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2 | |
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4 | |
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5 | \section{Introduction} |
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6 | |
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7 | |
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8 | Underground water Cherenkov detectors have |
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9 | found unambiguous evidence for |
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10 | neutino oscillations and therefore beyond-the Standard Model |
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11 | physics. |
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12 | % focused much attention on neutrino physics. |
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13 | The atmospheric neutrino results of Super- Kamiokande(SK), |
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14 | followed by the solar observations of SK, SNO and KamLAND, |
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15 | have confirmed that neutrinos have mass and |
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16 | two large mixing angles. |
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17 | However, there remain many questions |
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18 | about the parameters and properties of leptons, |
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19 | some of which could be addressed by a larger (megatonne) |
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20 | underground neutrino detector. |
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21 | %nonetheless there are questions |
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22 | %remaining. More statistics are required to increase |
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23 | %the sensitivity to unknown neutino parameters, |
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24 | If the location of such a detector was |
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25 | judiciously selected, it could be |
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26 | a suitable distance along the path of |
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27 | a new high intensity |
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28 | $\nu_\mu$ beam (superbeam), and/or or $\nu_e$ beam ($\beta$ beam). |
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29 | %source = beam, not astro |
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30 | %{\it build beam and detector so can do an accelerator expt}. |
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31 | |
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32 | The observation of neutrinos from SN1987A forshadowed |
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33 | the linked results on astrophysics and neutrino physics |
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34 | that can be obtained from a supernova. Such an exploding |
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35 | star is an extraordinary source, for which it |
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36 | would be reasonable to have a detector. |
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37 | A megatonne detector could perhaps even |
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38 | see relic neutrinos |
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39 | accumulated from past supernovae. |
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40 | |
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41 | Originally, large underground detectors were built |
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42 | to look for proton decay, a prediction of |
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43 | Grand Unified Theories. Nucleon decay is |
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44 | a ``smoking gun'' for quark lepton |
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45 | unification, observation of which would |
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46 | confirm many years of theoretical speculation. |
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47 | The current lower bound on the proton lifetime from SK has |
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48 | ruled out the simplest non-supersymmetric GUT, |
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49 | a megatonne detector would |
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50 | cover a substantial area of interesting parameter |
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51 | space. |
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52 | |
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53 | |
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54 | |
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55 | \section{Bread and Butter: $\nu$ Physics} |
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56 | |
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57 | A megatonne detector would have improved sensitivity to |
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58 | currently unknown parameters of neutrino mixing. |
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59 | The neutrinos could be of astrophysical origin--- |
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60 | solar, atmospheric or from supernovae--- or $\nu$ |
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61 | beams of specific flavour and energy could be directed |
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62 | at the detector. |
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63 | %The solar and atmospheric neutrino fluxes would |
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64 | %arrive for free. |
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65 | A high intensity $\nu_\mu$ ``superbeam'', |
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66 | could be produced by increasing the intensity of the |
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67 | proton driver at the source, |
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68 | or a very pure $\nu_e$ beam could be produced |
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69 | in the $\beta$ decay of an ion beam. |
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70 | |
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71 | |
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72 | |
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73 | \subsection{status} |
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74 | |
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75 | A review of our current knowledge of neutrino parameters |
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76 | was presented by G. Fogli. |
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77 | |
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78 | Information |
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79 | \footnote{The numerical values are from the global fit |
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80 | presented by Fogli} on $\sin ^2 \theta_{23} = 0.45 |
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81 | \pm \stackrel{0.18}{_{0.11}}$, |
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82 | $\Delta m_{23}^2 = 2.4 \pm \stackrel{0.5}{_{0.6}} \times 10^{-3}$ eV$^{2}$ |
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83 | and $\sin ^2 \theta_{13} \leq 0.035$ |
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84 | is obtained from SuperKamiokande, K2K and CHOOZ. |
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85 | The evidence for atmospheric neutrino |
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86 | oscillations with large, or maximal mixing |
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87 | is robust, and confirmed with neutrinos |
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88 | from the K2K beam. |
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89 | SK has found evidence for a decrease |
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90 | in $\nu_\mu$ flux at the location |
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91 | expected for the first dip in the oscillation |
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92 | probability---this despite the smearing in |
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93 | energy and path length. |
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94 | As discussed by Fogli, the data sets can be |
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95 | combined in various ways to determine the parameters. |
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96 | The results quoted were obtained |
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97 | from the combined data of all three experiments, by |
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98 | using a three-dimensional simulation for |
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99 | the atmospheric neutrino fluxes, by including |
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100 | subleading effects due to |
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101 | $\Delta m_{12}^2$ and $\sin ^2 \theta_{12}$, |
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102 | and leaving $\sin ^2 \theta_{13}$ free. |
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103 | Letting |
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104 | $\sin ^2 \theta_{13}$ float has little effect |
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105 | because the data prefers it small. |
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106 | |
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107 | |
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108 | SNO, SK and KamLAND are sensitive to the solar mass |
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109 | difference $\Delta m_{12}^2 = 8.0 |
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110 | \pm \stackrel{0.8}{_{0.7}} \times |
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111 | 10^{-5} $ eV$^2$ and |
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112 | a large but not maximal mixing |
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113 | angle $\sin ^2 \theta_{23} = 0.31 \pm \stackrel{0.05}{_{ 0.04}} $. |
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114 | These data also prefer |
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115 | $\sin ^2 \theta_{13} \sim 0$ (a non-trivial |
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116 | consistency check with atmospheric and CHOOZ), |
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117 | so the allowed ranges for |
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118 | $\Delta m_{12}^2 $ and |
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119 | $\sin ^2 \theta_{23} $ are not significantly |
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120 | affected when $\theta_{13}$ is allowed to float. |
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121 | |
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122 | |
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123 | |
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124 | \subsection{ agenda for future experiments} |
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125 | |
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126 | The current bounds on the unknown neutrino parameters, |
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127 | and future prospects for measuring them were discussed by |
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128 | J. Ellis and G. Fogli, and T Schwetz. Some of these unknowns |
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129 | (items 4-7 of the following list) |
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130 | could be determined from more precise oscillation |
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131 | experiments. |
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132 | %---in particular from neutrino beams |
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133 | %directed at a megatonne detector. |
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134 | \begin{enumerate} |
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135 | \item the number of light neutrinos participating |
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136 | in oscillations is usually taken to be the three |
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137 | active neutrinos expected in the Standard Model. |
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138 | However, the LSND experiment found evidence |
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139 | for $\Delta m^2 \sim$ eV$^2$, which would require |
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140 | one (or more) |
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141 | additional light sterile neutrinos. |
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142 | MiniBoone is searching for oscillations |
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143 | in the LSND window; their results, |
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144 | expected in 2005, will confirm or |
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145 | rule out the LSND claim. |
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146 | \item The absolute neutrino mass scale |
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147 | is probed in three ways. |
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148 | Firstly, the endpoint spectrum of electrons in nucleon |
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149 | ($^3H$) $\beta$ decay is sensitive to the ``effective |
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150 | electron neutrino mass'' |
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151 | $$ m_e^2 = [c^2_{13} c_{12}^2 m_1^2 + |
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152 | c^2_{13} s_{12}^2 m_2^2 + |
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153 | s^2_{13} m_3^2 ]^2 \leq 1.8 ~{\rm eV}~~.$$ |
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154 | |
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155 | Cosmological Large Scale Structure is affected |
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156 | by neutrino masses, because neutrino free-streaming |
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157 | in the early Universe would suppress density fluctuations |
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158 | on small scales. Current cosmological data sets the constraint: |
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159 | $$ m_1 + m_2 + m_3 \leq 0.47 - 1.4 {\rm eV}$$ |
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160 | The range of the bound is representative of different |
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161 | results in the literature, which are based on |
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162 | inequivalent data sets. The strong bound uses |
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163 | Ly$\alpha$ data to probe small scale structure; |
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164 | this data is sometimes left out because of |
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165 | uncertain systematic errors. |
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166 | |
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167 | The final observable to which neutrino masses |
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168 | could contribute---if they are majorana--- |
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169 | is lepton number violating neutrino-less |
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170 | double $\beta$ decay ($0 \nu 2 \beta$). |
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171 | The amplitude can be written as a nuclear |
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172 | matrix element, |
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173 | $\times$ the coefficient of a $\Delta L = 2$ |
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174 | non-renormalisable operator. This coefficient |
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175 | can be calculated perturbatively from the |
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176 | new physics that permits the decay. |
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177 | When this new physics is |
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178 | majorana neutrino masses, the coefficient |
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179 | is proportional to |
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180 | $ m_{ee}$, where |
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181 | $$ |
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182 | m_{ee} = [c_{13}^2c_{12}^2m_1 + c_{13}^2s_{12}^2m_2e^{i \phi_2} |
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183 | + s_{13}^2m_3e^{i \phi_3} ] |
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184 | $$ |
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185 | The PMNS matrix has be taken |
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186 | $U = V P$, with $V$ CKM-like with one phase $\delta$ |
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187 | ($V_{13} = \sin \theta_{13}e ^{-i \delta}$), and $P = diag |
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188 | \{ 1, e^{ \phi_2/2}, e^{i (\phi_3/2 + \delta)} \} |
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189 | $ (See talk by G. Fogli.) |
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190 | |
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191 | There is a controversial claim that $0 \nu 2 \beta$ |
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192 | has been detected in $^{76}Ge$, with a rate corresponding |
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193 | to $|m_{ee}| \simeq 0.23 \pm 0.18 $ eV. A |
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194 | disagreement with the cosmological bound |
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195 | can be avoided by not using Ly$\alpha$ data. |
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196 | \item Are neutrinos Majorana or Dirac? |
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197 | Oscillation experiments are sensitive to |
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198 | mass$^2$ differences, so do not distinguish whether |
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199 | neutrinos are majorana |
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200 | or dirac. |
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201 | The majorana nature of neutrinos, which is |
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202 | ``natural'' in the popular seesaw mechanism, |
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203 | can be tested in processes that violate lepton number, |
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204 | such as $0 \nu 2 \beta$. |
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205 | \item Is the mass pattern hierarchical |
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206 | ($\Delta m_{13}^2 >0)$ or inverted ($\Delta m_{13}^2<0$)? |
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207 | Oscillation probabililities in matter, |
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208 | for neutrinos and antineutrinos, depend on this sign, |
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209 | because the matter contribution to the mass matrix |
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210 | changes sign between neutrinos and anti-neutrinos. |
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211 | Long baseline neutrino beams and the flux of |
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212 | neutrinos from supernovae are sensitive to this sign. |
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213 | \item What is $\theta_{13}$? There are |
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214 | only upper bounds on this remaining angle of the PMNS matrix, |
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215 | It can be probed by looking for a $\nu_e$ |
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216 | contribution to $\Delta m_{13}^2$ oscillations. |
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217 | This angle controls ``three flavour'' effects, like |
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218 | CP violation. |
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219 | \item What is $\delta$, the ``Dirac phase'' of the PMNS |
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220 | matrix, which contributes to CP violation in neutrino |
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221 | oscillations (multiplied by $\sin \theta_{13}$)? |
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222 | \item is $\theta_{23}$ maximal? |
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223 | \end{enumerate} |
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224 | %The sensitivity of various beam and |
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225 | %detector combinations is illustrated in figure |
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226 | %\ref{Ellis}. |
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227 | |
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228 | % \begin{figure}[ht] |
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229 | %\vspace{4cm} |
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230 | %\epsfxsize=7cm\epsfbox{Fig2.ps} |
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231 | %\hspace{1cm} |
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232 | %\epsfxsize=7cm\epsfbox{fig3a.ps} |
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233 | %\caption{ plots shown in the presentation of J Ellis, |
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234 | %showing the sensitivity to $\theta_{13}$, $\Delta m_{12}^2$, |
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235 | %and $\delta$ of various beams. } |
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236 | %%\vspace{4cm} |
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237 | %\protect\label{Ellis} |
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238 | %\end{figure} |
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239 | |
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240 | |
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241 | |
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242 | |
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243 | \subsection{$\theta_{13}$, $\delta$ and and the sign of $\Delta m_{13}^2$ } |
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244 | \label{TS} |
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245 | |
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246 | |
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247 | %Summary of discussions by Kajita, Nakahata, elsewhere? |
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248 | |
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249 | Determining items 4-6 (of the above list) |
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250 | at a future megatonne detector was |
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251 | discussed by T. Schwetz, and |
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252 | J Ellis presented prospects for beams from CERN. |
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253 | |
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254 | It is known that |
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255 | the 3-flavour oscillation probability has degeneracies, |
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256 | as can be |
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257 | seen from |
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258 | \beq |
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259 | P_{\mu e} \simeq \sin^2 2\theta_{13} \sin^2 \theta_{23} \sin^2 \Delta_{ 31} |
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260 | + \alpha^2 \sin^2 \theta_{12} \cos^2 \theta_{23} |
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261 | \Delta^2_{31} + |
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262 | \alpha \sin 2\theta_{12} |
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263 | \sin 2\theta_{13} \sin2\theta_{23} \Delta_{ 31} \sin \Delta_{ 31} \cos( |
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264 | \Delta_{ 31} \pm \delta). |
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265 | \eeq |
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266 | where $\alpha = \Delta_{21}/ \Delta_{31}$, and |
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267 | $ \Delta_{31} = (m_3^2 - m_1^2)L/4 E_\nu$. |
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268 | For instance, a measured $P_{\mu e}$ could corresponds |
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269 | to several solutions in the ($\delta, \theta_{13}$) plane. |
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270 | This is refered to as the ``intrinsic'' degeneracy. |
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271 | There are additional degeneracies associated with |
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272 | the sign of $\Delta m_{13}^2$ (``hierarchy'' degeneracy), and with |
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273 | the sign of $\pi/4 - \theta_{23}$ (``quadrant'' degeneracy), if |
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274 | $\theta_{23}$ is not maximal. |
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275 | |
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276 | The degeneracies can be resolved with |
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277 | spectral information, and by looking at |
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278 | different channels. Having a $\beta$-beam and |
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279 | superbeam is helpful in this second respect. |
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280 | Spectral information is available with |
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281 | an off-axis beam, so the ($\delta, \theta_{13}$) |
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282 | degeneracy wouuld be absent at T2K-II |
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283 | (T2K to HyperK). |
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284 | |
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285 | T Schwetz discussed using atmospheric neutrino data to |
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286 | address the degeneracies, by measuring sub-dominant |
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287 | effects due to three-flavour mixing. He showed that |
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288 | there is an enhancement in the $\nu_e$ (or $\bar{\nu}_e$) |
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289 | flux, for multi-GeV events, due to $\theta_{13}$. |
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290 | The enhancement is for neutrinos in the |
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291 | normal hierarchy, and anti-neutrinos in the |
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292 | inverted case. Since the $\nu_e$ and $\bar{\nu}_e$ |
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293 | detection cross-sections are different, |
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294 | mesuring this enhancement would give information |
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295 | on $\theta_{13}$ and the sign of $\Delta m_{13}^2$. |
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296 | Sub-GeV events could be sensitive to |
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297 | the octant of $\theta_{23}$ via |
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298 | contributions arising due to $\Delta m_{12}^2$. |
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299 | |
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300 | |
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301 | The hierarchy and octant degeneracies could be reduced at T2K-II |
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302 | by using the the atmospheric neutrino data of HyperK. |
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303 | This was shown by combining |
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304 | a numerical 3-flavour atmospheric analysis, |
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305 | with long baseline simulation of |
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306 | the beam and detector using with |
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307 | the GloBES software |
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308 | ( http://www.ph.tum.de/globes/ ). |
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309 | An example figure is shown on the right below |
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310 | (figure \ref{TSfig}). |
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311 | Preliminary results, assuming a superbeam and |
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312 | $\beta$-beam from CERN, and including atmospheric data |
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313 | at a 450 kt Cherenkov detector at Frejus, were also |
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314 | shown. |
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315 | |
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316 | In summary, the combined analysis of atmospheric and |
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317 | long baseline neutrino data at a megatonne detector |
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318 | could resolve parameter degeneracies---with the advantage |
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319 | that atmospheric neutrinos arrive ``for free''. |
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320 | |
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321 | |
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322 | |
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323 | \begin{figure}[ht] |
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324 | %\vspace{4cm} |
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325 | \epsfxsize=17cm |
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326 | \epsfbox{TS.eps} |
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327 | %\epsfxsize=7cm\epsfbox{delta.eps} |
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328 | \caption{ Resolving hierarchy(H) and octant (O) |
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329 | degeneracies using atmospheric neutrinos. The |
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330 | figures compare $\beta$-beam and SPL from CERN to Fr\'ejus, |
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331 | (details of the experiments can be found |
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332 | in the NuFact05 talks of Mezzetto and Campagne), and T2K |
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333 | to HK |
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334 | The detector in all cases is 450 kt water Cherenkov. } |
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335 | %\vspace{4cm} |
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336 | \protect\label{TSfig} |
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337 | \end{figure} |
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338 | |
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339 | |
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340 | |
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341 | |
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342 | |
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343 | \subsection{ Theoretical interest} |
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344 | |
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345 | One of the outstanding puzzles for particle theorists |
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346 | is the origin of Yukawa couplings. There are many models, |
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347 | which fit the masses |
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348 | and mixing angles observed in the quark and lepton sector, |
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349 | %with a variety of free parameters, |
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350 | %However, |
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351 | but none are particularily compelling. Additional hints from |
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352 | the data --- symmetries respected by the masses, |
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353 | constraints on the Yukawa parameters--- would be particularily |
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354 | welcome. Measuring the third leptonic mixing angle $\theta_{13}$, |
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355 | and determining whether $\theta_{23}$ is maximal, |
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356 | are both important in this respect. |
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357 | |
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358 | |
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359 | A popular mechanism to explain the smallness of |
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360 | neutrino masses is the seesaw, which has 18 parameters |
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361 | in its simplest form (type I) with three $\nu_R$. |
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362 | Twelve of these parameters appear among |
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363 | the light leptons (although not all are realistically |
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364 | measurable), and some of the remaining unknowns |
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365 | affect $\mu$ and $\tau$ decays in SUSY. So |
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366 | measuring many neutrino parameters with |
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367 | good accuracy would reduce the parameter space of seesaw models. |
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368 | |
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369 | |
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370 | If $\theta_{13}$ is found to be large ($\gappeq .01$), |
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371 | %, seefigure \ref{Ellis}, |
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372 | the phase $\delta$ of the PMNS matrix |
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373 | could be experimentally accessible. Observing CP violation |
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374 | in the leptons, for the first time, would be an exciting |
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375 | phenomenological novelty. |
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376 | %\footnote{ |
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377 | %The PMNS matrix contains one |
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378 | %unremoveable phase, so CP violation in oscillations |
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379 | %is phenomenologically ``expected''. But it is |
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380 | %important to verify expectations---we also ``expected'' |
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381 | %mixing angles in the lepton sector to be small.} |
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382 | It is also tempting to relate $\delta$ to |
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383 | the CP violation required in the generation of |
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384 | the matter excess of the Universe (baryo/lepto-genesis). |
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385 | Various leptogenesis mechanisms |
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386 | can be implemented in the seesaw model, |
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387 | and depend on some combination |
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388 | of the seesaw's complex couplings. Observing |
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389 | $\delta \neq 0$ would demonstrate that at least one |
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390 | combination of couplings is complex, thereby |
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391 | suggesting that the phases relevant for leptogenesis |
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392 | might also be present. |
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393 | |
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394 | |
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395 | |
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396 | |
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397 | |
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398 | \section{Theory Dreams: Nucleon Decay} |
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399 | |
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400 | Nucleon decay was |
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401 | the original motivations for large underground detectors, |
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402 | ancestors of the megatonne, and |
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403 | attracted attention from many speakers during the |
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404 | workshop. |
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405 | The theoretical expectations for |
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406 | the proton's lifetime were discussed in some |
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407 | detail in the talks of of J. Ellis and L. Covi. |
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408 | |
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409 | Our concept of theoretical progress is |
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410 | that we advance by unifying apparently diverse |
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411 | concepts. An example of |
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412 | successful unification is the Standard Model, which |
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413 | united electromagnetism with the weak interactions. |
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414 | Some hints that quarks and leptons might be united |
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415 | in a larger theory are the curious anomaly cancellation |
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416 | among known fermions---where |
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417 | the quarks and leptons cancel each others contributions |
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418 | to dangerous operators which would destroy |
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419 | the consistency (and experimental accuracy) |
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420 | of the SM. Another tantalising hint is |
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421 | that the strong, and electroweak gauge couplings become equal |
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422 | at $\Lambda \sim 10^{16}$ GeV, suggesting a |
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423 | unique gauge interaction at this scale. |
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424 | |
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425 | Unifying the quarks and leptons into |
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426 | a multiplet means that there are particles |
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427 | in the theory that turn quarks into leptons, |
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428 | so baryons can decay. Observing proton decay would |
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429 | be a smoking gun for such theories, |
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430 | confirming that our theoretical preference |
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431 | for unified theories is reflected in nature---and |
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432 | it could probe higher energy scales, |
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433 | or shorter distances, than any previous observation. |
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434 | It also could give some information on mixing |
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435 | angles in the right-handed quark sector, about which |
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436 | the Standard Model says nothing. |
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437 | |
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438 | |
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439 | \subsection{SU(5)} |
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440 | |
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441 | |
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442 | The simplest GUT is SU(5), the |
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443 | lowest rank (``smallest'') group capable |
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444 | of accomodating all the SM particles. % is SU(5), |
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445 | %of rank 4, which was much studied at the birth of GUTS. |
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446 | SO(10) is the one possibility at rank 5, and it |
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447 | has the advantage over SU(5) of accomodating |
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448 | the right-handed neutrino (SM gauge singlet) |
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449 | in its 16-dimensional multiplets. At rank six |
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450 | is $E_6$, which appears in some string models. |
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451 | |
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452 | In the minimal SU(5) GUT, |
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453 | the colour-triplet $d^c = \overline{d_R}$ are combined with |
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454 | the lepton SU(2) doublet $\ell_L$ into a |
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455 | $\bar{5}$, and the $e^c$ shares a 10 |
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456 | with the $q_L$ and $u^c$. |
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457 | The X and Y gauge bosons, |
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458 | which acquire masses $\sim M_{GUT}$ when |
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459 | SU(5) is broken, have Baryon + Lepton |
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460 | number violating gauge interactions because |
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461 | they mix different multiplet members. |
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462 | They mediate proton decay |
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463 | via dimension six operators such as |
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464 | \beq |
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465 | \frac{ g_5^2}{M_X^2} \epsilon_{\alpha \beta \gamma} |
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466 | (\overline{d^c}_{\alpha,k} |
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467 | \overline{u^c}_{\beta,j} q_{\gamma , j} \ell _k - |
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468 | \overline{e^c}_{k} |
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469 | \overline{u^c}_{\alpha,j} q_{\beta , j} q_{\gamma ,k} |
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470 | ) |
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471 | \eeq |
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472 | There are also operators induced by GUT Higgses, |
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473 | with baryon number violating Yukawa-strength couplings. |
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474 | |
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475 | Proton decay is expected |
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476 | at rates |
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477 | \beq |
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478 | \Gamma_{p} = C \frac{\alpha_{5}^2 m_p^5}{M_X^4} |
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479 | \eeq |
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480 | where $C$ is a constant englobing mixing angles, |
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481 | renormalisation group running, and strong |
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482 | interaction effects. The dominant decay channel in |
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483 | non-supersymmetric SU(5) is $ p \rightarrow \pi^0 e^+$. |
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484 | The experimental limit |
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485 | $\tau_{p \rightarrow \pi e} > 6.9 \times 10^{33}$ years, |
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486 | imposes $M_X \geq 7.3 \times 10^{15}$ GeV, |
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487 | so non-SUSY SU(5) is |
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488 | ruled out because this is above |
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489 | the mass scale where the gauge couplings approximately |
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490 | unify. |
---|
491 | |
---|
492 | |
---|
493 | |
---|
494 | |
---|
495 | Proton decay in supersymmetric SU(5) |
---|
496 | is different in many respects. The GUT scale |
---|
497 | (determined from gauge coupling unification) is |
---|
498 | higher, so decays mediated by |
---|
499 | $X$ and $Y$ are slower. However, there are new |
---|
500 | {\it dimension 5} operators, induced by |
---|
501 | the coloured triplet Higgsino |
---|
502 | that shares a 5 with SM-type doublet Higgsinos, and which |
---|
503 | has Yukawa couplings to SM fields. Schematically |
---|
504 | these operators can be written |
---|
505 | $$ |
---|
506 | \frac{Y^{ij}_{qq} Y^{km}_{ql}}{2 M_c } |
---|
507 | Q_iQ_jQ_kL_m + |
---|
508 | \frac{ Y^{ij}_{ue} Y^{km}_{ud} }{ M_c } U^c_i E^c_j U^c_k D^c_m |
---|
509 | $$ |
---|
510 | where $M_c$ is the triplet |
---|
511 | Higgsino mass $\leq M_X$, |
---|
512 | the capitals are superfields, two of which |
---|
513 | are scalars and two fermions. |
---|
514 | Dressing this operator with the exchange |
---|
515 | of a ``-ino'' gives a 4-fermion operator |
---|
516 | $\propto 1/(m_{SUSY} M_{c})$. This is |
---|
517 | enhanced with respect to the $X$-boson |
---|
518 | exchange, but suppressed by small Yukawa couplings. |
---|
519 | In addition, the SM SU(2) and SU(3) |
---|
520 | contractions are antisymmetric, so |
---|
521 | the operator is flavour non-diagonal, giving |
---|
522 | a dominant decay $p \rightarrow K^+ \bar{\nu}$. |
---|
523 | |
---|
524 | There are relations among the quark and lepton |
---|
525 | Yukawa couplings, |
---|
526 | which depend on the GUT Higgs content of |
---|
527 | the model. |
---|
528 | The simplest would be for all the Yukawa matrices |
---|
529 | to be equal at the GUT scale, but some |
---|
530 | differences must be included to |
---|
531 | fit the observed fermion masses. |
---|
532 | The proton lifetime in SUSY SU(5) depends |
---|
533 | which Yukawa matrices are equal at the GUT scale: |
---|
534 | setting $Y_{ql} = Y_{ud}$ equal to the down |
---|
535 | Yukawa matrix $Y_d$ predicts a a proton lifetime shorter |
---|
536 | than the current SK limit of $ |
---|
537 | \tau_{p \rightarrow K \bar{\nu}} >1.9 \times 10^{33}$ years. |
---|
538 | However, setting $Y_{ql} = Y_{ud}$ equal to the |
---|
539 | charged lepton Yukawa $Y_e$ changes the |
---|
540 | dependence of $\tau_p$ on the fermion mixing |
---|
541 | angles, so lifetimes |
---|
542 | in excess |
---|
543 | of the bound |
---|
544 | can be found. |
---|
545 | The proton lifetime in SUSY SU(5) |
---|
546 | is uncertain due to the non-unification of |
---|
547 | Yukawa couplings. |
---|
548 | |
---|
549 | |
---|
550 | |
---|
551 | A possible string-motivated GUT model, discussed |
---|
552 | by J Ellis, is |
---|
553 | flipped SU(5)$\times U(1)$, where |
---|
554 | the SU(2) doublets of the SM are inverted |
---|
555 | ($\nu \leftrightarrow e, u \leftrightarrow d$) |
---|
556 | in the GUT multiplets. This extends |
---|
557 | the $p \rightarrow K^+ \bar{\nu}$ lifetime |
---|
558 | to $\tau \gsim 10^{35} - 10^{36}$ years, |
---|
559 | %CITE ? %\cite{Ellis:2002vk} |
---|
560 | %\bibitem{Ellis:2002vk} |
---|
561 | %J.~R.~Ellis, D.~V.~Nanopoulos and J.~Walker, |
---|
562 | %%``Flipping SU(5) out of trouble,'' |
---|
563 | %Phys.\ Lett.\ B {\bf 550} (2002) 99 |
---|
564 | %[arXiv:hep-ph/0205336]. |
---|
565 | %%%CITATION = HEP-PH 0205336;%%, |
---|
566 | potentially testable at a megatonne detector. |
---|
567 | |
---|
568 | \subsection{ SO(10) in six space dimensions} |
---|
569 | |
---|
570 | |
---|
571 | In recent years, theorists have |
---|
572 | constructed models in $d>4$ dimensional |
---|
573 | space, with the additional dimensions |
---|
574 | compactified at some scale $\ll m_{pl}$. |
---|
575 | These models offer a framework to |
---|
576 | study new physics possibilities not |
---|
577 | included in the MSSM. L Covi discussed proton |
---|
578 | decay in a 6-dimensional SUSY SO(10) model, where |
---|
579 | the extra 2 dimensions are compactified |
---|
580 | on a torus (that has additional discrete symmetries). |
---|
581 | The four fixed points of this torus correspond |
---|
582 | to 4-dimensional branes, where SM |
---|
583 | particles can reside. Each |
---|
584 | SM generation lives at a different fixed point, |
---|
585 | with a different breaking of SO(10), so the Yukawas |
---|
586 | in this model are different from 4-dimensional |
---|
587 | SO(10). The higgsino mixing |
---|
588 | which allowed the dimension 5 proton decay |
---|
589 | operators is suppressed, so |
---|
590 | the dimension 6 $X$-mediated diagrams |
---|
591 | dominate in this supersymmetric extra-dimensional |
---|
592 | model. The proton decay rates |
---|
593 | are slightly larger than 4-dimensional SU(5) due to |
---|
594 | the sum over the tower of Kaluza-Klein $X$ modes, |
---|
595 | but they differ in the flavour |
---|
596 | structure. This has characteristic |
---|
597 | signatures, such as suppressing |
---|
598 | $p \rightarrow K^0 \mu^+$. The |
---|
599 | current bound $\tau_{p \rightarrow \pi^0 e^+} |
---|
600 | \geq 6.9 \times 10^{33}$ years implies in |
---|
601 | this model |
---|
602 | $M_X > 9.6 \times 10^{15}$ GeV $ \sim M_{GUT}$, |
---|
603 | suggesting that the proton could |
---|
604 | be discovered to have a lifetime $\sim 10^{34}$ years. |
---|
605 | |
---|
606 | |
---|
607 | |
---|
608 | In summary, proton decay is an unmistakable |
---|
609 | footprint of Unification, and is just around |
---|
610 | the corner in many models. Looking to the |
---|
611 | future, once proton decay is observed, |
---|
612 | the branching ratios will open a new |
---|
613 | perspective on the structure and origin |
---|
614 | of the Yukawa matrices, giving new |
---|
615 | information on the Yukawa puzzle. |
---|
616 | |
---|
617 | |
---|
618 | |
---|
619 | \section{From the Sky: Supernova Neutrinos} |
---|
620 | |
---|
621 | Supernova neutrinos were discussed by A Dighe |
---|
622 | (galactic supernovae) and S Ando(relic neutrinos), |
---|
623 | and also by G Fogli. Astrophysical |
---|
624 | observation of nearby galaxies suggests |
---|
625 | that 1-4 supernovae should take place in our galaxy |
---|
626 | per century. Neutrinos carry $ 99 \%$ of the |
---|
627 | star's binding energy, |
---|
628 | so these infrequent events could |
---|
629 | be a fund of information about |
---|
630 | neutrino parameters and supernova astrophysics. |
---|
631 | |
---|
632 | |
---|
633 | A real-time SN within 10 kpc may determine whether the |
---|
634 | hierarchy is normal or inverted, and be sensitive to |
---|
635 | very small values of $\sin \theta_{13}$. |
---|
636 | A megatonne detector is probably required to see |
---|
637 | these effects. |
---|
638 | The neutrino signal could also trace |
---|
639 | the outward propagation of the shock which powers the optical |
---|
640 | explosion. |
---|
641 | |
---|
642 | |
---|
643 | %determine the location |
---|
644 | %of the SN in the sky to $\sim 10 ^o$ ( this could |
---|
645 | %be improved by a factor of 2 to 3 with Gadolinium). |
---|
646 | |
---|
647 | |
---|
648 | |
---|
649 | While waiting for the next galactic supernova, |
---|
650 | detectors could look for ``supernovae relic |
---|
651 | neutrinos'' (SRN), the diffuse background of neutrinos |
---|
652 | emitted by past supernovae. SK's present limit on |
---|
653 | this flux is background-limited, and |
---|
654 | just above predictions. Detecting these neutrinos |
---|
655 | could give useful information on neutrinos and the |
---|
656 | history of star formation. |
---|
657 | |
---|
658 | \subsection{soon in our galaxy?} |
---|
659 | |
---|
660 | |
---|
661 | A star of mass $\gsim 8 {\cal M}_{\odot}$ becomes |
---|
662 | unstable at the end of its life. It resembles |
---|
663 | an onion, with the different layers burning lighter |
---|
664 | elements into heavier, the end-products of one |
---|
665 | layer serving as fuel for the one underneath. |
---|
666 | At the centre develops an iron core, which eventually |
---|
667 | cannot support the outer layers, and collapses. |
---|
668 | Most of the binding energy is released as |
---|
669 | neutrinos. |
---|
670 | |
---|
671 | The SN neutrino flux has various components. |
---|
672 | The neutronisation burst takes place |
---|
673 | in the first 10 ms, as the |
---|
674 | heavy nuclei break up. It consists of $\nu_e$ |
---|
675 | from $p + e \rightarrow n + \nu_e$, and is |
---|
676 | emitted from the ``neutrinosphere'', that is, |
---|
677 | the radius from which neutrinos can free-stream |
---|
678 | outwards. The core density is near nuclear, above |
---|
679 | the $\sim 10^{10}$ g/cm$^3$ required |
---|
680 | to trap a 10 MeV neutrino. |
---|
681 | |
---|
682 | For the following 10 seconds, the core cools |
---|
683 | by emitting $\nu$ and $\bar{\nu}$ of all flavours. |
---|
684 | 99 $\%$ of the SN energy is emitted in |
---|
685 | these fluxes, refered to as ``initial'' |
---|
686 | fluxes $F^0$, whose |
---|
687 | characteristics are predicted to be flavour dependent. |
---|
688 | In particular, the average energies |
---|
689 | of $\nu_e$, $\bar{\nu}_e$ |
---|
690 | and $\nu_x$ are predicted to differ: |
---|
691 | %with the average energies |
---|
692 | $E_0(\nu_e) \sim 10-12$ MeV, |
---|
693 | $E_0(\bar{\nu}_e) \sim 13-16$ MeV, |
---|
694 | and $E_0({\nu}_x) \sim 15-25$ MeV. |
---|
695 | The more weakly interacting neutrinos are |
---|
696 | more energetic because they escape |
---|
697 | from closer to the hot centre of the star. |
---|
698 | |
---|
699 | As the neutrinos travel outwards, they pass |
---|
700 | through ever-decreasing density, so |
---|
701 | matter effects on the mixing are |
---|
702 | crucial. Level-crossing occurs when |
---|
703 | $\Delta m^2 \cos 2 \theta = \pm 2 \sqrt{2} E_\nu G_F n_e$, |
---|
704 | where the $+$ ($-$) refers to (anti) neutrinos. |
---|
705 | Flavour conversion is |
---|
706 | possible at two level crossings, |
---|
707 | corresponding to the solar and atmospheric |
---|
708 | mass differences, and can |
---|
709 | appear in the $\nu$ or the $\bar{\nu}$ |
---|
710 | depending on the mass hierarchy. This will mix the |
---|
711 | initial neutrino fluxes, which were labelled by flavour. |
---|
712 | |
---|
713 | Towards the centre of the star, $\nu_e$ is the heaviest neutrino. |
---|
714 | In the normal mass hierarchy, $\nu_e$ |
---|
715 | has a level crossing at the |
---|
716 | H resonance, which arises at a matter density |
---|
717 | $\sim 10^3$ g/cm$^3$, |
---|
718 | where $\nu_3$ can |
---|
719 | transform to $\nu_2$ via the atmospheric |
---|
720 | mass difference and $\theta_{13}$. % at this |
---|
721 | %resonance. |
---|
722 | The H resonance takes place in the $\bar{\nu}_e$ |
---|
723 | channel, for the inverted mass hierachy. |
---|
724 | The L resonance arises at a matter density |
---|
725 | $\sim 10$ g/cm$^3$. It is in the $\nu$ channel for |
---|
726 | both hierarchies, and crosses $\nu_2$ with |
---|
727 | $\nu_1$ via the solar mass difference and angle. |
---|
728 | The level crossing probability is adiabatic |
---|
729 | for the L resonance, and for the H resonance |
---|
730 | when $\sin^2 \theta_{13} \gappeq 10^{-3}$. |
---|
731 | %(refered to as ``large'' for the remainder |
---|
732 | %of this section.) |
---|
733 | It is non-adiabatic |
---|
734 | at the H resonance if |
---|
735 | $\sin^2 \theta_{13} \lappeq 10^{-3}$. |
---|
736 | %(``small, for the remainder of this section.) |
---|
737 | The fluxes arriving at the earth ($F$) depend on |
---|
738 | the initial fluxes ($F^0$) and the oscillation probabilities |
---|
739 | ($p$ and $\bar{p}$): |
---|
740 | $$ |
---|
741 | F_{\nu_e} = pF^0_{\nu_e} + (1 - p)F^0_{\nu_x} |
---|
742 | ~~~ |
---|
743 | F_{\bar{\nu}_e} = \bar{p} F^0_{\bar{\nu}_e} + (1 - \bar{p})F^0_{\nu_x} |
---|
744 | $$ |
---|
745 | (There is a related formula for $F_{{\nu}_x}$.) |
---|
746 | There are three interesting cases: |
---|
747 | \begin{itemize} |
---|
748 | \item Case A: normal hierarchy, $\sin^2 \theta_{13} \gappeq 10^{-3}$, |
---|
749 | ($p = 0$, $\bar{p} = \cos^2 \theta_{\odot}$) |
---|
750 | \item Case B: inverted hierarchy, $\sin^2 \theta_{13} \gappeq 10^{-3}$ |
---|
751 | (($p = \sin^2 \theta_{\odot}$, $\bar{p} = 0$) |
---|
752 | \item Case C: any hierarchy, $\sin^2 \theta_{13} \lappeq 10^{-3}$ |
---|
753 | ($p = \sin^2 \theta_{\odot}$, $\bar{p} = \cos^2 \theta_{\odot}$) |
---|
754 | \end{itemize} |
---|
755 | |
---|
756 | |
---|
757 | A Dighe discussed whether these cases could be distinguished |
---|
758 | in the observable signal, given that the initial |
---|
759 | spectra are poorly known, and only the final spectra for |
---|
760 | $\bar{\nu}_e$ are cleanly available. It is |
---|
761 | difficult to find observables that do not |
---|
762 | depend on assumptions about the initial spectra. |
---|
763 | a possibility, if the SN neutrino flux crosses |
---|
764 | the earth, is to look for oscillations in the |
---|
765 | signal due to matter effects in the earth. |
---|
766 | This would contribute high frequency |
---|
767 | wiggles to the spectrum, which could be |
---|
768 | extracted form the data at a megatonne |
---|
769 | detector. |
---|
770 | For the normal hierarchy or small |
---|
771 | $\theta_{13}$, these earth effects would |
---|
772 | appear in the $\bar{\nu}_e$ channel, so |
---|
773 | observing such wiggles would eliminate case B. |
---|
774 | |
---|
775 | It could also be possible to identify |
---|
776 | earth effects if the SN is observed with two detectors, |
---|
777 | where one is in the earth's shadow and |
---|
778 | the other not. As A. Dighe discussed, IceCube could |
---|
779 | be the second detector, which would be complementary |
---|
780 | to Hyper-K. |
---|
781 | |
---|
782 | |
---|
783 | Neutrinos have a crucial role in the explosion of supernovae, |
---|
784 | for instance the energy they deposit in the shock may |
---|
785 | be the critical contribution that allows |
---|
786 | the star to explode. The interactions between |
---|
787 | the shock and the outgoing neutrinos may also |
---|
788 | provide information on the neutrino parameters. As the shock passes |
---|
789 | through the $H$ resonance region, it can |
---|
790 | make adiabatic transitions non-adiabatic, |
---|
791 | thereby temporarily turning scenarios A and B, |
---|
792 | into scenario C. One can therefore hope to |
---|
793 | to track the shock fronts through the |
---|
794 | star in the time-dependent neutrino signal. |
---|
795 | |
---|
796 | |
---|
797 | A nearby supernova would illuminate |
---|
798 | the earth with neutrinos. This flux can be |
---|
799 | used to simultaneously obtain information about |
---|
800 | the source, and about neutrino properties. |
---|
801 | At a megatonne detector, |
---|
802 | ``earth effects'' in the |
---|
803 | neutrino spectra could be observed, |
---|
804 | which would give SN-model |
---|
805 | independent information on the hierarchy |
---|
806 | (inverted vs normal) and whether $\theta_{13}$ |
---|
807 | is large or small. Alternatively, if |
---|
808 | the SN neutrinos do not cross the earth, |
---|
809 | information about neutrino parameters |
---|
810 | could be extracted from shock wave |
---|
811 | propagation effects in the neutrino |
---|
812 | spectra. |
---|
813 | |
---|
814 | |
---|
815 | \subsection{relics} |
---|
816 | |
---|
817 | |
---|
818 | Most of the energy of a supernova is released |
---|
819 | as neutrinos. The diffuse background of |
---|
820 | these neutrinos, today, depends on the |
---|
821 | neutrino spectrum emitted from each explosion, |
---|
822 | on the oscillation of those neutrinos in |
---|
823 | the SN and in the earth, and on the |
---|
824 | supernova rate over the past history of |
---|
825 | the Universe. |
---|
826 | |
---|
827 | As discussed in the previous section, the neutrino |
---|
828 | fluxes emitted from the SN core are expected to |
---|
829 | be flavour dependent, and to oscillate |
---|
830 | due to matter effects as they leave the star. For |
---|
831 | instance, in the normal hierarchy, a $\bar{\nu}_e$ |
---|
832 | emitted from the core is the lightest $\bar{\nu}$, |
---|
833 | due to matter effects, so it will exit |
---|
834 | the star as $\bar{\nu}_1$. The observed $\bar{\nu}_e$ |
---|
835 | flux will therefore be |
---|
836 | $$ F_{\bar{\nu}_e} = | U_{ei}|^2 F_{\bar{\nu}_i} |
---|
837 | = | U_{e1}|^2 F^0_{\bar{\nu}_e } |
---|
838 | + (1 - | U_{e1}|^2) F^0_{\bar{\nu}_x} |
---|
839 | $$ |
---|
840 | so $ (1 - | U_{e1}|^2) \sim 30 \% $ comes from the |
---|
841 | harder $\nu_x$ spectrum. The oscillations |
---|
842 | enhance the high-energy tail, but not dramatically |
---|
843 | in the detectable energy range ($< 30$ MeV). |
---|
844 | |
---|
845 | |
---|
846 | The SN rate is infered from the star formation rate, |
---|
847 | which can be extracted from other cosmological observables. |
---|
848 | Using the recent Galactic Evolution Explorer data, |
---|
849 | the event rate at SK can be calculated, and is |
---|
850 | found to be mostly due to SN at $z < 1$. |
---|
851 | A few $\bar{\nu}_e p \rightarrow n e^+$ events |
---|
852 | per year are predicted in the $E > 18$ MeV window |
---|
853 | where the flux exceeds the solar and armospheric |
---|
854 | neutrinos. Unfortunately, in this range there |
---|
855 | is a background from the decays of slowly moving muons, |
---|
856 | which are produced |
---|
857 | by atmospheric $\nu_\mu$ and are invisible at SK. |
---|
858 | So SK can set an upper limit on the SRN flux, |
---|
859 | which can then be inverted into a constraint |
---|
860 | on the supernova rate. The bound is just above |
---|
861 | theoretical predictions, so SRN might be seen |
---|
862 | using 5-10 years of data. |
---|
863 | |
---|
864 | The background could be reduced by |
---|
865 | adding Gadolinium to a water Cherenkov |
---|
866 | detector. This would tag the neutrons produced |
---|
867 | in $\bar{\nu}_e p \rightarrow n e^+$, |
---|
868 | and therefore distinguish the $\bar{\nu}_e$ |
---|
869 | from other neutrinos. Liquid Argon detectors |
---|
870 | are sensitive to $\nu_e$, so would be complementary |
---|
871 | to a water detector. |
---|
872 | |
---|
873 | S. Ando also discussed the possibility of observing, |
---|
874 | at a megatonne detector, a few neutrinos from SN |
---|
875 | in nearby galaxies ($\sim$ Mpc away). This would give |
---|
876 | the time of the collapse, helpful for gravitational |
---|
877 | wave searches. |
---|
878 | |
---|
879 | In summary, the SK limit on supernovae relic |
---|
880 | neutrinos is just above the theoretical prediction; |
---|
881 | a future megatonne detector should therefore |
---|
882 | have a good chance to see them. |
---|
883 | At a megatonne Cerenkov detector, a 5 $\sigma$ detection could |
---|
884 | be possible with pure water after a few years, |
---|
885 | ($\sim$ 300 events/yr would be expected with Gd). |
---|
886 | A 100 kt liquid Argon detector would expect |
---|
887 | $\sim 57 \pm 12 $ events after 5 years. |
---|
888 | |
---|
889 | |
---|
890 | |
---|
891 | |
---|
892 | %\section*{Acknowledgements} |
---|
893 | |
---|
894 | \begin{thebibliography}{222222} |
---|
895 | |
---|
896 | |
---|
897 | \end{thebibliography} |
---|
898 | |
---|
899 | |
---|
900 | |
---|
901 | |
---|
902 | |
---|
903 | |
---|
904 | |
---|
905 | |
---|
906 | |
---|
907 | |
---|
908 | |
---|
909 | |
---|
910 | |
---|
911 | |
---|
912 | |
---|
913 | |
---|