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c6b60c38 | 1 | <chapter name="Total Cross Sections"> |
2 | ||
3 | <h2>Total Cross Sections</h2> | |
4 | ||
5 | The <code>SigmaTotal</code> class returns the total, elastic, diffractive | |
6 | and nondiffractive cross sections in hadronic collisions, and also the | |
7 | slopes of the <ei>d(sigma)/dt</ei> distributions. Most of the parametrizations | |
8 | used are from <ref>Sch94, Sch97</ref> which borrows some of the total cross | |
9 | sections from <ref>Don92</ref>. If you use the MBR (Minimum Bias Rockefeller) | |
10 | model <ref>Cie12</ref>, <code>Diffraction:PomFlux = 5</code>, this model | |
11 | contains its own parametrizations of all cross sections in <ei>p p</ei> | |
12 | and <ei>pbar p</ei> collisions. | |
13 | ||
14 | <p/> | |
15 | There are strong indications that the currently implemented diffractive | |
16 | cross section parametrizations, which should be in reasonable agreement | |
17 | with data at lower energies, overestimate the diffractive rate at larger | |
18 | values. If you wish to explore this (or other) aspect, it is possible to | |
19 | override the cross section values in two different ways. The first offers | |
20 | (almost) complete freedom, but needs to be defined separately for each | |
21 | CM energy, while the second introduces a simpler parametrized damping. | |
22 | The two cannot be combined. Furthermore the Coulomb term for elastic | |
23 | scattering, which by default is off, can be switched on. | |
24 | ||
25 | <p/> | |
26 | The allowed combinations of incoming particles are <ei>p + p</ei>, | |
27 | <ei>pbar + p</ei>, <ei>pi+ + p</ei>, <ei>pi- + p</ei>, | |
28 | <ei>pi0/rho0 + p</ei>, <ei>phi + p</ei>, <ei>J/psi + p</ei>, | |
29 | <ei>rho + rho</ei>, <ei>rho + phi</ei>, <ei>rho + J/psi</ei>, | |
30 | <ei>phi + phi</ei>, <ei>phi + J/psi</ei>, <ei>J/psi + J/psi</ei>. | |
31 | The strong emphasis on vector mesons is related to the description | |
32 | of <ei>gamma + p</ei> and <ei>gamma + gamma</ei> interactions in a | |
33 | Vector Dominance Model framework (which will not be available for some | |
34 | time to come, so this is a bit of overkill). Nevertheless, the sections | |
35 | below, with allowed variations, are mainly intended to make sense for | |
36 | <ei>p + p</ei>. | |
37 | ||
38 | <h3>Central diffraction</h3> | |
39 | ||
40 | Central diffraction (CD), a.k.a. double Pomeron exchange (DPE), was not | |
41 | part of the framework in <ref>Sch94</ref>. It has now been added for | |
42 | multiparticle states, i.e. excluding the resonance region below 1 GeV | |
43 | mass, as well as other exclusive states, but only for <ei>p p</ei> or | |
44 | <ei>pbar p</ei>. It uses the same proton-Pomeron vertex as in single | |
45 | diffraction, twice, to describe <ei>x_Pomeron</ei> and <ei>t</ei> spectra. | |
46 | This fixes the energy dependence, which has been integrated and | |
47 | parametrized. The absolute normalization has been left open, however. | |
48 | Furthermore, since CD has not been included in previous tunes to data, | |
49 | a special flag is available to reproduce the old behaviour (with due | |
50 | complications when one does not want to do this). | |
51 | ||
52 | <parm name="SigmaTotal:sigmaAXB2TeV" default="1.5" min="0."> | |
53 | The CD cross section for <ei>p p</ei> and <ei>pbar p</ei> collisions, | |
54 | normalized to its value at 2 TeV CM energy, expressed in mb. The energy | |
55 | dependence is then parametrized, and behaves roughly like | |
56 | <ei>ln^1.5(s)</ei>. Is used for the options | |
57 | <code>Diffraction:PomFlux = 1 - 4</code>, while the MBR model | |
58 | (<code>= 5</code>) has its own parametrization. | |
59 | </parm> | |
60 | ||
61 | <flag name="SigmaTotal:zeroAXB" default="off"> | |
62 | several existing <aloc href="Tunes">tunes</aloc> do not include CD. | |
63 | An inclusion of a nonvanishing CD cross section directly affects | |
64 | the minbias phenomenology (even if not dramatically), and so | |
65 | this flag is used to switch off the CD cross section in such tunes. | |
66 | You can switch it back on <i>after</i> the selection of a tune, if you | |
67 | so wish. This option has no effect for the MBR model | |
68 | (<code>Diffraction:PomFlux = 5</code>), where the CD cross section | |
69 | has been included from the onset. | |
70 | </flag> | |
71 | ||
72 | <h3>Set cross sections</h3> | |
73 | ||
74 | <flag name="SigmaTotal:setOwn" default="off"> | |
75 | Allow a user to set own cross sections by hand; on/off = true/false. | |
76 | </flag> | |
77 | ||
78 | <p/> | |
79 | When <code>SigmaTotal:setOwn = on</code>, the user is expected to set | |
80 | values for the corresponding cross sections: | |
81 | ||
82 | <parm name="SigmaTotal:sigmaTot" default="80." min="0."> | |
83 | Total cross section in mb. | |
84 | </parm> | |
85 | ||
86 | <parm name="SigmaTotal:sigmaEl" default="20." min="0."> | |
87 | Elastic cross section in mb. | |
88 | </parm> | |
89 | ||
90 | <parm name="SigmaTotal:sigmaXB" default="8." min="0."> | |
91 | Single Diffractive cross section <ei>A + B -> X + B</ei> in mb. | |
92 | </parm> | |
93 | ||
94 | <parm name="SigmaTotal:sigmaAX" default="8." min="0."> | |
95 | Single Diffractive cross section <ei>A + B -> A + X</ei> in mb. | |
96 | </parm> | |
97 | ||
98 | <parm name="SigmaTotal:sigmaXX" default="4." min="0."> | |
99 | Double Diffractive cross section <ei>A + B -> X_1 + X_2</ei> in mb. | |
100 | </parm> | |
101 | ||
102 | <parm name="SigmaTotal:sigmaAXB" default="1." min="0."> | |
103 | Central Diffractive cross section <ei>A + B -> A + X + B</ei> in mb. | |
104 | </parm> | |
105 | ||
106 | <p/> | |
107 | Note that the total cross section subtracted by the elastic and various | |
108 | diffractive ones gives the inelastic nondiffractive cross section, | |
109 | which therefore is not set separately. If this cross section evaluates | |
110 | to be negative the internal parametrizations are used instead of the | |
111 | ones here. However, since the nondiffractive inelastic cross section | |
112 | is what makes up the minimum-bias event class, and plays a major role | |
113 | in the description of multiparton interactions, it is important that a | |
114 | consistent set is used. | |
115 | ||
116 | <h3>Dampen diffractive cross sections</h3> | |
117 | ||
118 | As already noted, unitarization effects may dampen the rise of diffractive | |
119 | cross sections relative to the default parametrizations. The settings | |
120 | here allows one way to introduce a dampening, which is used in some | |
121 | of the existing <aloc href="Tunes">tunes</aloc>. | |
122 | ||
123 | <flag name="SigmaDiffractive:dampen" default="no"> | |
124 | Allow a user to dampen diffractive cross sections; on/off = true/false. | |
125 | </flag> | |
126 | ||
127 | <p/> | |
128 | When <code>SigmaDiffractive:dampen = on</code>, the three diffractive | |
129 | cross sections are damped so that they never can exceed the respective | |
130 | values below. Specifically, if the standard parametrization gives | |
131 | the cross section <ei>sigma_old(s)</ei> and a fixed <ei>sigma_max</ei> | |
132 | is set, the actual cross section becomes <ei>sigma_new(s) | |
133 | = sigma_old(s) * sigma_max / (sigma_old(s) + sigma_max)</ei>. | |
134 | This reduces to <ei>sigma_old(s)</ei> at low energies and to | |
135 | <ei>sigma_max</ei> at high ones. Note that the asymptotic value | |
136 | is approached quite slowly, however. | |
137 | ||
138 | <parm name="SigmaDiffractive:maxXB" default="15." min="0."> | |
139 | The above <ei>sigma_max</ei> for <ei>A + B -> X + B</ei> in mb. | |
140 | </parm> | |
141 | ||
142 | <parm name="SigmaDiffractive:maxAX" default="15." min="0."> | |
143 | The above <ei>sigma_max</ei> for <ei>A + B -> A + X</ei> in mb. | |
144 | </parm> | |
145 | ||
146 | <parm name="SigmaDiffractive:maxXX" default="15." min="0."> | |
147 | The above <ei>sigma_max</ei> for <ei>A + B -> X_1 + X_2</ei> in mb. | |
148 | </parm> | |
149 | ||
150 | <parm name="SigmaDiffractive:maxAXB" default="3." min="0."> | |
151 | The above <ei>sigma_max</ei> for <ei>A + B -> A + X + B</ei> in mb. | |
152 | </parm> | |
153 | ||
154 | <p/> | |
155 | As above, a reduced diffractive cross section automatically translates | |
156 | into an increased nondiffractive one, such that the total (and elastic) | |
157 | cross section remains fixed. | |
158 | ||
159 | ||
160 | <h3>Set elastic cross section</h3> | |
161 | ||
162 | <p/> | |
163 | In the above option the <ei>t</ei> slopes are based on the internal | |
164 | parametrizations. In addition there is no Coulomb-term contribution | |
165 | to the elastic (or total) cross section, which of course becomes | |
166 | infinite if this contribution is included. If you have switched on | |
167 | <code>SigmaTotal:setOwn</code> you can further switch on a machinery | |
168 | to include the Coulomb term, including interference with the conventional | |
169 | strong-interaction Pomeron one <ref>Ber87</ref>. Then the elastic cross | |
170 | section is no longer taken from <code>SigmaTotal:sigmaEl</code> but | |
171 | derived from the parameters below and <code>SigmaTotal:sigmaTot</code>, | |
172 | using the optical theorem. The machinery is only intended to be used for | |
173 | <ei>p p</ei> and <ei>pbar p</ei> collisions. The description of | |
174 | diffractive events, and especially their slopes, remains unchanged. | |
175 | ||
176 | <flag name="SigmaElastic:setOwn" default="no"> | |
177 | Allow a user to set parameters for the normalization and shape of the | |
178 | elastic cross section the by hand; yes/no = true/false. | |
179 | </flag> | |
180 | ||
181 | <parm name="SigmaElastic:bSlope" default="18." min="0."> | |
182 | the slope <ei>b</ei> of the strong-interaction term <ei>exp(bt)</ei>, | |
183 | in units of GeV^-2. | |
184 | </parm> | |
185 | ||
186 | <parm name="SigmaElastic:rho" default="0.13" min="-1." max="1."> | |
187 | the ratio of the real to the imaginary parts of the nuclear scattering | |
188 | amplitude. | |
189 | </parm> | |
190 | ||
191 | <parm name="SigmaElastic:lambda" default="0.71" min="0.1" max="2."> | |
192 | the main parameter of the electric form factor | |
193 | <ei>G(t) = lambda^2 / (lambda + |t|)^2</ei>, in units of GeV^2. | |
194 | </parm> | |
195 | ||
196 | <parm name="SigmaElastic:tAbsMin" default="5e-5" min="1e-10"> | |
197 | since the Coulomb contribution is infinite a lower limit on | |
198 | <ei>|t|</ei> must be set to regularize the divergence, | |
199 | in units of GeV^2. | |
200 | </parm> | |
201 | ||
202 | <parm name="SigmaElastic:phaseConst" default="0.577"> | |
203 | The Coulomb term is taken to contain a phase factor | |
204 | <ei>exp(+- i alpha phi(t))</ei>, with + for <ei>p p</ei> and - for | |
205 | <ei>pbar p</ei>, where <ei>phi(t) = - phaseConst - ln(-B t/2)</ei>. | |
206 | This constant is model dependent <ref>Cah82</ref>. | |
207 | </parm> | |
208 | ||
209 | </chapter> | |
210 | ||
211 | <!-- Copyright (C) 2013 Torbjorn Sjostrand --> |