Total Cross Sections
The SigmaTotal class returns the total, elastic, diffractive
and nondiffractive cross sections in hadronic collisions, and also the
slopes of the d(sigma)/dt distributions. Most of the parametrizations
used are from [Sch94, Sch97] which borrows some of the total cross
sections from [Don92]. If you use the MBR (Minimum Bias Rockefeller)
model [Cie12], Diffraction:PomFlux = 5, this model
contains its own parametrizations of all cross sections in p p
and pbar p collisions.
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.
The allowed combinations of incoming particles are p + p,
pbar + p, pi+ + p, pi- + p,
pi0/rho0 + p, phi + p, J/psi + p,
rho + rho, rho + phi, rho + J/psi,
phi + phi, phi + J/psi, J/psi + J/psi.
The strong emphasis on vector mesons is related to the description
of gamma + p and gamma + gamma 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
p + p.
Central diffraction
Central diffraction (CD), a.k.a. double Pomeron exchange (DPE), was not
part of the framework in [Sch94]. 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 p p or
pbar p. It uses the same proton-Pomeron vertex as in single
diffraction, twice, to describe x_Pomeron and t 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).
parm SigmaTotal:sigmaAXB2TeV
(default = 1.5; minimum = 0.)
The CD cross section for p p and pbar p collisions,
normalized to its value at 2 TeV CM energy, expressed in mb. The energy
dependence is then parametrized, and behaves roughly like
ln^1.5(s). Is used for the options
Diffraction:PomFlux = 1 - 4, while the MBR model
(= 5) has its own parametrization.
flag SigmaTotal:zeroAXB
(default = on)
several existing tunes 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 forcibly set the CD cross section to vanish
in such tunes. You can switch CD back on after the selection of
a tune, if you so wish, by resetting SigmaTotal:zeroAXB = off.
This option has no effect for the MBR model
(Diffraction:PomFlux = 5), where the CD cross section
has been included from the onset.
Set cross sections
flag SigmaTotal:setOwn
(default = off)
Allow a user to set own cross sections by hand; on/off = true/false.
When SigmaTotal:setOwn = on, the user is expected to set
values for the corresponding cross sections:
parm SigmaTotal:sigmaTot
(default = 80.; minimum = 0.)
Total cross section in mb.
parm SigmaTotal:sigmaEl
(default = 20.; minimum = 0.)
Elastic cross section in mb.
parm SigmaTotal:sigmaXB
(default = 8.; minimum = 0.)
Single Diffractive cross section A + B → X + B in mb.
parm SigmaTotal:sigmaAX
(default = 8.; minimum = 0.)
Single Diffractive cross section A + B → A + X in mb.
parm SigmaTotal:sigmaXX
(default = 4.; minimum = 0.)
Double Diffractive cross section A + B → X_1 + X_2 in mb.
parm SigmaTotal:sigmaAXB
(default = 1.; minimum = 0.)
Central Diffractive cross section A + B → A + X + B in mb.
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.
Modify diffractive cross sections
The default description of diffractive interactions was
parameterized and fit in [Sch94, Sch97]. The following
parameters allow for some modification of the mass distribution of
the diffractive system, which then integrates to a modified diffractive
cross section. Note that these parameters have no effect on the MBR model.
parm SigmaDiffractive:mMin
(default = 0.28; minimum = 0.0)
Lowest mass of a diffractive system is set to be mHadron + mMin.
parm SigmaDiffractive:lowMEnhance
(default = 2.0; minimum = 0.0)
Normalization factor for the contribution of low-mass resonances
to the diffractive cross section (cRes in eq. (22) of
[Sch94]).
parm SigmaDiffractive:mResMax
(default = 1.062; minimum = 0.0)
The contribution of low-mass resonances is dampened at around the
scale mHadron + mResMax (the sum is Mres in eq. (22)
of [Sch94]). To make sense, we should have
mResMax > mMin.
Dampen diffractive cross sections
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 tunes.
flag SigmaDiffractive:dampen
(default = on)
Allow a user to dampen diffractive cross sections; on/off = true/false.
When SigmaDiffractive:dampen = on, 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 sigma_old(s) and a fixed sigma_max
is set, the actual cross section becomes sigma_new(s)
= sigma_old(s) * sigma_max / (sigma_old(s) + sigma_max).
This reduces to sigma_old(s) at low energies and to
sigma_max at high ones. Note that the asymptotic value
is approached quite slowly, however.
parm SigmaDiffractive:maxXB
(default = 65.; minimum = 0.)
The above sigma_max for A + B → X + B in mb.
parm SigmaDiffractive:maxAX
(default = 65.; minimum = 0.)
The above sigma_max for A + B → A + X in mb.
parm SigmaDiffractive:maxXX
(default = 65.; minimum = 0.)
The above sigma_max for A + B → X_1 + X_2 in mb.
parm SigmaDiffractive:maxAXB
(default = 3.; minimum = 0.)
The above sigma_max for A + B → A + X + B in mb.
As above, a reduced diffractive cross section automatically translates
into an increased nondiffractive one, such that the total (and elastic)
cross section remains fixed.
Set elastic cross section
In the above option the t 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
SigmaTotal:setOwn you can further switch on a machinery
to include the Coulomb term, including interference with the conventional
strong-interaction Pomeron one [Ber87]. Then the elastic cross
section is no longer taken from SigmaTotal:sigmaEl but
derived from the parameters below and SigmaTotal:sigmaTot,
using the optical theorem. The machinery is only intended to be used for
p p and pbar p collisions. The description of
diffractive events, and especially their slopes, remains unchanged.
flag SigmaElastic:setOwn
(default = no)
Allow a user to set parameters for the normalization and shape of the
elastic cross section the by hand; yes/no = true/false.
parm SigmaElastic:bSlope
(default = 18.; minimum = 0.)
the slope b of the strong-interaction term exp(bt),
in units of GeV^-2.
parm SigmaElastic:rho
(default = 0.13; minimum = -1.; maximum = 1.)
the ratio of the real to the imaginary parts of the nuclear scattering
amplitude.
parm SigmaElastic:lambda
(default = 0.71; minimum = 0.1; maximum = 2.)
the main parameter of the electric form factor
G(t) = lambda^2 / (lambda + |t|)^2, in units of GeV^2.
parm SigmaElastic:tAbsMin
(default = 5e-5; minimum = 1e-10)
since the Coulomb contribution is infinite a lower limit on
|t| must be set to regularize the divergence,
in units of GeV^2.
parm SigmaElastic:phaseConst
(default = 0.577)
The Coulomb term is taken to contain a phase factor
exp(+- i alpha phi(t)), with + for p p and - for
pbar p, where phi(t) = - phaseConst - ln(-B t/2).
This constant is model dependent [Cah82].