\subsection {$\theta_{13}$ and CP violation in oscillations}

In the recent years, a series of experiments have provided strong evidence
for oscillations of solar and atmospheric neutrinos, and have started to
precisely constrain the associated parameters $\Delta m^2_{23}$,
$\Delta m^2_{12}$, $\theta_{23}$ and $\theta_{12}$. The third mixing angle
$\theta_{13}$ is still unknown: all we have is an upper bound of
$\theta_{13} \leq 13^\circ$ coming from the CHOOZ 
experiment \cite{Apollonio:1999ae}. Its
measurement, as well as the determination of the sign of $\Delta m^2_{23}$
and therefore of the type of mass hierarchy, is crucial for
discriminating between different neutrino mass and mixing scenarios.
Moreover a precise determination of the PMNS matrix (which contrary
to the CKM matrix is free from hadronic uncertainties) would put very severe
constraints on models
of fermion masses, including realistic GUT models, and thus shed some light
on the underlying flavour theory. A neutrino super-beam from the CERN
SPL to a megaton water \v{C}erenkov detector located at Fr\'ejus would allow
to make a significant progress in this programme, reaching in particular
a sensitivity to $\sin^2(2\theta_{13})$ close to $10^{-3}$ %one degree 
and close to $2\cdot 10^{-4}$ %0.4 degree 
with a Beta-beam (and $1\cdot 10^{-4}$ %0.3 degree 
with both Super-beam and
Beta-beam), see section~\ref{sec:oscillations}.

Due to its sensitivity to $\theta_{13}$, a megaton water \v{C}erenkov
detector would also be sensitive to the CP violating phase
$\delta$ in a large portion of the ($\Delta m^2_{12}$,
$\theta_{13}$) parameter space. Establishing CP violation in the
lepton sector would represent a major progress in particle
physics, since CP violation has only been observed in the quark
sector so far. Moreover, CP violation is a crucial ingredient of
leptogenesis, a mechanism for creating the matter-antimatter
asymmetry of the Universe which relies on the out-of-equilibrium
decay of heavy Majorana neutrinos. Although the phase involved in
oscillations is generally distinct from the phase responsible for
leptogenesis, the measurement of a nonzero $\delta$ would be a
strong indication that leptogenesis may be at the origin of the
baryon asymmetry \cite{Fukugita:1986hr}. 
Indeed, standard electroweak baryogenesis would
require a very light Higgs boson, which is now excluded by LEP,
and only a small window remains for supersymmetric electroweak
baryogenesis.
%After the discovery of neutrino oscillations, leptogenesis
%therefore appears as one of the most plausible explanations of the
%baryon asymmetry.
Another necessary ingredient of leptogenesis is the existence of Majorana
neutrinos, which could be established by a positive signal in future
neutrinoless double beta decay experiments.
