[387] | 1 | \subsection {$\theta_{13}$ and CP violation in oscillations} |
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| 2 | |
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| 3 | In the recent years, a series of experiments have provided strong evidence |
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| 4 | for oscillations of solar and atmospheric neutrinos, and have started to |
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| 5 | precisely constrain the associated parameters $\Delta m^2_{23}$, |
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| 6 | $\Delta m^2_{12}$, $\theta_{23}$ and $\theta_{12}$. The third mixing angle |
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| 7 | $\theta_{13}$ is still unknown: all we have is an upper bound of |
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| 8 | $\theta_{13} \leq 13^\circ$ coming from the CHOOZ |
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| 9 | experiment \cite{Apollonio:1999ae}. Its |
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| 10 | measurement, as well as the determination of the sign of $\Delta m^2_{23}$ |
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| 11 | and therefore of the type of mass hierarchy, is crucial for |
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| 12 | discriminating between different neutrino mass and mixing scenarios. |
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| 13 | Moreover a precise determination of the PMNS matrix (which contrary |
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| 14 | to the CKM matrix is free from hadronic uncertainties) would put very severe |
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| 15 | constraints on models |
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| 16 | of fermion masses, including realistic GUT models, and thus shed some light |
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| 17 | on the underlying flavour theory. A neutrino super-beam from the CERN |
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| 18 | SPL to a megaton water \v{C}erenkov detector located at Fr\'ejus would allow |
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| 19 | to make a significant progress in this programme, reaching in particular |
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| 20 | a sensitivity to $\sin^2(2\theta_{13})$ close to $10^{-3}$ %one degree |
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| 21 | and close to $2\cdot 10^{-4}$ %0.4 degree |
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| 22 | with a Beta-beam (and $1\cdot 10^{-4}$ %0.3 degree |
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| 23 | with both Super-beam and |
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| 24 | Beta-beam), see section~\ref{sec:oscillations}. |
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| 25 | |
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| 26 | Due to its sensitivity to $\theta_{13}$, a megaton water \v{C}erenkov |
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| 27 | detector would also be sensitive to the CP violating phase |
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| 28 | $\delta$ in a large portion of the ($\Delta m^2_{12}$, |
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| 29 | $\theta_{13}$) parameter space. Establishing CP violation in the |
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| 30 | lepton sector would represent a major progress in particle |
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| 31 | physics, since CP violation has only been observed in the quark |
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| 32 | sector so far. Moreover, CP violation is a crucial ingredient of |
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| 33 | leptogenesis, a mechanism for creating the matter-antimatter |
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| 34 | asymmetry of the Universe which relies on the out-of-equilibrium |
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| 35 | decay of heavy Majorana neutrinos. Although the phase involved in |
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| 36 | oscillations is generally distinct from the phase responsible for |
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| 37 | leptogenesis, the measurement of a nonzero $\delta$ would be a |
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| 38 | strong indication that leptogenesis may be at the origin of the |
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| 39 | baryon asymmetry \cite{Fukugita:1986hr}. |
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| 40 | Indeed, standard electroweak baryogenesis would |
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| 41 | require a very light Higgs boson, which is now excluded by LEP, |
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| 42 | and only a small window remains for supersymmetric electroweak |
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| 43 | baryogenesis. |
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| 44 | %After the discovery of neutrino oscillations, leptogenesis |
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| 45 | %therefore appears as one of the most plausible explanations of the |
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| 46 | %baryon asymmetry. |
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| 47 | Another necessary ingredient of leptogenesis is the existence of Majorana |
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| 48 | neutrinos, which could be established by a positive signal in future |
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| 49 | neutrinoless double beta decay experiments. |
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