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