# 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.