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28 | <form method='post' action='CouplingsAndScales.php'> |
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29 | |
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30 | <h2>Couplings and Scales</h2> |
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31 | |
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32 | Here is collected some possibilities to modify the scale choices |
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33 | of couplings and parton densities for all internally implemented |
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34 | hard processes. This is based on them all being derived from the |
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35 | <code>SigmaProcess</code> base class. The matrix-element coding is |
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36 | also used by the multiparton-interactions machinery, but there with a |
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37 | separate choice of <i>alpha_strong(M_Z^2)</i> value and running, |
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38 | and separate PDF scale choices. Also, in <i>2 -> 2</i> and |
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39 | <i>2 -> 3</i> processes where resonances are produced, their |
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40 | couplings and thereby their Breit-Wigner shapes are always evaluated |
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41 | with the resonance mass as scale, irrespective of the choices below. |
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42 | |
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43 | <h3>Couplings and K factor</h3> |
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44 | |
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45 | The size of QCD cross sections is mainly determined by |
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46 | <br/><br/><table><tr><td><strong>SigmaProcess:alphaSvalue </td><td></td><td> <input type="text" name="1" value="0.1265" size="20"/> (<code>default = <strong>0.1265</strong></code>; <code>minimum = 0.06</code>; <code>maximum = 0.25</code>)</td></tr></table> |
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47 | The <i>alpha_strong</i> value at scale <i>M_Z^2</i>. |
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48 | |
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49 | |
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50 | <p/> |
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51 | The actual value is then regulated by the running to the <i>Q^2</i> |
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52 | renormalization scale, at which <i>alpha_strong</i> is evaluated |
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53 | <br/><br/><table><tr><td><strong>SigmaProcess:alphaSorder </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table> |
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54 | Order at which <ei>alpha_strong</ei> runs, |
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55 | <br/> |
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56 | <input type="radio" name="2" value="0"><strong>0 </strong>: zeroth order, i.e. <ei>alpha_strong</ei> is kept fixed.<br/> |
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57 | <input type="radio" name="2" value="1" checked="checked"><strong>1 </strong>: first order, which is the normal value.<br/> |
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58 | <input type="radio" name="2" value="2"><strong>2 </strong>: second order. Since other parts of the code do not go to second order there is no strong reason to use this option, but there is also nothing wrong with it.<br/> |
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59 | |
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60 | <p/> |
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61 | QED interactions are regulated by the <i>alpha_electromagnetic</i> |
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62 | value at the <i>Q^2</i> renormalization scale of an interaction. |
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63 | <br/><br/><table><tr><td><strong>SigmaProcess:alphaEMorder </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = -1</code>; <code>maximum = 1</code>)</td></tr></table> |
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64 | The running of <ei>alpha_em</ei> used in hard processes. |
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65 | <br/> |
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66 | <input type="radio" name="3" value="1" checked="checked"><strong>1 </strong>: first-order running, constrained to agree with <code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass. <br/> |
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67 | <input type="radio" name="3" value="0"><strong>0 </strong>: zeroth order, i.e. <ei>alpha_em</ei> is kept fixed at its value at vanishing momentum transfer.<br/> |
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68 | <input type="radio" name="3" value="-1"><strong>-1 </strong>: zeroth order, i.e. <ei>alpha_em</ei> is kept fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value at the <ei>Z^0</ei> mass. <br/> |
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69 | |
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70 | <p/> |
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71 | In addition there is the possibility of a global rescaling of |
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72 | cross sections (which could not easily be accommodated by a |
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73 | changed <i>alpha_strong</i>, since <i>alpha_strong</i> runs) |
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74 | <br/><br/><table><tr><td><strong>SigmaProcess:Kfactor </td><td></td><td> <input type="text" name="4" value="1.0" size="20"/> (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 4.0</code>)</td></tr></table> |
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75 | Multiply almost all cross sections by this common fix factor. Excluded |
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76 | are only unresolved processes, where cross sections are better |
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77 | <?php $filepath = $_GET["filepath"]; |
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78 | echo "<a href='TotalCrossSections.php?filepath=".$filepath."' target='page'>";?>set directly</a>, and |
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79 | multiparton interactions, which have a separate <i>K</i> factor |
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80 | <?php $filepath = $_GET["filepath"]; |
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81 | echo "<a href='MultipartonInteractions.php?filepath=".$filepath."' target='page'>";?>of their own</a>. |
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82 | This degree of freedom is primarily intended for hadron colliders, and |
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83 | should not normally be used for <i>e^+e^-</i> annihilation processes. |
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84 | |
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85 | |
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86 | <h3>Renormalization scales</h3> |
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87 | |
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88 | The <i>Q^2</i> renormalization scale can be chosen among a few different |
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89 | alternatives, separately for <i>2 -> 1</i>, <i>2 -> 2</i> and two |
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90 | different kinds of <i>2 -> 3</i> processes. In addition a common |
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91 | multiplicative factor may be imposed. |
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92 | |
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93 | <br/><br/><table><tr><td><strong>SigmaProcess:renormScale1 </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 1</code>; <code>maximum = 2</code>)</td></tr></table> |
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94 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 1</ei> processes. |
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95 | The same options also apply for those <ei>2 -> 2</ei> and <ei>2 -> 3</ei> |
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96 | processes that have been specially marked as proceeding only through |
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97 | an <ei>s</ei>-channel resonance, by the <code>isSChannel()</code> virtual |
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98 | method of <code>SigmaProcess</code>. |
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99 | <br/> |
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100 | <input type="radio" name="5" value="1" checked="checked"><strong>1 </strong>: the squared invariant mass, i.e. <ei>sHat</ei>. <br/> |
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101 | <input type="radio" name="5" value="2"><strong>2 </strong>: fix scale set in <code>SigmaProcess:renormFixScale</code> below. <br/> |
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102 | |
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103 | <br/><br/><table><tr><td><strong>SigmaProcess:renormScale2 </td><td> (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>; <code>maximum = 5</code>)</td></tr></table> |
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104 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 2</ei> processes. |
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105 | <br/> |
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106 | <input type="radio" name="6" value="1"><strong>1 </strong>: the smaller of the squared transverse masses of the two outgoing particles, i.e. <ei>min(mT_3^2, mT_4^2) = pT^2 + min(m_3^2, m_4^2)</ei>. <br/> |
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107 | <input type="radio" name="6" value="2" checked="checked"><strong>2 </strong>: the geometric mean of the squared transverse masses of the two outgoing particles, i.e. <ei>mT_3 * mT_4 = sqrt((pT^2 + m_3^2) * (pT^2 + m_4^2))</ei>. <br/> |
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108 | <input type="radio" name="6" value="3"><strong>3 </strong>: the arithmetic mean of the squared transverse masses of the two outgoing particles, i.e. <ei>(mT_3^2 + mT_4^2) / 2 = pT^2 + 0.5 * (m_3^2 + m_4^2)</ei>. Useful for comparisons with PYTHIA 6, where this is the default. <br/> |
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109 | <input type="radio" name="6" value="4"><strong>4 </strong>: squared invariant mass of the system, i.e. <ei>sHat</ei>. Useful for processes dominated by <ei>s</ei>-channel exchange. <br/> |
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110 | <input type="radio" name="6" value="5"><strong>5 </strong>: fix scale set in <code>SigmaProcess:renormFixScale</code> below. <br/> |
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111 | |
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112 | <br/><br/><table><tr><td><strong>SigmaProcess:renormScale3 </td><td> (<code>default = <strong>3</strong></code>; <code>minimum = 1</code>; <code>maximum = 6</code>)</td></tr></table> |
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113 | The <ei>Q^2</ei> renormalization scale for "normal" <ei>2 -> 3</ei> |
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114 | processes, i.e excepting the vector-boson-fusion processes below. |
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115 | Here it is assumed that particle masses in the final state either match |
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116 | or are heavier than that of any <ei>t</ei>-channel propagator particle. |
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117 | (Currently only <ei>g g / q qbar -> H^0 Q Qbar</ei> processes are |
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118 | implemented, where the "match" criterion holds.) |
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119 | <br/> |
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120 | <input type="radio" name="7" value="1"><strong>1 </strong>: the smaller of the squared transverse masses of the three outgoing particles, i.e. min(mT_3^2, mT_4^2, mT_5^2). <br/> |
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121 | <input type="radio" name="7" value="2"><strong>2 </strong>: the geometric mean of the two smallest squared transverse masses of the three outgoing particles, i.e. <ei>sqrt( mT_3^2 * mT_4^2 * mT_5^2 / max(mT_3^2, mT_4^2, mT_5^2) )</ei>. <br/> |
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122 | <input type="radio" name="7" value="3" checked="checked"><strong>3 </strong>: the geometric mean of the squared transverse masses of the three outgoing particles, i.e. <ei>(mT_3^2 * mT_4^2 * mT_5^2)^(1/3)</ei>. <br/> |
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123 | <input type="radio" name="7" value="4"><strong>4 </strong>: the arithmetic mean of the squared transverse masses of the three outgoing particles, i.e. <ei>(mT_3^2 + mT_4^2 + mT_5^2)/3</ei>. <br/> |
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124 | <input type="radio" name="7" value="5"><strong>5 </strong>: squared invariant mass of the system, i.e. <ei>sHat</ei>. <br/> |
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125 | <input type="radio" name="7" value="6"><strong>6 </strong>: fix scale set in <code>SigmaProcess:renormFixScale</code> below. <br/> |
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126 | |
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127 | <br/><br/><table><tr><td><strong>SigmaProcess:renormScale3VV </td><td> (<code>default = <strong>3</strong></code>; <code>minimum = 1</code>; <code>maximum = 6</code>)</td></tr></table> |
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128 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 3</ei> |
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129 | vector-boson-fusion processes, i.e. <ei>f_1 f_2 -> H^0 f_3 f_4</ei> |
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130 | with <ei>Z^0</ei> or <ei>W^+-</ei> <ei>t</ei>-channel propagators. |
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131 | Here the transverse masses of the outgoing fermions do not reflect the |
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132 | virtualities of the exchanged bosons. A better estimate is obtained |
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133 | by replacing the final-state fermion masses by the vector-boson ones |
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134 | in the definition of transverse masses. We denote these combinations |
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135 | <ei>mT_Vi^2 = m_V^2 + pT_i^2</ei>. |
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136 | <br/> |
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137 | <input type="radio" name="8" value="1"><strong>1 </strong>: the squared mass <ei>m_V^2</ei> of the exchanged vector boson. <br/> |
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138 | <input type="radio" name="8" value="2"><strong>2 </strong>: the geometric mean of the two propagator virtuality estimates, i.e. <ei>sqrt(mT_V3^2 * mT_V4^2)</ei>. <br/> |
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139 | <input type="radio" name="8" value="3" checked="checked"><strong>3 </strong>: the geometric mean of the three relevant squared transverse masses, i.e. <ei>(mT_V3^2 * mT_V4^2 * mT_H^2)^(1/3)</ei>. <br/> |
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140 | <input type="radio" name="8" value="4"><strong>4 </strong>: the arithmetic mean of the three relevant squared transverse masses, i.e. <ei>(mT_V3^2 + mT_V4^2 + mT_H^2)/3</ei>. <br/> |
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141 | <input type="radio" name="8" value="5"><strong>5 </strong>: squared invariant mass of the system, i.e. <ei>sHat</ei>. <br/> |
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142 | <input type="radio" name="8" value="6"><strong>6 </strong>: fix scale set in <code>SigmaProcess:renormFixScale</code> below. <br/> |
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143 | |
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144 | <br/><br/><table><tr><td><strong>SigmaProcess:renormMultFac </td><td></td><td> <input type="text" name="9" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)</td></tr></table> |
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145 | The <i>Q^2</i> renormalization scale for <i>2 -> 1</i>, |
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146 | <i>2 -> 2</i> and <i>2 -> 3</i> processes is multiplied by |
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147 | this factor relative to the scale described above (except for the options |
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148 | with a fix scale). Should be use sparingly for <i>2 -> 1</i> processes. |
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149 | |
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150 | |
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151 | <br/><br/><table><tr><td><strong>SigmaProcess:renormFixScale </td><td></td><td> <input type="text" name="10" value="10000." size="20"/> (<code>default = <strong>10000.</strong></code>; <code>minimum = 1.</code>)</td></tr></table> |
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152 | A fix <i>Q^2</i> value used as renormalization scale for <i>2 -> 1</i>, |
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153 | <i>2 -> 2</i> and <i>2 -> 3</i> processes in some of the options above. |
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154 | |
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155 | |
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156 | <h3>Factorization scales</h3> |
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157 | |
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158 | Corresponding options exist for the <i>Q^2</i> factorization scale |
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159 | used as argument in PDF's. Again there is a choice of form for |
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160 | <i>2 -> 1</i>, <i>2 -> 2</i> and <i>2 -> 3</i> processes separately. |
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161 | For simplicity we have let the numbering of options agree, for each event |
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162 | class separately, between normalization and factorization scales, and the |
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163 | description has therefore been slightly shortened. The default values are |
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164 | <b>not</b> necessarily the same, however. |
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165 | |
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166 | <br/><br/><table><tr><td><strong>SigmaProcess:factorScale1 </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 1</code>; <code>maximum = 2</code>)</td></tr></table> |
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167 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 1</ei> processes. |
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168 | The same options also apply for those <ei>2 -> 2</ei> and <ei>2 -> 3</ei> |
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169 | processes that have been specially marked as proceeding only through |
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170 | an <ei>s</ei>-channel resonance. |
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171 | <br/> |
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172 | <input type="radio" name="11" value="1" checked="checked"><strong>1 </strong>: the squared invariant mass, i.e. <ei>sHat</ei>. <br/> |
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173 | <input type="radio" name="11" value="2"><strong>2 </strong>: fix scale set in <code>SigmaProcess:factorFixScale</code> below. <br/> |
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174 | |
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175 | <br/><br/><table><tr><td><strong>SigmaProcess:factorScale2 </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 1</code>; <code>maximum = 5</code>)</td></tr></table> |
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176 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 2</ei> processes. |
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177 | <br/> |
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178 | <input type="radio" name="12" value="1" checked="checked"><strong>1 </strong>: the smaller of the squared transverse masses of the two outgoing particles. <br/> |
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179 | <input type="radio" name="12" value="2"><strong>2 </strong>: the geometric mean of the squared transverse masses of the two outgoing particles. <br/> |
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180 | <input type="radio" name="12" value="3"><strong>3 </strong>: the arithmetic mean of the squared transverse masses of the two outgoing particles. Useful for comparisons with PYTHIA 6, where this is the default. <br/> |
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181 | <input type="radio" name="12" value="4"><strong>4 </strong>: squared invariant mass of the system, i.e. <ei>sHat</ei>. Useful for processes dominated by <ei>s</ei>-channel exchange. <br/> |
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182 | <input type="radio" name="12" value="5"><strong>5 </strong>: fix scale set in <code>SigmaProcess:factorFixScale</code> below. <br/> |
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183 | |
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184 | <br/><br/><table><tr><td><strong>SigmaProcess:factorScale3 </td><td> (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>; <code>maximum = 6</code>)</td></tr></table> |
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185 | The <ei>Q^2</ei> factorization scale for "normal" <ei>2 -> 3</ei> |
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186 | processes, i.e excepting the vector-boson-fusion processes below. |
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187 | <br/> |
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188 | <input type="radio" name="13" value="1"><strong>1 </strong>: the smaller of the squared transverse masses of the three outgoing particles. <br/> |
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189 | <input type="radio" name="13" value="2" checked="checked"><strong>2 </strong>: the geometric mean of the two smallest squared transverse masses of the three outgoing particles. <br/> |
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190 | <input type="radio" name="13" value="3"><strong>3 </strong>: the geometric mean of the squared transverse masses of the three outgoing particles. <br/> |
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191 | <input type="radio" name="13" value="4"><strong>4 </strong>: the arithmetic mean of the squared transverse masses of the three outgoing particles. <br/> |
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192 | <input type="radio" name="13" value="5"><strong>5 </strong>: squared invariant mass of the system, i.e. <ei>sHat</ei>. <br/> |
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193 | <input type="radio" name="13" value="6"><strong>6 </strong>: fix scale set in <code>SigmaProcess:factorFixScale</code> below. <br/> |
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194 | |
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195 | <br/><br/><table><tr><td><strong>SigmaProcess:factorScale3VV </td><td> (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>; <code>maximum = 6</code>)</td></tr></table> |
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196 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 3</ei> |
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197 | vector-boson-fusion processes, i.e. <ei>f_1 f_2 -> H^0 f_3 f_4</ei> |
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198 | with <ei>Z^0</ei> or <ei>W^+-</ei> <ei>t</ei>-channel propagators. |
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199 | Here we again introduce the combinations <ei>mT_Vi^2 = m_V^2 + pT_i^2</ei> |
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200 | as replacements for the normal squared transverse masses of the two |
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201 | outgoing quarks. |
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202 | <br/> |
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203 | <input type="radio" name="14" value="1"><strong>1 </strong>: the squared mass <ei>m_V^2</ei> of the exchanged vector boson. <br/> |
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204 | <input type="radio" name="14" value="2" checked="checked"><strong>2 </strong>: the geometric mean of the two propagator virtuality estimates. <br/> |
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205 | <input type="radio" name="14" value="3"><strong>3 </strong>: the geometric mean of the three relevant squared transverse masses. <br/> |
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206 | <input type="radio" name="14" value="4"><strong>4 </strong>: the arithmetic mean of the three relevant squared transverse masses. <br/> |
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207 | <input type="radio" name="14" value="5"><strong>5 </strong>: squared invariant mass of the system, i.e. <ei>sHat</ei>. <br/> |
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208 | <input type="radio" name="14" value="6"><strong>6 </strong>: fix scale set in <code>SigmaProcess:factorFixScale</code> below. <br/> |
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209 | |
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210 | <br/><br/><table><tr><td><strong>SigmaProcess:factorMultFac </td><td></td><td> <input type="text" name="15" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)</td></tr></table> |
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211 | The <i>Q^2</i> factorization scale for <i>2 -> 1</i>, |
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212 | <i>2 -> 2</i> and <i>2 -> 3</i> processes is multiplied by |
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213 | this factor relative to the scale described above (except for the options |
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214 | with a fix scale). Should be use sparingly for <i>2 -> 1</i> processes. |
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215 | |
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216 | |
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217 | <br/><br/><table><tr><td><strong>SigmaProcess:factorFixScale </td><td></td><td> <input type="text" name="16" value="10000." size="20"/> (<code>default = <strong>10000.</strong></code>; <code>minimum = 1.</code>)</td></tr></table> |
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218 | A fix <i>Q^2</i> value used as factorization scale for <i>2 -> 1</i>, |
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219 | <i>2 -> 2</i> and <i>2 -> 3</i> processes in some of the options above. |
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220 | |
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221 | |
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222 | <input type="hidden" name="saved" value="1"/> |
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223 | |
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224 | <?php |
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225 | echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?> |
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226 | |
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227 | <table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table> |
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228 | </form> |
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229 | |
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230 | <?php |
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231 | |
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232 | if($_POST["saved"] == 1) |
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233 | { |
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234 | $filepath = $_POST["filepath"]; |
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235 | $handle = fopen($filepath, 'a'); |
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236 | |
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237 | if($_POST["1"] != "0.1265") |
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238 | { |
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239 | $data = "SigmaProcess:alphaSvalue = ".$_POST["1"]."\n"; |
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240 | fwrite($handle,$data); |
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241 | } |
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242 | if($_POST["2"] != "1") |
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243 | { |
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244 | $data = "SigmaProcess:alphaSorder = ".$_POST["2"]."\n"; |
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245 | fwrite($handle,$data); |
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246 | } |
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247 | if($_POST["3"] != "1") |
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248 | { |
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249 | $data = "SigmaProcess:alphaEMorder = ".$_POST["3"]."\n"; |
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250 | fwrite($handle,$data); |
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251 | } |
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252 | if($_POST["4"] != "1.0") |
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253 | { |
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254 | $data = "SigmaProcess:Kfactor = ".$_POST["4"]."\n"; |
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255 | fwrite($handle,$data); |
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256 | } |
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257 | if($_POST["5"] != "1") |
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258 | { |
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259 | $data = "SigmaProcess:renormScale1 = ".$_POST["5"]."\n"; |
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260 | fwrite($handle,$data); |
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261 | } |
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262 | if($_POST["6"] != "2") |
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263 | { |
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264 | $data = "SigmaProcess:renormScale2 = ".$_POST["6"]."\n"; |
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265 | fwrite($handle,$data); |
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266 | } |
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267 | if($_POST["7"] != "3") |
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268 | { |
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269 | $data = "SigmaProcess:renormScale3 = ".$_POST["7"]."\n"; |
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270 | fwrite($handle,$data); |
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271 | } |
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272 | if($_POST["8"] != "3") |
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273 | { |
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274 | $data = "SigmaProcess:renormScale3VV = ".$_POST["8"]."\n"; |
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275 | fwrite($handle,$data); |
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276 | } |
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277 | if($_POST["9"] != "1.") |
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278 | { |
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279 | $data = "SigmaProcess:renormMultFac = ".$_POST["9"]."\n"; |
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280 | fwrite($handle,$data); |
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281 | } |
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282 | if($_POST["10"] != "10000.") |
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283 | { |
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284 | $data = "SigmaProcess:renormFixScale = ".$_POST["10"]."\n"; |
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285 | fwrite($handle,$data); |
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286 | } |
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287 | if($_POST["11"] != "1") |
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288 | { |
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289 | $data = "SigmaProcess:factorScale1 = ".$_POST["11"]."\n"; |
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290 | fwrite($handle,$data); |
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291 | } |
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292 | if($_POST["12"] != "1") |
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293 | { |
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294 | $data = "SigmaProcess:factorScale2 = ".$_POST["12"]."\n"; |
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295 | fwrite($handle,$data); |
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296 | } |
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297 | if($_POST["13"] != "2") |
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298 | { |
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299 | $data = "SigmaProcess:factorScale3 = ".$_POST["13"]."\n"; |
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300 | fwrite($handle,$data); |
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301 | } |
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302 | if($_POST["14"] != "2") |
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303 | { |
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304 | $data = "SigmaProcess:factorScale3VV = ".$_POST["14"]."\n"; |
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305 | fwrite($handle,$data); |
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306 | } |
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307 | if($_POST["15"] != "1.") |
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308 | { |
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309 | $data = "SigmaProcess:factorMultFac = ".$_POST["15"]."\n"; |
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310 | fwrite($handle,$data); |
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311 | } |
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312 | if($_POST["16"] != "10000.") |
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313 | { |
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314 | $data = "SigmaProcess:factorFixScale = ".$_POST["16"]."\n"; |
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315 | fwrite($handle,$data); |
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316 | } |
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317 | fclose($handle); |
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318 | } |
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319 | |
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320 | ?> |
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321 | </body> |
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322 | </html> |
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323 | |
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324 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |
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