# 5.11. Multiple interactions¶

The basic MPI model is described in [SvZ87] while Sherpa’s implementation details are discussed in [A+a].

The following parameters are used to steer the MPI setup:

## 5.11.1. MI_HANDLER¶

Specifies the MPI handler. The two possible values
at the moment are `None`

and `Amisic`

.

## 5.11.2. AMISIC¶

Amisic can simulate the interaction of three different combinations of incoming particles:
proton–proton, photon–proton and photon–photon collision. The parameters for the simulation of photonic multiple
interactions can be found in [SS94]. It has several parameters to control the simulation of the
multiple-parton interactions, they are listed below. Each of these parameters has to be set in the
subsetting `AMISIC`

, like so

```
AMISIC:
PT_0: 2.5
```

The usual rules for yaml structure apply, c.f. Input structure.

`PT_0(ref)`

Value \(p_\text{T,0}^\text{(ref)}\) for the calculation of the IR regulator, see formula below. Defaults to

`2.2`

.`PT_0(IR)`

The absolute minimum of the IR regulator, see formula below. Defaults to

`0.5`

.`PT_Min(ref)`

Value \(p_\text{T,min}^\text{(ref)}\) for the calculation of the IR cutoff, see formula below. Defaults to

`3`

.`Eta`

The pseudorapidity \(\eta\) used to calculate the IR cutoff and regulator, \(p_\text{T,min}\) and \(p_\text{T,0}\). Defaults to

`0.16`

.`E(ref)`

Reference energy to normalise the actual cms energy for the calculation of the IR cutoff and regulator. Defaults to

`7000`

.`PT_Min`

The IR cut-off for the 2->2 scatters. It is calculated as

\[p_\text{T,min} = p_\text{T,min}^\text{(ref)} \left( \frac{E_\text{cms}}{E_\text{cms}^\text{(ref)}} \right)^\eta\]but can also be set explicitly.

`PT_0`

IR regulator \(p_\text{T,0}\) in the propagator and in the strong coupling. It is calculated as

\[p_\text{T,0} = p_\text{T,0}^\text{(ref)} \left( \frac{E_\text{cms}}{E_\text{cms}^\text{(ref)}} \right)^\eta\]but can also be set explicitly.

`MU_R_SCHEME`

Defaults to

`PT`

scheme. More schemes have yet to be added.`MU_R_FACTOR`

Factor to scale the renormalisation scale \(\mu_R\), defaults to

`0.5`

.`MU_F_FACTOR`

Factor to scale the factorisation scale \(\mu_F\), defaults to

`1.0`

.`SIGMA_ND_NORM`

Specifies the factor to scale the non-diffractive cross section calculated in the MPI initialisation. Defaults to

`0.4`

.`MATTER_FRACTION1`

Only to be used for double-gaussian matter form, where it will control the distribution of matter over the two gaussians. It assumes that a fraction \(f^2\) is distributed by the inner gaussian \(r_1\), another fraction \((1-f)^2\) is distributed by the outer gaussian \(r_2\), and the remaining fraction \(2f(1-f)\) is distributed by the combined radius \(r_\text{tot} = \sqrt{\frac{r_1^2+r_2^2}{2}}\). Defaults to

`0.5`

.`MATTER_RADIUS1`

Defaults to

`0.4`

. Is used to control the radius of the (inner) gaussian. If used with the double-gaussian matter form, this value must be smaller than MATTER_RADIUS2.`MATTER_RADIUS2`

Defaults to

`1.0`

. It is only used for the case of a double-gaussian overlap, see below.`MATTER_FORM`

Defaults to

`Single_Gaussian`

. Alternatively,`Double_Gaussian`

can be used to model the overlap between the colliding particles, however, it has not been tested yet.`nPT_bins`

Controls the number of bins for the numerical integration of

\[\int_{p_T^2}^{s/4} dp_T^2 \frac{d \sigma}{dp_T^2}\]Defaults to

`200`

.`nMC_points`

Number of points to estimate the the cross-section during the integration. The error should behave as \(\frac{1}{\sqrt{n_\text{MC}}}\). Defaults to

`1000`

.`nS_bins`

Number of points to sample in the center-of-mass energy \(\sqrt{s}\). This is only used if the energy is not fixed, i.e. in the case of EPA photons. Defaults to

`100`

.

The total cross-section is calculated with

\[\sigma_{tot} = X s^\epsilon + Y s^\eta\]where \(s\) is the Mandelstam invariant.

`PomeronIntercept`

The parameter \(\epsilon\) in the above equation, defaults to

`0.0808`

.`ReggeonIntercept`

The parameter \(\eta\) in the above equation, defaults to

`-0.4525`

.

The single- and double-diffractive cross-sections in the Regge picture have two free parameters:

`PomeronSlope`

The parameter \(\alpha^\prime\), default is

`0.25`

.`TriplePomeronCoupling`

The parameter \(g_{3\mathbb{P}}\) at an input scale of 20 GeV, given in \(\text{mb}^{-0.5}\), with default

`0.318`

.

## 5.11.3. MI ISR parameters¶

The following two parameters can be used to overwrite the ISR parameters
in the context of multiple interactions: `MPI_PDF_SET`

,
`MPI_PDF_SET_VERSIONS`

.