PH 9906539;%%

\bibitem{Fornengo:2001pm}
N.~Fornengo et al, 
%``Probing neutrino non-standard interactions with atmospheric neutrino  data,''
Phys.\ Rev.\ D {\bf 65}, 013010 (2002)
%%CITATION = HEP-PH 0108043;%%

\bibitem{Huber:2001zw}
P.~Huber and J.~W.~Valle,
%``Non-standard interactions: Atmospheric versus neutrino factory  experiments,''
Phys.\ Lett.\ B {\bf 523}, 151 (2001) 
%%CITATION = HEP-PH 0108193;%%

\bibitem{Huber:2001de}
P.~Huber, T.~Schwetz and J.~W.~Valle,
%``How sensitive is a neutrino factory to the angle Theta(13)?,''
Phys.\ Rev.\ Lett.\ {\bf 88}, 101804 (2002) and
%%CITATION = HEP-PH 0111224;%%
%``Confusing non-standard neutrino interactions with oscillations at a  neutrino factory,''
Phys.\ Rev.\ D {\bf 66}, 013006 (2002) 
%%CITATION = HEP-PH 0202048;%%

\bibitem{Allanach:1999bf}
B.~Allanach et al,
%``Searching for R-parity violation at Run-II of the Tevatron,''
arXiv:hep-ph/9906224.
%%CITATION = HEP-PH 9906224;%%

\end{thebibliography}
\end{document}














