1 | <html> |
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2 | <head> |
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3 | <title>Fourth-Generation Processes</title> |
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28 | <form method='post' action='FourthGenerationProcesses.php'> |
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29 | |
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30 | <h2>Fourth-Generation Processes</h2> |
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31 | |
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32 | A fourth generation can be accommodated within the Standard Model, |
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33 | without the introduction of any new concepts. Many experimental |
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34 | constraints exist, but it has not been fully excluded. Therefore |
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35 | we offer a simple implementation, along the lines of the top. |
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36 | It could also be useful as a template for studies of other |
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37 | new particles with similar characteristics. |
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38 | |
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39 | <p/> |
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40 | The fourth generation are given names as in the third, but with a prime, |
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41 | i.e. <i>b'</i> with PDG code 7, <i>t'</i> with code 8, |
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42 | <i>tau'</i> with code 17, and <i>nu'_tau</i> with code 18. |
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43 | Most important for you is to assign a mass hierarchy, to decide which |
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44 | fermions can decay into which. The current implementation assumes that |
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45 | mass splittings are big enough that fourth-generation fermions can |
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46 | decay to third-generation ones by the emission of an on-shell <i>W</i>. |
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47 | To this end, the standard three-generation CKM mixing matrix has been |
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48 | extended to include a fourth generation, see below. Since no mixing has |
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49 | been implemented in the neutrino sector it would be assumed that the |
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50 | lighter of <i>tau'</i> and <i>nu'_tau</i> is stable. No decay modes |
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51 | have been implemented that go beyond the Standard Model, so |
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52 | modifications would be needed if e.g. also SUSY is included in the game. |
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53 | |
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54 | <h3>Production processes</h3> |
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55 | |
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56 | <h4>1) <i>b'</i> processes</h4> |
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57 | |
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58 | Different ways to produce <i>b'</i> quarks, singly or in pairs. |
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59 | For a <i>b' t'</i> pair see section 3 below. |
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60 | |
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61 | <br/><br/><strong>FourthBottom:all</strong> <input type="radio" name="1" value="on"><strong>On</strong> |
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62 | <input type="radio" name="1" value="off" checked="checked"><strong>Off</strong> |
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63 | (<code>default = <strong>off</strong></code>)<br/> |
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64 | Common switch for the group of <i>b'</i> production. |
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65 | Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below. |
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66 | |
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67 | |
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68 | <br/><br/><strong>FourthBottom:gg2bPrimebPrimebar</strong> <input type="radio" name="2" value="on"><strong>On</strong> |
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69 | <input type="radio" name="2" value="off" checked="checked"><strong>Off</strong> |
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70 | (<code>default = <strong>off</strong></code>)<br/> |
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71 | Scatterings <i>g g -> b' b'bar</i>. |
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72 | Code 801. |
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73 | |
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74 | |
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75 | <br/><br/><strong>FourthBottom:qqbar2bPrimebPrimebar</strong> <input type="radio" name="3" value="on"><strong>On</strong> |
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76 | <input type="radio" name="3" value="off" checked="checked"><strong>Off</strong> |
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77 | (<code>default = <strong>off</strong></code>)<br/> |
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78 | Scatterings <i>q qbar -> b' b'bar</i> by gluon exchange. |
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79 | Code 802. |
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80 | |
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81 | |
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82 | <br/><br/><strong>FourthBottom:qq2bPrimeq(t:W)</strong> <input type="radio" name="4" value="on"><strong>On</strong> |
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83 | <input type="radio" name="4" value="off" checked="checked"><strong>Off</strong> |
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84 | (<code>default = <strong>off</strong></code>)<br/> |
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85 | Scatterings <i>q q' -> b' q''</i> by <i>t</i>-channel exchange |
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86 | of a <i>W^+-</i> boson. |
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87 | Code 803. |
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88 | |
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89 | |
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90 | <br/><br/><strong>FourthBottom:ffbar2bPrimebPrimebar(s:gmZ)</strong> <input type="radio" name="5" value="on"><strong>On</strong> |
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91 | <input type="radio" name="5" value="off" checked="checked"><strong>Off</strong> |
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92 | (<code>default = <strong>off</strong></code>)<br/> |
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93 | Scatterings <i>f fbar -> b' b'bar</i> by <i>s</i>-channel exchange |
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94 | of a <i>gamma^*/Z^0</i> boson. |
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95 | Code 804. |
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96 | |
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97 | |
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98 | <br/><br/><strong>FourthBottom:ffbar2bPrimeqbar(s:W)</strong> <input type="radio" name="6" value="on"><strong>On</strong> |
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99 | <input type="radio" name="6" value="off" checked="checked"><strong>Off</strong> |
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100 | (<code>default = <strong>off</strong></code>)<br/> |
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101 | Scatterings <i>f fbar' -> b' qbar''</i> by <i>s</i>-channel exchange |
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102 | of a <i>W^+-</i> boson. Here <i>q''</i> is either <i>u</i> or |
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103 | <i>c</i>. |
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104 | Code 805. |
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105 | |
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106 | |
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107 | <br/><br/><strong>FourthBottom:ffbar2bPrimetbar(s:W)</strong> <input type="radio" name="7" value="on"><strong>On</strong> |
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108 | <input type="radio" name="7" value="off" checked="checked"><strong>Off</strong> |
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109 | (<code>default = <strong>off</strong></code>)<br/> |
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110 | Scatterings <i>f fbar' -> b' tbar</i> by <i>s</i>-channel exchange |
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111 | of a <i>W^+-</i> boson. |
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112 | Code 806. |
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113 | |
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114 | |
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115 | <h4>2) <i>t'</i> processes</h4> |
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116 | |
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117 | Different ways to produce <i>t'</i> quarks, singly or in pairs. |
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118 | For a <i>b' t'</i> pair see section 3 below. |
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119 | |
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120 | <br/><br/><strong>FourthTop:all</strong> <input type="radio" name="8" value="on"><strong>On</strong> |
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121 | <input type="radio" name="8" value="off" checked="checked"><strong>Off</strong> |
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122 | (<code>default = <strong>off</strong></code>)<br/> |
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123 | Common switch for the group of <i>t'</i> production. |
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124 | Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below. |
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125 | |
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126 | |
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127 | <br/><br/><strong>FourthTop:gg2tPrimetPrimebar</strong> <input type="radio" name="9" value="on"><strong>On</strong> |
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128 | <input type="radio" name="9" value="off" checked="checked"><strong>Off</strong> |
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129 | (<code>default = <strong>off</strong></code>)<br/> |
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130 | Scatterings <i>g g -> t' t'bar</i>. |
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131 | Code 821. |
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132 | |
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133 | |
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134 | <br/><br/><strong>FourthTop:qqbar2tPrimetPrimebar</strong> <input type="radio" name="10" value="on"><strong>On</strong> |
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135 | <input type="radio" name="10" value="off" checked="checked"><strong>Off</strong> |
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136 | (<code>default = <strong>off</strong></code>)<br/> |
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137 | Scatterings <i>q qbar -> t' t'bar</i> by gluon exchange. |
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138 | Code 822. |
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139 | |
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140 | |
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141 | <br/><br/><strong>FourthTop:qq2tPrimeq(t:W)</strong> <input type="radio" name="11" value="on"><strong>On</strong> |
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142 | <input type="radio" name="11" value="off" checked="checked"><strong>Off</strong> |
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143 | (<code>default = <strong>off</strong></code>)<br/> |
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144 | Scatterings <i>q q' -> t' q''</i> by <i>t</i>-channel exchange |
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145 | of a <i>W^+-</i> boson. |
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146 | Code 823. |
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147 | |
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148 | |
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149 | <br/><br/><strong>FourthTop:ffbar2tPrimetPrimebar(s:gmZ)</strong> <input type="radio" name="12" value="on"><strong>On</strong> |
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150 | <input type="radio" name="12" value="off" checked="checked"><strong>Off</strong> |
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151 | (<code>default = <strong>off</strong></code>)<br/> |
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152 | Scatterings <i>f fbar -> t' t'bar</i> by <i>s</i>-channel exchange |
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153 | of a <i>gamma^*/Z^0</i> boson. |
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154 | Code 824. |
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155 | |
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156 | |
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157 | <br/><br/><strong>FourthTop:ffbar2tPrimeqbar(s:W)</strong> <input type="radio" name="13" value="on"><strong>On</strong> |
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158 | <input type="radio" name="13" value="off" checked="checked"><strong>Off</strong> |
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159 | (<code>default = <strong>off</strong></code>)<br/> |
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160 | Scatterings <i>f fbar' -> t' qbar''</i> by <i>s</i>-channel exchange |
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161 | of a <i>W^+-</i> boson. |
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162 | Code 825. |
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163 | |
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164 | |
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165 | <h4>3) Pair-processes with different flavours</h4> |
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166 | |
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167 | Different ways to produce two different fourth-generation fermions. |
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168 | |
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169 | <br/><br/><strong>FourthPair:ffbar2tPrimebPrimebar(s:W)</strong> <input type="radio" name="14" value="on"><strong>On</strong> |
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170 | <input type="radio" name="14" value="off" checked="checked"><strong>Off</strong> |
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171 | (<code>default = <strong>off</strong></code>)<br/> |
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172 | Scatterings <i>f fbar' -> t' b'bar</i> by <i>s</i>-channel exchange |
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173 | of a <i>W^+-</i> boson. |
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174 | Code 841. |
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175 | |
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176 | |
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177 | <br/><br/><strong>FourthPair:ffbar2tauPrimenuPrimebar(s:W)</strong> <input type="radio" name="15" value="on"><strong>On</strong> |
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178 | <input type="radio" name="15" value="off" checked="checked"><strong>Off</strong> |
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179 | (<code>default = <strong>off</strong></code>)<br/> |
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180 | Scatterings <i>f fbar' -> tau' nu'_taubar</i> by <i>s</i>-channel |
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181 | exchange of a <i>W^+-</i> boson. |
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182 | Code 842. |
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183 | |
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184 | |
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185 | <p/> |
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186 | Missing in this list is scatterings <i>q q' -> t' b'</i> by |
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187 | <i>t</i>-channel exchange of a <i>W^+-</i> boson, since currently |
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188 | the matrix element for such processes have not been implemented for |
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189 | two massive particles in the final state. Since this process would |
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190 | involve two CKM-suppressed vertices it ought to be small. |
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191 | |
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192 | <h3>Parameters</h3> |
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193 | |
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194 | The Cabibbo-Kobayashi-Maskawa matrix is extended by seven further values. |
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195 | So as not to mess up the Standard Model, the normal 3 * 3 matrix is |
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196 | kept unitary, and so the new off-diagonal elements lead to a slight |
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197 | breaking of this. For exploratory studies this should be good enough; |
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198 | more detailed 4 * 4 tunes to data would only make sense the day there |
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199 | are evidence for the existence of a fourth generation. |
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200 | |
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201 | <br/><br/><table><tr><td><strong>FourthGeneration:VubPrime </td><td></td><td> <input type="text" name="16" value="0.001" size="20"/> (<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table> |
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202 | The <i>V_ub'</i> matrix element in the 4 * 4 CKM matrix. |
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203 | |
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204 | |
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205 | <br/><br/><table><tr><td><strong>FourthGeneration:VcbPrime </td><td></td><td> <input type="text" name="17" value="0.01" size="20"/> (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table> |
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206 | The <i>V_cb'</i> matrix element in the 4 * 4 CKM matrix. |
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207 | |
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208 | |
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209 | <br/><br/><table><tr><td><strong>FourthGeneration:VtbPrime </td><td></td><td> <input type="text" name="18" value="0.1" size="20"/> (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table> |
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210 | The <i>V_tb'</i> matrix element in the 4 * 4 CKM matrix. |
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211 | |
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212 | |
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213 | <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimed </td><td></td><td> <input type="text" name="19" value="0.001" size="20"/> (<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table> |
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214 | The <i>V_t'd</i> matrix element in the 4 * 4 CKM matrix. |
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215 | |
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216 | |
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217 | <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimes </td><td></td><td> <input type="text" name="20" value="0.01" size="20"/> (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table> |
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218 | The <i>V_t's</i> matrix element in the 4 * 4 CKM matrix. |
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219 | |
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220 | |
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221 | <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimeb </td><td></td><td> <input type="text" name="21" value="0.1" size="20"/> (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table> |
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222 | The <i>V_t'b</i> matrix element in the 4 * 4 CKM matrix. |
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223 | |
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224 | |
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225 | <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimebPrime </td><td></td><td> <input type="text" name="22" value="0.99" size="20"/> (<code>default = <strong>0.99</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table> |
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226 | The <i>V_t'b'</i> matrix element in the 4 * 4 CKM matrix. |
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227 | |
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228 | |
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229 | <input type="hidden" name="saved" value="1"/> |
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230 | |
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231 | <?php |
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232 | echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?> |
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233 | |
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234 | <table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table> |
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235 | </form> |
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236 | |
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237 | <?php |
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238 | |
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239 | if($_POST["saved"] == 1) |
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240 | { |
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241 | $filepath = $_POST["filepath"]; |
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242 | $handle = fopen($filepath, 'a'); |
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243 | |
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244 | if($_POST["1"] != "off") |
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245 | { |
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246 | $data = "FourthBottom:all = ".$_POST["1"]."\n"; |
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247 | fwrite($handle,$data); |
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248 | } |
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249 | if($_POST["2"] != "off") |
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250 | { |
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251 | $data = "FourthBottom:gg2bPrimebPrimebar = ".$_POST["2"]."\n"; |
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252 | fwrite($handle,$data); |
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253 | } |
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254 | if($_POST["3"] != "off") |
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255 | { |
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256 | $data = "FourthBottom:qqbar2bPrimebPrimebar = ".$_POST["3"]."\n"; |
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257 | fwrite($handle,$data); |
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258 | } |
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259 | if($_POST["4"] != "off") |
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260 | { |
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261 | $data = "FourthBottom:qq2bPrimeq(t:W) = ".$_POST["4"]."\n"; |
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262 | fwrite($handle,$data); |
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263 | } |
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264 | if($_POST["5"] != "off") |
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265 | { |
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266 | $data = "FourthBottom:ffbar2bPrimebPrimebar(s:gmZ) = ".$_POST["5"]."\n"; |
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267 | fwrite($handle,$data); |
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268 | } |
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269 | if($_POST["6"] != "off") |
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270 | { |
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271 | $data = "FourthBottom:ffbar2bPrimeqbar(s:W) = ".$_POST["6"]."\n"; |
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272 | fwrite($handle,$data); |
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273 | } |
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274 | if($_POST["7"] != "off") |
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275 | { |
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276 | $data = "FourthBottom:ffbar2bPrimetbar(s:W) = ".$_POST["7"]."\n"; |
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277 | fwrite($handle,$data); |
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278 | } |
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279 | if($_POST["8"] != "off") |
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280 | { |
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281 | $data = "FourthTop:all = ".$_POST["8"]."\n"; |
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282 | fwrite($handle,$data); |
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283 | } |
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284 | if($_POST["9"] != "off") |
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285 | { |
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286 | $data = "FourthTop:gg2tPrimetPrimebar = ".$_POST["9"]."\n"; |
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287 | fwrite($handle,$data); |
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288 | } |
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289 | if($_POST["10"] != "off") |
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290 | { |
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291 | $data = "FourthTop:qqbar2tPrimetPrimebar = ".$_POST["10"]."\n"; |
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292 | fwrite($handle,$data); |
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293 | } |
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294 | if($_POST["11"] != "off") |
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295 | { |
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296 | $data = "FourthTop:qq2tPrimeq(t:W) = ".$_POST["11"]."\n"; |
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297 | fwrite($handle,$data); |
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298 | } |
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299 | if($_POST["12"] != "off") |
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300 | { |
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301 | $data = "FourthTop:ffbar2tPrimetPrimebar(s:gmZ) = ".$_POST["12"]."\n"; |
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302 | fwrite($handle,$data); |
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303 | } |
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304 | if($_POST["13"] != "off") |
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305 | { |
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306 | $data = "FourthTop:ffbar2tPrimeqbar(s:W) = ".$_POST["13"]."\n"; |
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307 | fwrite($handle,$data); |
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308 | } |
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309 | if($_POST["14"] != "off") |
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310 | { |
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311 | $data = "FourthPair:ffbar2tPrimebPrimebar(s:W) = ".$_POST["14"]."\n"; |
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312 | fwrite($handle,$data); |
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313 | } |
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314 | if($_POST["15"] != "off") |
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315 | { |
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316 | $data = "FourthPair:ffbar2tauPrimenuPrimebar(s:W) = ".$_POST["15"]."\n"; |
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317 | fwrite($handle,$data); |
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318 | } |
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319 | if($_POST["16"] != "0.001") |
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320 | { |
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321 | $data = "FourthGeneration:VubPrime = ".$_POST["16"]."\n"; |
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322 | fwrite($handle,$data); |
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323 | } |
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324 | if($_POST["17"] != "0.01") |
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325 | { |
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326 | $data = "FourthGeneration:VcbPrime = ".$_POST["17"]."\n"; |
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327 | fwrite($handle,$data); |
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328 | } |
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329 | if($_POST["18"] != "0.1") |
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330 | { |
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331 | $data = "FourthGeneration:VtbPrime = ".$_POST["18"]."\n"; |
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332 | fwrite($handle,$data); |
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333 | } |
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334 | if($_POST["19"] != "0.001") |
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335 | { |
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336 | $data = "FourthGeneration:VtPrimed = ".$_POST["19"]."\n"; |
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337 | fwrite($handle,$data); |
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338 | } |
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339 | if($_POST["20"] != "0.01") |
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340 | { |
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341 | $data = "FourthGeneration:VtPrimes = ".$_POST["20"]."\n"; |
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342 | fwrite($handle,$data); |
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343 | } |
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344 | if($_POST["21"] != "0.1") |
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345 | { |
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346 | $data = "FourthGeneration:VtPrimeb = ".$_POST["21"]."\n"; |
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347 | fwrite($handle,$data); |
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348 | } |
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349 | if($_POST["22"] != "0.99") |
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350 | { |
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351 | $data = "FourthGeneration:VtPrimebPrime = ".$_POST["22"]."\n"; |
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352 | fwrite($handle,$data); |
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353 | } |
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354 | fclose($handle); |
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355 | } |
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356 | |
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357 | ?> |
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358 | </body> |
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359 | </html> |
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360 | |
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361 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |
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362 | |
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