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5ad4eb21 | 1 | <chapter name="Couplings and Scales"> |
2 | ||
3 | <h2>Couplings and Scales</h2> | |
4 | ||
5 | Here is collected some possibilities to modify the scale choices | |
6 | of couplings and parton densities for all internally implemented | |
7 | hard processes. This is based on them all being derived from the | |
8 | <code>SigmaProcess</code> base class. The matrix-element coding is | |
9 | also used by the multiple-interactions machinery, but there with a | |
10 | separate choice of <ei>alpha_strong(M_Z^2)</ei> value and running, | |
11 | and separate PDF scale choices. Also, in <ei>2 -> 2</ei> and | |
12 | <ei>2 -> 3</ei> processes where resonances are produced, their | |
13 | couplings and thereby their Breit-Wigner shapes are always evaluated | |
14 | with the resonance mass as scale, irrespective of the choices below. | |
15 | ||
16 | <h3>Couplings and K factor</h3> | |
17 | ||
18 | The size of QCD cross sections is mainly determined by | |
19 | <parm name="SigmaProcess:alphaSvalue" default="0.1265" | |
20 | min="0.06" max="0.25"> | |
21 | The <ei>alpha_strong</ei> value at scale <ei>M_Z^2</ei>. | |
22 | </parm> | |
23 | ||
24 | <p/> | |
25 | The actual value is then regulated by the running to the <ei>Q^2</ei> | |
26 | renormalization scale, at which <ei>alpha_strong</ei> is evaluated | |
27 | <modepick name="SigmaProcess:alphaSorder" default="1" min="0" max="2"> | |
28 | Order at which <ei>alpha_strong</ei> runs, | |
29 | <option value="0">zeroth order, i.e. <ei>alpha_strong</ei> is kept | |
30 | fixed.</option> | |
31 | <option value="1">first order, which is the normal value.</option> | |
32 | <option value="2">second order. Since other parts of the code do | |
33 | not go to second order there is no strong reason to use this option, | |
34 | but there is also nothing wrong with it.</option> | |
35 | </modepick> | |
36 | ||
37 | <p/> | |
38 | QED interactions are regulated by the <ei>alpha_electromagnetic</ei> | |
39 | value at the <ei>Q^2</ei> renormalization scale of an interaction. | |
40 | <modepick name="SigmaProcess:alphaEMorder" default="1" min="-1" max="1"> | |
41 | The running of <ei>alpha_em</ei> used in hard processes. | |
42 | <option value="1">first-order running, constrained to agree with | |
43 | <code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass. | |
44 | </option> | |
45 | <option value="0">zeroth order, i.e. <ei>alpha_em</ei> is kept | |
46 | fixed at its value at vanishing momentum transfer.</option> | |
47 | <option value="-1">zeroth order, i.e. <ei>alpha_em</ei> is kept | |
48 | fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value | |
49 | at the <ei>Z^0</ei> mass. | |
50 | </option> | |
51 | </modepick> | |
52 | ||
53 | <p/> | |
54 | In addition there is the possibility of a global rescaling of | |
55 | cross sections (which could not easily be accommodated by a | |
56 | changed <ei>alpha_strong</ei>, since <ei>alpha_strong</ei> runs) | |
57 | <parm name="SigmaProcess:Kfactor" default="1.0" min="0.5" max="4.0"> | |
58 | Multiply almost all cross sections by this common fix factor. Excluded | |
59 | are only unresolved processes, where cross sections are better | |
60 | <aloc href="TotalCrossSections">set directly</aloc>, and | |
61 | multiple interactions, which have a separate <ei>K</ei> factor | |
62 | <aloc href="MultipleInteractions">of their own</aloc>. | |
63 | This degree of freedom is primarily intended for hadron colliders, and | |
64 | should not normally be used for <ei>e^+e^-</ei> annihilation processes. | |
65 | </parm> | |
66 | ||
67 | <h3>Renormalization scales</h3> | |
68 | ||
69 | The <ei>Q^2</ei> renormalization scale can be chosen among a few different | |
70 | alternatives, separately for <ei>2 -> 1</ei>, <ei>2 -> 2</ei> and two | |
71 | different kinds of <ei>2 -> 3</ei> processes. In addition a common | |
72 | multiplicative factor may be imposed. | |
73 | ||
74 | <modepick name="SigmaProcess:renormScale1" default="1" min="1" max="2"> | |
75 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 1</ei> processes. | |
76 | The same options also apply for those <ei>2 -> 2</ei> and <ei>2 -> 3</ei> | |
77 | processes that have been specially marked as proceeding only through | |
78 | an <ei>s</ei>-channel resonance, by the <code>isSChannel()</code> virtual | |
79 | method of <code>SigmaProcess</code>. | |
80 | <option value="1">the squared invariant mass, i.e. <ei>sHat</ei>. | |
81 | </option> | |
82 | <option value="2">fix scale set in <code>SigmaProcess:renormFixScale</code> | |
83 | below. | |
84 | </option> | |
85 | </modepick> | |
86 | ||
87 | <modepick name="SigmaProcess:renormScale2" default="2" min="1" max="5"> | |
88 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 2</ei> processes. | |
89 | <option value="1">the smaller of the squared transverse masses of the two | |
90 | outgoing particles, i.e. <ei>min(mT_3^2, mT_4^2) = | |
91 | pT^2 + min(m_3^2, m_4^2)</ei>. | |
92 | </option> | |
93 | <option value="2">the geometric mean of the squared transverse masses of | |
94 | the two outgoing particles, i.e. <ei>mT_3 * mT_4 = | |
95 | sqrt((pT^2 + m_3^2) * (pT^2 + m_4^2))</ei>. | |
96 | </option> | |
97 | <option value="3">the arithmetic mean of the squared transverse masses of | |
98 | the two outgoing particles, i.e. <ei>(mT_3^2 + mT_4^2) / 2 = | |
99 | pT^2 + 0.5 * (m_3^2 + m_4^2)</ei>. Useful for comparisons | |
100 | with PYTHIA 6, where this is the default. | |
101 | </option> | |
102 | <option value="4">squared invariant mass of the system, | |
103 | i.e. <ei>sHat</ei>. Useful for processes dominated by | |
104 | <ei>s</ei>-channel exchange. | |
105 | </option> | |
106 | <option value="5">fix scale set in <code>SigmaProcess:renormFixScale</code> | |
107 | below. | |
108 | </option> | |
109 | </modepick> | |
110 | ||
111 | <modepick name="SigmaProcess:renormScale3" default="3" min="1" max="6"> | |
112 | The <ei>Q^2</ei> renormalization scale for "normal" <ei>2 -> 3</ei> | |
113 | processes, i.e excepting the vector-boson-fusion processes below. | |
114 | Here it is assumed that particle masses in the final state either match | |
115 | or are heavier than that of any <ei>t</ei>-channel propagator particle. | |
116 | (Currently only <ei>g g / q qbar -> H^0 Q Qbar</ei> processes are | |
117 | implemented, where the "match" criterion holds.) | |
118 | <option value="1">the smaller of the squared transverse masses of the three | |
119 | outgoing particles, i.e. min(mT_3^2, mT_4^2, mT_5^2). | |
120 | </option> | |
121 | <option value="2">the geometric mean of the two smallest squared transverse | |
122 | masses of the three outgoing particles, i.e. | |
123 | <ei>sqrt( mT_3^2 * mT_4^2 * mT_5^2 / max(mT_3^2, mT_4^2, mT_5^2) )</ei>. | |
124 | </option> | |
125 | <option value="3">the geometric mean of the squared transverse masses of the | |
126 | three outgoing particles, i.e. <ei>(mT_3^2 * mT_4^2 * mT_5^2)^(1/3)</ei>. | |
127 | </option> | |
128 | <option value="4">the arithmetic mean of the squared transverse masses of | |
129 | the three outgoing particles, i.e. <ei>(mT_3^2 + mT_4^2 + mT_5^2)/3</ei>. | |
130 | </option> | |
131 | <option value="5">squared invariant mass of the system, | |
132 | i.e. <ei>sHat</ei>. | |
133 | </option> | |
134 | <option value="6">fix scale set in <code>SigmaProcess:renormFixScale</code> | |
135 | below. | |
136 | </option> | |
137 | </modepick> | |
138 | ||
139 | <modepick name="SigmaProcess:renormScale3VV" default="3" min="1" max="6"> | |
140 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 3</ei> | |
141 | vector-boson-fusion processes, i.e. <ei>f_1 f_2 -> H^0 f_3 f_4</ei> | |
142 | with <ei>Z^0</ei> or <ei>W^+-</ei> <ei>t</ei>-channel propagators. | |
143 | Here the transverse masses of the outgoing fermions do not reflect the | |
144 | virtualities of the exchanged bosons. A better estimate is obtained | |
145 | by replacing the final-state fermion masses by the vector-boson ones | |
146 | in the definition of transverse masses. We denote these combinations | |
147 | <ei>mT_Vi^2 = m_V^2 + pT_i^2</ei>. | |
148 | <option value="1">the squared mass <ei>m_V^2</ei> of the exchanged | |
149 | vector boson. | |
150 | </option> | |
151 | <option value="2">the geometric mean of the two propagator virtuality | |
152 | estimates, i.e. <ei>sqrt(mT_V3^2 * mT_V4^2)</ei>. | |
153 | </option> | |
154 | <option value="3">the geometric mean of the three relevant squared | |
155 | transverse masses, i.e. <ei>(mT_V3^2 * mT_V4^2 * mT_H^2)^(1/3)</ei>. | |
156 | </option> | |
157 | <option value="4">the arithmetic mean of the three relevant squared | |
158 | transverse masses, i.e. <ei>(mT_V3^2 + mT_V4^2 + mT_H^2)/3</ei>. | |
159 | </option> | |
160 | <option value="5">squared invariant mass of the system, | |
161 | i.e. <ei>sHat</ei>. | |
162 | </option> | |
163 | <option value="6">fix scale set in <code>SigmaProcess:renormFixScale</code> | |
164 | below. | |
165 | </option> | |
166 | </modepick> | |
167 | ||
168 | <parm name="SigmaProcess:renormMultFac" default="1." min="0.1" max="10."> | |
169 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 1</ei>, | |
170 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes is multiplied by | |
171 | this factor relative to the scale described above (except for the options | |
172 | with a fix scale). Should be use sparingly for <ei>2 -> 1</ei> processes. | |
173 | </parm> | |
174 | ||
175 | <parm name="SigmaProcess:renormFixScale" default="10000." min="1."> | |
176 | A fix <ei>Q^2</ei> value used as renormalization scale for <ei>2 -> 1</ei>, | |
177 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes in some of the options above. | |
178 | </parm> | |
179 | ||
180 | <h3>Factorization scales</h3> | |
181 | ||
182 | Corresponding options exist for the <ei>Q^2</ei> factorization scale | |
183 | used as argument in PDF's. Again there is a choice of form for | |
184 | <ei>2 -> 1</ei>, <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes separately. | |
185 | For simplicity we have let the numbering of options agree, for each event | |
186 | class separately, between normalization and factorization scales, and the | |
187 | description has therefore been slightly shortened. The default values are | |
188 | <b>not</b> necessarily the same, however. | |
189 | ||
190 | <modepick name="SigmaProcess:factorScale1" default="1" min="1" max="2"> | |
191 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 1</ei> processes. | |
192 | The same options also apply for those <ei>2 -> 2</ei> and <ei>2 -> 3</ei> | |
193 | processes that have been specially marked as proceeding only through | |
194 | an <ei>s</ei>-channel resonance. | |
195 | <option value="1">the squared invariant mass, i.e. <ei>sHat</ei>. | |
196 | </option> | |
197 | <option value="2">fix scale set in <code>SigmaProcess:factorFixScale</code> | |
198 | below. | |
199 | </option> | |
200 | </modepick> | |
201 | ||
202 | <modepick name="SigmaProcess:factorScale2" default="1" min="1" max="5"> | |
203 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 2</ei> processes. | |
204 | <option value="1">the smaller of the squared transverse masses of the two | |
205 | outgoing particles. | |
206 | </option> | |
207 | <option value="2">the geometric mean of the squared transverse masses of | |
208 | the two outgoing particles. | |
209 | </option> | |
210 | <option value="3">the arithmetic mean of the squared transverse masses of | |
211 | the two outgoing particles. Useful for comparisons with PYTHIA 6, where | |
212 | this is the default. | |
213 | </option> | |
214 | <option value="4">squared invariant mass of the system, | |
215 | i.e. <ei>sHat</ei>. Useful for processes dominated by | |
216 | <ei>s</ei>-channel exchange. | |
217 | </option> | |
218 | <option value="5">fix scale set in <code>SigmaProcess:factorFixScale</code> | |
219 | below. | |
220 | </option> | |
221 | </modepick> | |
222 | ||
223 | <modepick name="SigmaProcess:factorScale3" default="2" min="1" max="6"> | |
224 | The <ei>Q^2</ei> factorization scale for "normal" <ei>2 -> 3</ei> | |
225 | processes, i.e excepting the vector-boson-fusion processes below. | |
226 | <option value="1">the smaller of the squared transverse masses of the three | |
227 | outgoing particles. | |
228 | </option> | |
229 | <option value="2">the geometric mean of the two smallest squared transverse | |
230 | masses of the three outgoing particles. | |
231 | </option> | |
232 | <option value="3">the geometric mean of the squared transverse masses of the | |
233 | three outgoing particles. | |
234 | </option> | |
235 | <option value="4">the arithmetic mean of the squared transverse masses of | |
236 | the three outgoing particles. | |
237 | </option> | |
238 | <option value="5">squared invariant mass of the system, | |
239 | i.e. <ei>sHat</ei>. | |
240 | </option> | |
241 | <option value="6">fix scale set in <code>SigmaProcess:factorFixScale</code> | |
242 | below. | |
243 | </option> | |
244 | </modepick> | |
245 | ||
246 | <modepick name="SigmaProcess:factorScale3VV" default="2" min="1" max="6"> | |
247 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 3</ei> | |
248 | vector-boson-fusion processes, i.e. <ei>f_1 f_2 -> H^0 f_3 f_4</ei> | |
249 | with <ei>Z^0</ei> or <ei>W^+-</ei> <ei>t</ei>-channel propagators. | |
250 | Here we again introduce the combinations <ei>mT_Vi^2 = m_V^2 + pT_i^2</ei> | |
251 | as replacements for the normal squared transverse masses of the two | |
252 | outgoing quarks. | |
253 | <option value="1">the squared mass <ei>m_V^2</ei> of the exchanged | |
254 | vector boson. | |
255 | </option> | |
256 | <option value="2">the geometric mean of the two propagator virtuality | |
257 | estimates. | |
258 | </option> | |
259 | <option value="3">the geometric mean of the three relevant squared | |
260 | transverse masses. | |
261 | </option> | |
262 | <option value="4">the arithmetic mean of the three relevant squared | |
263 | transverse masses. | |
264 | </option> | |
265 | <option value="5">squared invariant mass of the system, | |
266 | i.e. <ei>sHat</ei>. | |
267 | </option> | |
268 | <option value="6">fix scale set in <code>SigmaProcess:factorFixScale</code> | |
269 | below. | |
270 | </option> | |
271 | </modepick> | |
272 | ||
273 | <parm name="SigmaProcess:factorMultFac" default="1." min="0.1" max="10."> | |
274 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 1</ei>, | |
275 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes is multiplied by | |
276 | this factor relative to the scale described above (except for the options | |
277 | with a fix scale). Should be use sparingly for <ei>2 -> 1</ei> processes. | |
278 | </parm> | |
279 | ||
280 | <parm name="SigmaProcess:factorFixScale" default="10000." min="1."> | |
281 | A fix <ei>Q^2</ei> value used as factorization scale for <ei>2 -> 1</ei>, | |
282 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes in some of the options above. | |
283 | </parm> | |
284 | ||
285 | </chapter> | |
286 | ||
287 | <!-- Copyright (C) 2008 Torbjorn Sjostrand --> |