.. _Minimum Bias:
*******************
Minimum bias events
*******************
Minimum bias events are simulated through the Shrimps module in Sherpa.
Physics of Shrimps
==================
Inclusive part of the model
---------------------------
Shrimps is based on the KMR model :cite:`Ryskin2009tj`, which is a
multi-channel eikonal model. The incoming hadrons are written as a
superposition of Good-Walker states, which are diffractive eigenstates
that diagalonise the T-matrix. This allows to include low-mass
diffractive excitation. Each combination of colliding Good-Walker
states gives rise to a single-channel eikonal. The final eikonal is
the superposition of the single-channel eikonals. The number of
Good-Walker states is 2 in Shrimps (the original KMR model includes 3
states).
Each single-channel eikonal can be seen as the product of two parton
densities, one from each of the colliding Good-Walker states. The
evolution of the parton densities in rapidity due to extra emissions
and absoption on either of the two hadrons is described by a set of
coupled differential equations. The parameter ``Delta``, which can be
interpreted as the Pomeron intercept, is the probability for emitting
an extra parton per unit of rapidity. The strength of absorptive
corrections is quantified by the parameter ``lambda``, which can also
be seen as the triple-Pomeron coupling. A small region of size
``deltaY`` around the beams is excluded from the evolution due to the
finite longitudinal size of the parton densities.
The boundary conditions for the parton densities are form factors,
which have a dipole form characterised by the parameters ``Lambda2``,
``beta_02(mb)``, ``kappa`` and ``xi``.
In this framework the eikonals and the cross sections for the
different modes (elastic, inelastic, single- and double-diffractive)
are calculated.
Exclusive part of the model
---------------------------
The description of this part of the model is outdated and needs to be updated.
Please contact the :ref:`Authors` if you need more information.
..
All parameters of the following section do not exist in the code.
Therefore we have commented out this section and replaced it with the
stub above.
TODO: This has to be resolved
..
Exclusive part of the model
---------------------------
Inelastic events are generated by explicitely simulating the exchange and
rescattering of gluon ladders. The number of primary ladders is given by a
Poisson distribution whose parameter is the single-channel eikonal. The
decomposition of the incoming hadrons into partons proceeds via suitably
infra-red continued PDFs.
The emissions from the ladders are then generated in
a Markov chain. The pseudo-Sudakov form factor contains several factors: an
ordinary gluon emission term, a factor accounting for the Reggeisation of the
gluons and a recombination weight taking absorptive corrections into account.
The emission term has the perturbative form @math{alpha_s(k_T^2)/k_T^2}, that
needs to
be continued into the infra-red region. In the case of @math{alpha_s} the
transition into the infra-red region happens at ``Q_as^2`` while in the case
of @math{1/k_T^2} the transition scale is generated dynamically and depends on
the parton densities and is scaled by ``Q_0^2``.
The propagators of the filled ladder can be either in a colour singlet or octet
state, the probabilities are again given through the parton densities. The
probability for a singlet can also be regulated by hand through the parameter
``Chi_S``. A singlet propagator is the result of an implicit rescattering.
After all emissions have been generated and the colours assigned, further
radiation is generated by the parton shower to resum also the logrithms in
@math{1/Q^2}. The amount of radiation from the parton shower can be regulated
with ``KT2_Factor``, which multiplies the shower starting scale. After
parton showering partons emitted from the ladder or the parton shower are
subject to explicit rescattering, i.e. they can exchange secondary ladders. The
probability for the exchange of a rescattering ladder is characterised by
``RescProb``. The probability for rescattering over a singlet propagator
receives an extra factor ``RescProb1``. After all ladder exchanges and
rescatterings but before hadronsation colour can be re-arrangd in the event.
Finally, the event is hadronised using the standard Sherpa cluster
hadronisation.
Parameters and settings
=======================
Below is a list of all relevant parameters to steer the Shrimps module.
Generating minimum bias events
------------------------------
.. index:: EVENT_TYPE
.. index:: SOFT_COLLISIONS
To generate minimum bias events with Shrimps ``EVENT_TYPE`` has to be
set to ``MinimumBias`` and ``SOFT_COLLISIONS`` to ``Shrimps``.
Shrimps Mode
------------
.. index:: Shrimps_Mode
The setup of minimum bias events is done via top-level settings. The
exact choice is steered through the parameter ``Shrimps_Mode``
(default ``Inelastic``), which allows the following settings:
* ``Xsecs``, which will only calculate total, elastic, inelastic,
single- and double-diffractive cross sections at various relevant energies
and write them to a file, typically 'InclusiveQuantities/Xsecs.dat';
* ``Elastic``
generates elastic events at a fixed energy;
* ``Single-diffractive``
generates low-mass single-diffractive events at a fixed energy,
modelled by the transition of one of the protons to a N(1440) state;
* ``Double-diffractive``
generates low-mass single-diffractive events at a fixed energy,
modelled by the transition of both protons to N(1440) states;
* ``Quasi-elastic``
generates a combination of elastic, single- and double-diffractive
events in due proportion;
* ``Inelastic``
generates inelastic minimum bias events through the exchange of t-channel
gluons or singlets (pomerons). This mode actually will include
large mass diffraction;
* ``All``
generates a combination of quasi-elastic and inelastic events in due
proportion.
Parameters of the eikonals
--------------------------
.. index:: Lambda2
.. index:: beta02(mb)
.. index:: kappa
.. index:: xi
.. index:: deltaY
.. index:: lambda
.. index:: Delta
The parameters of the differential equations for the parton densities are
* ``Delta`` (default 0.3): perturbative Pomeron intercept
* ``lambda`` (default 0.5): triple Pomeron coupling
* ``deltaY`` (default 1.5): rapidity interval excluded from evolution
The form factors are of the form:
.. math::
F_{1/2}(q_T) = \beta_0^2 (1 \pm \kappa) \frac{\exp(\frac{-\xi (1
\pm \kappa)q_T^2}{\Lambda^2})}{(1 + (1 \pm
\kappa)q_T^2/\Lambda^2)^2}
with the parameters
* :math:`\Lambda^2` (default 1.7 GeV^2)
* :math:`\beta_0^2(mb)` (default 25.0 mb)
* :math:`\kappa` (default 0.6)
* :math:`\xi` (default 0.2)
Parameters for event generation
-------------------------------
The description of these parameters is outdated and needs to be updated.
Please contact the :ref:`Authors` if you need more information.
..
All parameters of the following section do not exist in the code.
Therefore we have commented out this section and replaced it with the
stub above.
TODO: This has to be resolved
Parameters for event generation
-------------------------------
.. index:: Q_0^2
.. index:: Q_as^2
.. index:: Chi_S
.. index:: Shower_Min_KT2
.. index:: KT2_Factor
.. index:: RescProb
.. index:: RescProb1
.. index:: Resc_KTMin
.. index:: ReconnProb
.. index:: Q_RC^2
The parameters related to the generation of inelastic events are
* ``Q_0^2`` (default @math{0.58 GeV^2}): factor scaling the infra-red
scale of ladder emissions
* ``Q_as^2`` (default @math{1.0 GeV^2}): infra-red scale of the strong
coupling
* ``Chi_S`` (default 0.60): factor scaling probability for singlet
propagators in ladders
* ``Shower_Min_KT2`` (default 2.0 GeV^2): minimum shower starting scale
* ``KT2_Factor`` (default 0.89): factor scaling the parton shower starting
scale
* ``RescProb`` (default 5.0): parameter controlling probability for
rescattering
* ``RescProb1`` (default 0.54): factor scaling rescatter
probility over singlet propagators
* ``Resc_KTMin`` (default 'off'): require minimum kt in rescattering (switch)
* ``ReconnProb`` (default -15.0): parameter regulating the strength of colour reconnections (logarithmic)
* ``Q_RC^2`` (default 0.72 GeV^2): regulator entering distance measure in colour reconnections