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{\noindent\LARGE{\bf Astri Kleppe}\\[1cm]
\noindent\bf{Extending the Standard Model by including right-handed neutrinos}}
\\
To introduce right-handed modes is
the simplest way of extending the Standard Model. Whereas for example the
addition of a fourth standard family does not add any new features to the
model,
the introduction of right-handed neutrinos adds structures such as massive
neutrinos, which could be the answer to the solar neutrino deficit and
the atmospheric neutrino puzzle. Massive neutrinos are also prime candidates
for hot dark matter. In such a scheme, we may also get lepton mixing
and CP-violation in the leptonic sector.
In the Standard Model adding right-handed neutrinos results in a generic mass
matrix of the form
\begin{equation}\label{dima}
\cal{M}=\left(\begin{array}{rcl}
m_{L} & m_{D}\\
m_{D} & m_{R}\nonumber
\end{array}
\right)
\end{equation}
where $m_L$, $m_R$ and $m_D$ are in general matrices. Unless the Higgs sector
is modified, $m_L$ is zero.
If the lepton number is to be conserved, $m_{L}=m_{R}=0$, and the neutrino is a
four-component Dirac spinor endowed with mass by the standard Higgs mechanism
with one Higgs doublet. If however lepton number conservation is not imposed,
nonvanishing Majorana mass terms from $m_L$ and/or $m_R$ are allowed.
In the case with one left-handed and one right-handed neutrino and
with $m_{L}=0$, $ \cal{M}$
corresponds to two nonvanishing mass eigenvalues. With the the assumption
$m_{D} \ll m_{R}$,
one gets one very light and one very heavy mass value, $m_{D}^{2}/m_{R}$ and
$m_{R}$ correspondingly. This is the "standard" see-saw mechansim for
generating light neutrino masses.
In the see-saw scheme, the neutrinos are Majorana particles,
and the smallness of the neutrino masses is explained by the presence of
the big mass scale $m_R$. In this approach, when more than one right-handed
neutrino is introduced, it is however necessary to make extra assumptions,
like introducing three mass scales in order to obtain three light neutrinos.
I present an alternative scheme, where very light neutrino masses are
obtained by including right-handed neutrinos, but without making any mass
scale assumptions.
The simplest case, with three left-handed but only one right-handed
neutrino included, gives rise to two
very light and two massive neutrino states. We however want a
situation with three light neutrinos, which needs the addition of
at least two right-handed neutrinos.
I also discuss some properties of the usual (Nambu) democratic mass
matrix. These properties also pertain to the neutrino mass matrix
in the presented scheme, where
in order for the mass spectrum to contain
three vanishing (light), and two or three massive
neutrinos, the neutrino
mass matrix must display a specific form.
So while there is no assumption about any large mass scales, like in
the see-saw scheme, constraints are nevertheless imposed on the form of the
neutrino mass matrix.
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