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9419eeef | 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. The parametrizations | |
8 | used are from <ref>Sch94, Sch97</ref> which borrows some of the total cross | |
9 | sections from <ref>Don92</ref>. | |
10 | ||
11 | <p/> | |
12 | There are strong indications that the currently implemented diffractive | |
13 | cross section parametrizations, which should be in reasonable agreement | |
14 | with data at lower energies, overestimate the diffractive rate at larger | |
15 | values. If you wish to explore this (or other) aspect, it is possible to | |
16 | override the cross section values in two different ways. The first offers | |
17 | (almost) complete freedom, but needs to be defined separately for each | |
18 | CM energy, while the second introduces a simpler parametrized damping. | |
19 | The two cannot be combined. Furthermore the Coulomb term for elastic | |
20 | scattering, which by default is off, can be switched on. | |
21 | ||
22 | <p/> | |
23 | The allowed combinations of incoming particles are <ei>p + p</ei>, | |
24 | <ei>pbar + p</ei>, <ei>pi+ + p</ei>, <ei>pi- + p</ei>, | |
25 | <ei>pi0/rho0 + p</ei>, <ei>phi + p</ei>, <ei>J/psi + p</ei>, | |
26 | <ei>rho + rho</ei>, <ei>rho + phi</ei>, <ei>rho + J/psi</ei>, | |
27 | <ei>phi + phi</ei>, <ei>phi + J/psi</ei>, <ei>J/psi + J/psi</ei>. | |
28 | The strong emphasis on vector mesons is related to the description | |
29 | of <ei>gamma + p</ei> and <ei>gamma + gamma</ei> interactions in a | |
30 | Vector Dominance Model framework (which will not be available for some | |
31 | time to come, so this is a bit of overkill). Nevertheless, the sections | |
32 | below, with allowed variations, are mainly intended to make sense for | |
33 | <ei>p + p</ei>. | |
34 | ||
35 | <h3>Set cross sections</h3> | |
36 | ||
37 | <flag name="SigmaTotal:setOwn" default="off"> | |
38 | Allow a user to set own cross sections by hand; on/off = true/false. | |
39 | </flag> | |
40 | ||
41 | <p/> | |
42 | When <code>SigmaTotal:setOwn = on</code>, the user is expected to set | |
43 | values for the corresponding cross sections: | |
44 | ||
45 | <parm name="SigmaTotal:sigmaTot" default="80." min="0."> | |
46 | Total cross section in mb. | |
47 | </parm> | |
48 | ||
49 | <parm name="SigmaTotal:sigmaEl" default="20." min="0."> | |
50 | Elastic cross section in mb. | |
51 | </parm> | |
52 | ||
53 | <parm name="SigmaTotal:sigmaXB" default="8." min="0."> | |
54 | Single Diffractive cross section <ei>A + B -> X + B</ei> in mb. | |
55 | </parm> | |
56 | ||
57 | <parm name="SigmaTotal:sigmaAX" default="8." min="0."> | |
58 | Single Diffractive cross section <ei>A + B -> A + X</ei> in mb. | |
59 | </parm> | |
60 | ||
61 | <parm name="SigmaTotal:sigmaXX" default="4." min="0."> | |
62 | Double Diffractive cross section <ei>A + B -> X_1 + X_2</ei> in mb. | |
63 | </parm> | |
64 | ||
65 | <p/> | |
66 | Note that the total cross section subtracted by the elastic and various | |
67 | diffractive ones gives the inelastic nondiffractive cross section, | |
68 | which therefore is not set separately. If this cross section evaluates | |
69 | to be negative the internal parametrizations are used instead of the | |
70 | ones here. However, since the nondiffractive inelastic cross section | |
71 | is what makes up the minimum-bias event class, and plays a major role | |
72 | in the description of multiple interactions, it is important that a | |
73 | consistent set is used. | |
74 | ||
75 | <h3>Dampen diffractive cross sections</h3> | |
76 | ||
77 | <flag name="SigmaDiffractive:dampen" default="no"> | |
78 | Allow a user to dampen diffractive cross sections; on/off = true/false. | |
79 | </flag> | |
80 | ||
81 | <p/> | |
82 | When <code>SigmaDiffractive:dampen = on</code>, the three diffractive | |
83 | cross sections are damped so that they never can exceed the respective | |
84 | values below. Specifically, if the standard parametrization gives | |
85 | the cross section <ei>sigma_old(s)</ei> and a fixed <ei>sigma_max</ei> | |
86 | is set, the actual cross section becomes <ei>sigma_new(s) | |
87 | = sigma_old(s) * sigma_max / (sigma_old(s) + sigma_max)</ei>. | |
88 | This reduces to <ei>sigma_old(s)</ei> at low energies and to | |
89 | <ei>sigma_max</ei> at high ones. Note that the asymptotic value | |
90 | is approached quite slowly, however. | |
91 | ||
92 | <parm name="SigmaDiffractive:maxXB" default="15." min="0."> | |
93 | The above <ei>sigma_max</ei> for <ei>A + B -> X + B</ei> in mb. | |
94 | </parm> | |
95 | ||
96 | <parm name="SigmaDiffractive:maxAX" default="15." min="0."> | |
97 | The above <ei>sigma_max</ei> for <ei>A + B -> X + B</ei> in mb. | |
98 | </parm> | |
99 | ||
100 | <parm name="SigmaDiffractive:maxXX" default="15." min="0."> | |
101 | The above <ei>sigma_max</ei> for <ei>A + B -> X + B</ei> in mb. | |
102 | </parm> | |
103 | ||
104 | <p/> | |
105 | As above, a reduced diffractive cross section automatically translates | |
106 | into an increased nondiffractive one, such that the total (and elastic) | |
107 | cross section remains fixed. | |
108 | ||
109 | ||
110 | <h3>Set elastic cross section</h3> | |
111 | ||
112 | <p/> | |
113 | In the above option the <ei>t</ei> slopes are based on the internal | |
114 | parametrizations. In addition there is no Coulomb-term contribution | |
115 | to the elastic (or total) cross section, which of course becomes | |
116 | infinite if this contribution is included. If you have switched on | |
117 | <code>SigmaTotal:setOwn</code> you can further switch on a machinery | |
118 | to include the Coulomb term, including interference with the conventional | |
119 | strong-interaction Pomeron one <ref>Ber87</ref>. Then the elastic cross | |
120 | section is no longer taken from <code>SigmaTotal:sigmaEl</code> but | |
121 | derived from the parameters below and <code>SigmaTotal:sigmaTot</code>, | |
122 | using the optical theorem. The machinery is only intended to be used for | |
123 | <ei>p p</ei> and <ei>pbar p</ei> collisions. The description of | |
124 | diffractive events, and especially their slopes, remains unchanged. | |
125 | ||
126 | <flag name="SigmaElastic:setOwn" default="no"> | |
127 | Allow a user to set parameters for the normalization and shape of the | |
128 | elastic cross section the by hand; yes/no = true/false. | |
129 | </flag> | |
130 | ||
131 | <parm name="SigmaElastic:bSlope" default="18." min="0."> | |
132 | the slope <ei>b</ei> of the strong-interaction term <ei>exp(bt)</ei>, | |
133 | in units of GeV^-2. | |
134 | </parm> | |
135 | ||
136 | <parm name="SigmaElastic:rho" default="0.13" min="-1." max="1."> | |
137 | the ratio of the real to the imaginary parts of the nuclear scattering | |
138 | amplitude. | |
139 | </parm> | |
140 | ||
141 | <parm name="SigmaElastic:lambda" default="0.71" min="0.1" max="2."> | |
142 | the main parameter of the electric form factor | |
143 | <ei>G(t) = lambda^2 / (lambda + |t|)^2</ei>, in units of GeV^2. | |
144 | </parm> | |
145 | ||
146 | <parm name="SigmaElastic:tAbsMin" default="5e-5" min="1e-10"> | |
147 | since the Coulomb contribution is infinite a lower limit on | |
148 | <ei>|t|</ei> must be set to regularize the divergence, | |
149 | in units of GeV^2. | |
150 | </parm> | |
151 | ||
152 | <parm name="SigmaElastic:phaseConst" default="0.577"> | |
153 | The Coulomb term is taken to contain a phase factor | |
154 | <ei>exp(+- i alpha phi(t))</ei>, with + for <ei>p p</ei> and - for | |
155 | <ei>pbar p</ei>, where <ei>phi(t) = - phaseConst - ln(-B t/2)</ei>. | |
156 | This constant is model dependent <ref>Cah82</ref>. | |
157 | </parm> | |
158 | ||
159 | </chapter> | |
160 | ||
161 | <!-- Copyright (C) 2010 Torbjorn Sjostrand --> |