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 2.05.

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 2.25.

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

\[p_\text{T,min} = p_\text{T,min}^\text{(ref)} \left( \frac{E_\text{cms}}{E_\text{cms}^\text{(ref)}} \right)^{2\eta}\]

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

\[p_\text{T,0} = p_\text{T,0}^\text{(ref)} \left( \frac{E_\text{cms}}{E_\text{cms}^\text{(ref)}} \right)^{2\eta}\]

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 1.02.

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 40.

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.