1 | \subsection{Proton decay} |
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2 | |
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3 | Proton decay is one of the few predictions of Grand Unified Theories |
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4 | that can be tested in low-energy experiments. Its discovery would |
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5 | definitely testify for a more fundamental structure beyond the Standard |
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6 | Model. |
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7 | |
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8 | In the past twenty years, the first generation (IMB, Fr{\'e}jus, Kamiokande) |
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9 | and second generation (Super-Kamiokande) proton decay experiments have |
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10 | already put stringent lower limits on the partial proton lifetimes, |
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11 | qualitatively ruling out non-supersymmetric $SU(5)$ theories (first generation) |
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12 | and the minimal supersymmetric $SU(5)$ theory (second generation). |
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13 | A megaton-scale |
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14 | water \v{C}erenkov detector would improve further the experimental sensitivity |
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15 | to proton decay by more than one order of magnitude and allow to probe |
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16 | non-minimal $SU(5)$ models as well as other types of GUTs, such as $SO(10)$, |
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17 | flipped $SU(5)$ and higher-dimensional GUTs. |
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18 | Indeed, recent experimental and theoretical progresses point |
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19 | towards smaller values of the partial lifetime of the proton into |
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20 | $\pi^0 e^+$, implying that this decay mode -- the most |
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21 | model-independent one -- is not out of reach, contrary to previous |
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22 | expectations. Using the new, more accurate lattice calculation of |
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23 | the nucleon decay matrix element one can estimate |
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24 | $\tau (p \rightarrow \pi^0 e^+) |
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25 | \approx 10^{35}\, \mbox{yrs}\, (M_X / 10^{16}\, |
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26 | \mbox{GeV})^4\, |
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27 | ((1/25) / \alpha_{GUT})^2$, |
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28 | where $M_X$ is the mass of the |
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29 | superheavy gauge bosons mediating proton decay, |
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30 | $\alpha_{GUT} |
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31 | \equiv g^2_{GUT} / 4 \pi$ and $g_{GUT}$ is the value of the GUT |
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32 | gauge coupling at the unification scale. This is to be compared |
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33 | with the present Super-Kamiokande lower limit ($5 \times 10^{33}\, |
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34 | \mbox{yrs}$), and with the expected sensivity of a megaton water |
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35 | \v{C}erenkov detector ($10^{35}\, \mbox{yrs}$ after 10 years |
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36 | of data taking for MEMPHYS). |
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37 | |
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38 | The dominant decay channel in supersymmetric GUTs, |
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39 | $p \rightarrow K^+ \bar \nu$, is much more model-dependent. The corresponding |
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40 | decay rate indeed depends on the couplings and masses of the supersymmetric |
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41 | partners of the heavy colour-triplet Higgs bosons, and on the details of the |
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42 | sparticle spectrum. The effective triplet mass, in particular, is extremely |
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43 | dependent on the GUT model. |
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44 | %In the |
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45 | %simplest models, $\tau (p \rightarrow K^+ \bar \nu)$ strongly depends on |
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46 | %$\tan \beta$, the ratio of the vevs of the two Higgs bosons of the MSSM; |
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47 | %larger values of $\tan \beta$ yield shorter values of |
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48 | %$\tau (p \rightarrow K^+ \bar \nu)$. |
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49 | In many models, one finds an upper limit $\tau (p \rightarrow K^+ \bar \nu) |
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50 | \leq \mbox{few}\, 10^{34}\, \mbox{yrs}$ |
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51 | \cite{Dermisek:2000hr}\cite{Babu:1998wi}\cite{Altarelli:2000fu}, |
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52 | to be compared with the present Super-Kamioka nde lower limit |
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53 | ($1.6 \times 10^{33}\, \mbox{yrs}$), and with the expected sensivity of |
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54 | a megaton water \v{C}erenkov detector ($2 \times 10^{34}\, \mbox{yrs}$ after |
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55 | 10 years for MEMPHYS). |
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56 | |
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57 | There are many more decay channels that could be accessible to a megaton |
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58 | water \v{C}erenkov detector. The measurement of several partial lifetimes |
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59 | would allow to discriminate between different Grand Unified models, at a time |
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60 | when, after several years of LHC running, |
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61 | the supersymmetry landscape will be drastically clarified, |
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62 | through discovery or severe exclusion limits. Therefore the predictions |
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63 | of proton lifetime, in constrained or more general supersymmetric models, |
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64 | will be sharpened even further. |
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65 | |
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66 | |
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