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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