Multiple-Parton Interactions model

The default underlying event model of Herwig++ is currently based on the eikonal model. It models the underlying event activity as additional semi-hard and soft partonic interactions. In doing so, it allows the description of minimum bias events as well as the underlying event in hard scattering processes.

Main parameters of the model

The main parameters of the model are those controlling the matter distribution in the proton

  • \(\mu^2\), the inverse hadron radius squared which is set using:

    set /Herwig/UnderlyingEvent/MPIHandler:InvRadius x
    

and

  • \(p_\perp^{\min}\), a transition scale between soft and semi-hard nteractions [1] which by default is now set using a power-law energy extrapolation

    \(p_\perp^{\min}=p_{\perp,0}^{\min}\left(\frac{\sqrt{s}}{E_0}\right)^b\)

with parameters

  • \(p_{\perp,0}^{\min}\), the value of \(p_\perp^{\min}\) at the reference scale \(E_0\) set using:

    set /Herwig/UnderlyingEvent/MPIHandler:pTmin0 x*GeV
    
  • \(b\) the power for power law extrapolation which is set using:

    set /Herwig/UnderlyingEvent/MPIHandler:Power x
    
  • \(E_0\) the reference energy scale for power law energy extrapolation is set using:

    set /Herwig/UnderlyingEvent/MPIHandler:ReferenceScale x*GeV
    

    The default value is 7 TeV.

For colour reconnection, by default we use the so-called plain colour reconnection model with just one parameter:

  • \(p_{\rm reco}\) the colour reconnection probability in the plain colour reconnection model which is set using:

    set /Herwig/Hadronization/ColourReconnector:ReconnectionProbability x
    

    There is also more complicated statistical colour reconnection model available in Herwig++, see Colour reconnection models.

Colour reconnection models

Currently there are two colour reconnection models implemented in Herwig: the plain model (default) and more complicated the statistical model,

  • ColourReconnectionAlgorithm parameter selects the colour reconnection model to be used. Possible values are Plain for the plain model (PCR), and Statistical for the statistical model (SCR).

The PCR model was discussed above the more complex SCR has the following parameters:

  • \(c\), the initial temperature in the SCR model which is set using:

    set /Herwig/Hadronization/ColourReconnector:InitialTemperature x
    
  • \(\alpha\), in the SCR model, the number of reconnection tries per temperature step is the number of clusters times this factor. It is set using:

    set /Herwig/Hadronization/ColourReconnector:TriesPerStepFactor x
    
  • \(f\) the ratio of the temperatures in two successive temperature steps in the SCR model. It is set using:

    set /Herwig/Hadronization/ColourReconnector:AnnealingFactor x
    
  • \(N_{\rm steps}\) the number of temperature steps in the SCR model. It is set using:

    set /Herwig/Hadronization/ColourReconnector:AnnealingSteps x
    

Energy extrapolation

As we mentioned above the only energy dependent parameter of the model is \(p_\perp^{\min}\). There are three options how to set \(p_\perp^{\min}\) at different energies steered by:

  • EnergyExtrapolation parameter, which enables and selects the extrapolation of the ptmin cut-off. It is set using:

    set /Herwig/UnderlyingEvent/MPIHandler:EnergyExtrapolation x
    

    x takes three possible values:

    • Power: power-law (default), \(p_\perp^{\min}=p_{\perp,0}^{\min}\left(\frac{\sqrt{s}}{E_0}\right)^b\), see above how to set the parameters.

    • Log: logarithmic extrapolation, \(p_\perp^{\min}=A\log\left(\frac{\sqrt{s}}{B}\right)\), which is set using:

      set /Herwig/UnderlyingEvent/MPIHandler:EEparamA A
      set /Herwig/UnderlyingEvent/MPIHandler:EEparamB B
      
    • No: no extrapolation, use \(p_\perp^{\min}\) as explicitly set using the interface:

      set /Herwig/UnderlyingEvent/MPIHandler:pTmin x*GeV
      

      If no energy extrapolation is selected, MHatMin has to be set to exactly \(2p_\perp^{\min}\)!:

      set /Herwig/UnderlyingEvent/KtCut:MinKT x*GeV
      
[1]

If soft MPI model is switched off:

set /Herwig/UnderlyingEvent/MPIHandler:softInt No

the \(p_\perp^{\min}\) is not a transition scale but the minimum transverse momentum of additional semi-hard interactions.