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<title>Total Cross Sections</title>
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<h2>Total Cross Sections</h2>
The <code>SigmaTotal</code> class returns the total, elastic, diffractive
and nondiffractive cross sections in hadronic collisions, and also the
slopes of the <i>d(sigma)/dt</i> distributions. Most of the parametrizations
used are from [<a href="Bibliography.html" target="page">Sch94, Sch97</a>] which borrows some of the total cross
sections from [<a href="Bibliography.html" target="page">Don92</a>]. If you use the MBR (Minimum Bias Rockefeller)
model [<a href="Bibliography.html" target="page">Cie12</a>], <code>Diffraction:PomFlux = 5</code>, this model
contains its own parametrizations of all cross sections in <i>p p</i>
and <i>pbar p</i> collisions.
<p/>
There are strong indications that the currently implemented diffractive
cross section parametrizations, which should be in reasonable agreement
with data at lower energies, overestimate the diffractive rate at larger
values. If you wish to explore this (or other) aspect, it is possible to
override the cross section values in two different ways. The first offers
(almost) complete freedom, but needs to be defined separately for each
CM energy, while the second introduces a simpler parametrized damping.
The two cannot be combined. Furthermore the Coulomb term for elastic
scattering, which by default is off, can be switched on.
<p/>
The allowed combinations of incoming particles are <i>p + p</i>,
<i>pbar + p</i>, <i>pi+ + p</i>, <i>pi- + p</i>,
<i>pi0/rho0 + p</i>, <i>phi + p</i>, <i>J/psi + p</i>,
<i>rho + rho</i>, <i>rho + phi</i>, <i>rho + J/psi</i>,
<i>phi + phi</i>, <i>phi + J/psi</i>, <i>J/psi + J/psi</i>.
The strong emphasis on vector mesons is related to the description
of <i>gamma + p</i> and <i>gamma + gamma</i> interactions in a
Vector Dominance Model framework (which will not be available for some
time to come, so this is a bit of overkill). Nevertheless, the sections
below, with allowed variations, are mainly intended to make sense for
<i>p + p</i>.
<h3>Central diffraction</h3>
Central diffraction (CD), a.k.a. double Pomeron exchange (DPE), was not
part of the framework in [<a href="Bibliography.html" target="page">Sch94</a>]. It has now been added for
multiparticle states, i.e. excluding the resonance region below 1 GeV
mass, as well as other exclusive states, but only for <i>p p</i> or
<i>pbar p</i>. It uses the same proton-Pomeron vertex as in single
diffraction, twice, to describe <i>x_Pomeron</i> and <i>t</i> spectra.
This fixes the energy dependence, which has been integrated and
parametrized. The absolute normalization has been left open, however.
Furthermore, since CD has not been included in previous tunes to data,
a special flag is available to reproduce the old behaviour (with due
complications when one does not want to do this).
<p/><code>parm </code><strong> SigmaTotal:sigmaAXB2TeV </strong>
(<code>default = <strong>1.5</strong></code>; <code>minimum = 0.</code>)<br/>
The CD cross section for <i>p p</i> and <i>pbar p</i> collisions,
normalized to its value at 2 TeV CM energy, expressed in mb. The energy
dependence is then parametrized, and behaves roughly like
<i>ln^1.5(s)</i>. Is used for the options
<code>Diffraction:PomFlux = 1 - 4</code>, while the MBR model
(<code>= 5</code>) has its own parametrization.
<p/><code>flag </code><strong> SigmaTotal:zeroAXB </strong>
(<code>default = <strong>off</strong></code>)<br/>
several existing <a href="Tunes.html" target="page">tunes</a> do not include CD.
An inclusion of a nonvanishing CD cross section directly affects
the nondiffractive phenomenology (even if not dramatically), and so
this flag is used to switch off the CD cross section in such tunes.
You can switch it back on <i>after</i> the selection of a tune, if you
so wish. This option has no effect for the MBR model
(<code>Diffraction:PomFlux = 5</code>), where the CD cross section
has been included from the onset.
<h3>Set cross sections</h3>
<p/><code>flag </code><strong> SigmaTotal:setOwn </strong>
(<code>default = <strong>off</strong></code>)<br/>
Allow a user to set own cross sections by hand; on/off = true/false.
<p/>
When <code>SigmaTotal:setOwn = on</code>, the user is expected to set
values for the corresponding cross sections:
<p/><code>parm </code><strong> SigmaTotal:sigmaTot </strong>
(<code>default = <strong>80.</strong></code>; <code>minimum = 0.</code>)<br/>
Total cross section in mb.
<p/><code>parm </code><strong> SigmaTotal:sigmaEl </strong>
(<code>default = <strong>20.</strong></code>; <code>minimum = 0.</code>)<br/>
Elastic cross section in mb.
<p/><code>parm </code><strong> SigmaTotal:sigmaXB </strong>
(<code>default = <strong>8.</strong></code>; <code>minimum = 0.</code>)<br/>
Single Diffractive cross section <i>A + B → X + B</i> in mb.
<p/><code>parm </code><strong> SigmaTotal:sigmaAX </strong>
(<code>default = <strong>8.</strong></code>; <code>minimum = 0.</code>)<br/>
Single Diffractive cross section <i>A + B → A + X</i> in mb.
<p/><code>parm </code><strong> SigmaTotal:sigmaXX </strong>
(<code>default = <strong>4.</strong></code>; <code>minimum = 0.</code>)<br/>
Double Diffractive cross section <i>A + B → X_1 + X_2</i> in mb.
<p/><code>parm </code><strong> SigmaTotal:sigmaAXB </strong>
(<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>)<br/>
Central Diffractive cross section <i>A + B → A + X + B</i> in mb.
<p/>
Note that the total cross section subtracted by the elastic and various
diffractive ones gives the inelastic nondiffractive cross section,
which therefore is not set separately. If this cross section evaluates
to be negative the internal parametrizations are used instead of the
ones here. However, since the nondiffractive inelastic cross section
is what makes up the minimum-bias event class, and plays a major role
in the description of multiparton interactions, it is important that a
consistent set is used.
<h3>Dampen diffractive cross sections</h3>
As already noted, unitarization effects may dampen the rise of diffractive
cross sections relative to the default parametrizations. The settings
here allows one way to introduce a dampening, which is used in some
of the existing <a href="Tunes.html" target="page">tunes</a>.
<p/><code>flag </code><strong> SigmaDiffractive:dampen </strong>
(<code>default = <strong>no</strong></code>)<br/>
Allow a user to dampen diffractive cross sections; on/off = true/false.
<p/>
When <code>SigmaDiffractive:dampen = on</code>, the three diffractive
cross sections are damped so that they never can exceed the respective
values below. Specifically, if the standard parametrization gives
the cross section <i>sigma_old(s)</i> and a fixed <i>sigma_max</i>
is set, the actual cross section becomes <i>sigma_new(s)
= sigma_old(s) * sigma_max / (sigma_old(s) + sigma_max)</i>.
This reduces to <i>sigma_old(s)</i> at low energies and to
<i>sigma_max</i> at high ones. Note that the asymptotic value
is approached quite slowly, however.
<p/><code>parm </code><strong> SigmaDiffractive:maxXB </strong>
(<code>default = <strong>15.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>sigma_max</i> for <i>A + B → X + B</i> in mb.
<p/><code>parm </code><strong> SigmaDiffractive:maxAX </strong>
(<code>default = <strong>15.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>sigma_max</i> for <i>A + B → A + X</i> in mb.
<p/><code>parm </code><strong> SigmaDiffractive:maxXX </strong>
(<code>default = <strong>15.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>sigma_max</i> for <i>A + B → X_1 + X_2</i> in mb.
<p/><code>parm </code><strong> SigmaDiffractive:maxAXB </strong>
(<code>default = <strong>3.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>sigma_max</i> for <i>A + B → A + X + B</i> in mb.
<p/>
As above, a reduced diffractive cross section automatically translates
into an increased nondiffractive one, such that the total (and elastic)
cross section remains fixed.
<h3>Set elastic cross section</h3>
<p/>
In the above option the <i>t</i> slopes are based on the internal
parametrizations. In addition there is no Coulomb-term contribution
to the elastic (or total) cross section, which of course becomes
infinite if this contribution is included. If you have switched on
<code>SigmaTotal:setOwn</code> you can further switch on a machinery
to include the Coulomb term, including interference with the conventional
strong-interaction Pomeron one [<a href="Bibliography.html" target="page">Ber87</a>]. Then the elastic cross
section is no longer taken from <code>SigmaTotal:sigmaEl</code> but
derived from the parameters below and <code>SigmaTotal:sigmaTot</code>,
using the optical theorem. The machinery is only intended to be used for
<i>p p</i> and <i>pbar p</i> collisions. The description of
diffractive events, and especially their slopes, remains unchanged.
<p/><code>flag </code><strong> SigmaElastic:setOwn </strong>
(<code>default = <strong>no</strong></code>)<br/>
Allow a user to set parameters for the normalization and shape of the
elastic cross section the by hand; yes/no = true/false.
<p/><code>parm </code><strong> SigmaElastic:bSlope </strong>
(<code>default = <strong>18.</strong></code>; <code>minimum = 0.</code>)<br/>
the slope <i>b</i> of the strong-interaction term <i>exp(bt)</i>,
in units of GeV^-2.
<p/><code>parm </code><strong> SigmaElastic:rho </strong>
(<code>default = <strong>0.13</strong></code>; <code>minimum = -1.</code>; <code>maximum = 1.</code>)<br/>
the ratio of the real to the imaginary parts of the nuclear scattering
amplitude.
<p/><code>parm </code><strong> SigmaElastic:lambda </strong>
(<code>default = <strong>0.71</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.</code>)<br/>
the main parameter of the electric form factor
<i>G(t) = lambda^2 / (lambda + |t|)^2</i>, in units of GeV^2.
<p/><code>parm </code><strong> SigmaElastic:tAbsMin </strong>
(<code>default = <strong>5e-5</strong></code>; <code>minimum = 1e-10</code>)<br/>
since the Coulomb contribution is infinite a lower limit on
<i>|t|</i> must be set to regularize the divergence,
in units of GeV^2.
<p/><code>parm </code><strong> SigmaElastic:phaseConst </strong>
(<code>default = <strong>0.577</strong></code>)<br/>
The Coulomb term is taken to contain a phase factor
<i>exp(+- i alpha phi(t))</i>, with + for <i>p p</i> and - for
<i>pbar p</i>, where <i>phi(t) = - phaseConst - ln(-B t/2)</i>.
This constant is model dependent [<a href="Bibliography.html" target="page">Cah82</a>].
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