1 <chapter name="Total Cross Sections">
3 <h2>Total Cross Sections</h2>
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>.
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.
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
35 <h3>Set cross sections</h3>
37 <flag name="SigmaTotal:setOwn" default="off">
38 Allow a user to set own cross sections by hand; on/off = true/false.
42 When <code>SigmaTotal:setOwn = on</code>, the user is expected to set
43 values for the corresponding cross sections:
45 <parm name="SigmaTotal:sigmaTot" default="80." min="0.">
46 Total cross section in mb.
49 <parm name="SigmaTotal:sigmaEl" default="20." min="0.">
50 Elastic cross section in mb.
53 <parm name="SigmaTotal:sigmaXB" default="8." min="0.">
54 Single Diffractive cross section <ei>A + B -> X + B</ei> in mb.
57 <parm name="SigmaTotal:sigmaAX" default="8." min="0.">
58 Single Diffractive cross section <ei>A + B -> A + X</ei> in mb.
61 <parm name="SigmaTotal:sigmaXX" default="4." min="0.">
62 Double Diffractive cross section <ei>A + B -> X_1 + X_2</ei> in mb.
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.
75 <h3>Dampen diffractive cross sections</h3>
77 <flag name="SigmaDiffractive:dampen" default="no">
78 Allow a user to dampen diffractive cross sections; on/off = true/false.
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.
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.
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.
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.
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.
110 <h3>Set elastic cross section</h3>
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.
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.
131 <parm name="SigmaElastic:bSlope" default="18." min="0.">
132 the slope <ei>b</ei> of the strong-interaction term <ei>exp(bt)</ei>,
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
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.
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,
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>.
161 <!-- Copyright (C) 2010 Torbjorn Sjostrand -->