# 5.15. Minimum bias events¶

Minimum bias events are simulated through the Shrimps module in Sherpa.

## 5.15.1. Physics of Shrimps¶

### 5.15.1.1. Inclusive part of the model¶

Shrimps is based on the KMR model [RMK09], 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.

## 5.15.2. Parameters and settings¶

Below is a list of all relevant parameters to steer the Shrimps module.

### 5.15.2.1. Generating minimum bias events¶

To generate minimum bias events with Shrimps EVENT_TYPE has to be set to MinimumBias and SOFT_COLLISIONS to Shrimps.

### 5.15.2.2. 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.

### 5.15.2.3. Parameters of the eikonals¶

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:

$F_{1/2}(q_T) = \beta_0^2 (1 \pm \kappa) \frac{\exp(\frac{-\xi (1 \pm \kappa)q_T^2}{\Lambda^2})}{(1 + (1 \pm \kappa)q_T^2/\Lambda^2)^2}$

with the parameters

• $$\Lambda^2$$ (default 1.7 GeV^2)

• $$\beta_0^2(mb)$$ (default 25.0 mb)

• $$\kappa$$ (default 0.6)

• $$\xi$$ (default 0.2)