# Minimum-bias and underlying-event tunes¶

For a detailled discussion of the models used in this tunes, we refer to Eur.Phys.J. C72 (2012) 2225. That paper also explains the procedure used to deduce the tunes.

## Herwig 7.1 tunes¶

Herwig 7.1 comes with a set of default parameters for the parton shower cutoffs and hadronization that is set in the default input files. However, there are two sets of parameters for soft physics that come with the Herwig 7.1 release.

The model for multiple partonic interactions (MPI) is determined by the two parameters \(p_{\perp}^{\min}\) and \(\mu^2\). Emissions with \(p_\perp > p_{\perp}^{\min}\) are hard, while those below are soft. \(\mu^2\) gives the inverse of the proton radius, i.e. the transverse spatial extension of the partonic cloud that enters the collision. The minimum transverse momentum depends on the centre-of-mass energy \(\sqrt{s}\) and scales according to a power law

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

The parameter \(E_0\) is redundant and kept fixed at \(E_0=7\,{\rm TeV}\).

A second set of parameters governs the production of soft particles in a ladder, \(\langle N\rangle\), which was parametrized with the following power law:

\(\langle N\rangle =N_0\left(\frac{s}{1\,\mathrm{TeV}^2}\right)^P\).

\(p_{\rm reco}\) gives the probability to accept a proposed colour reconnection.

### Herwig 7.1 default tune¶

A default set of parameters for the simulation of the underlying event in all events is already given by the default input files.

Parameter | H7.1-Default |
---|---|

\(p_{\perp,0}^{\min}\) | 3.568157 |

\(b\) | 0.420445 |

\(\mu^2/{\rm GeV}^2\) | 1.489997 |

\(P\) | -0.088983 |

\(N_0\) | 1.086029 |

\(p_{\rm reco}\) | 0.652710 |

### Herwig 7.1 SoftTune¶

A second set of parameters was obtained with an energy dependent tuning procedure. The parameters \(P\) and \(N_0\) were fixed to their calculated values and the remaining parameters of the MPI model were tuned to minimum bias data at \(\sqrt{s}=900\,\mathrm{GeV}\), \(\sqrt{s}=7\,\mathrm{TeV}\) and \(\sqrt{s}=13\,\mathrm{TeV}\). The following set of parameters gives a good description of the whole range of minimum bias and underlying event data from from Tevatron’s lowest energy \(\sqrt{s}=300\,\mathrm{GeV}\) to the LHC’s \(\sqrt{s}=13\,\mathrm{TeV}\). Awaiting futher analyses a good description of 14 TeV data is also anticipated.

Parameter | H7.1-SoftTune |
---|---|

\(p_{\perp,0}^{\min}\) | 3.502 |

\(b\) | 0.416 |

\(\mu^2/{\rm GeV}^2\) | 1.402 |

\(P\) | -0.08 |

\(N_0\) | 0.95 |

\(p_{\rm reco}\) | 0.5 |

These parameters are set in the snippet `SoftTune.in`

which is used by
`LHC-MB.in`

as the default option and recommended for the simulation
of minimum bias and underlying event data.

## Tunes suitable for older versions of Herwig++¶

The improvements to both shower modules, as well as the inclusion of next-to-leading order cross sections in Herwig 7 have required a new tune to \(e^+ e^−\) data. Therefore, MPI tunes suitable for older version of Herwig can not be used with Herwig 7.

### Herwig 7.0 tune H7-UE-MMHT¶

It was shown in Ref.[JHEP 1310 (2013) 113] that a good description of both underlying event and double parton scattering data Ref.[JHEP 1303 (2013) 129] can be obtained if one includes the latter in the data being fit to with a sufficiently high weight. We followed the procedure described in Ref.[JHEP 1310 (2013) 113] using MMHT2014 LO parton distribution function [1] and obtained a tune consistent with double parton scattering data (\(\sigma_{\!\textit{eff}}\approx15\,\mathrm{mb}\)) which also gives a good description of the underlying event data from Tevatron’s lowest energy point \(\sqrt{s}=300\,\mathrm{GeV}\) to the LHC’s \(\sqrt{s}=7\,\mathrm{TeV}\).

Parameter | H7-UE-MMHT |
---|---|

\(p_{\perp,0}^{\min}\) | 4.39 |

\(b\) | 0.366 |

\(\mu^2/{\rm GeV}^2\) | 2.30 |

\(p_{\rm disrupt}\) | 0.798 |

\(p_{\rm reco}\) | 0.4276 |

Hw7.0 is released together with the tune H7-UE-MMHT, by default.

Please note that the tune is not suitable for lower energy runs (below \(\sqrt{s}=300\,\mathrm{GeV}\)). Please contact the authors to get more information.

### Herwig++ 2.7¶

Parameter | UE-EE-5-CTEQ6L1 | UE-EE-5 (MRST LO✶✶) |

\(p_{\perp,0}^{\min}\) | 3.91 | 4.620 |

\(b\) | 0.33 | 0.314 |

\(\mu^2/{\rm GeV}^2\) | 2.30 | 2.240 |

\(p_{\rm disrupt}\) | 0.80 | 0.860 |

\(p_{\rm reco}\) | 0.49 | 0.420 |

### Herwig++ 2.6¶

From Herwig++ 2.6 we use an automatic energy evolution of the \(p_\perp^{\min}\) governed by the equation:

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

In the table below we present the parameters of the energy-extrapolating underlying-event tunes. Two different tunes for the plain colour reconnection (PCR) model using two different PDF sets MRST LO✶✶ (UE-EE-4) and CTEQ6L1 (UE-EE-4-CTEQ6L1) and one tune for the statistical colour reconnection (SCR) using CTEQ6L1 PDF set, UE-EE-SCR-CTEQ6L1. The first two parameters in the table below describe the running of \(p_\perp^{\min}\) according to the equation above.

Parameter | UE-EE-4-CTEQ6L1 | UE-EE-4 (MRST LO✶✶) | UE-EE-SCR-CTEQ6L1 |

\(p_{\perp,0}^{\min}\) | 2.81 | 3.11 | 2.64 |

\(b\) | 0.24 | 0.21 | 0.21 |

\(\mu^2/{\rm GeV}^2\) | 1.35 | 1.11 | 1.5 |

\(p_{\rm disrupt}\) | 0.75 | 0.80 | 0.8 |

\(p_{\rm reco}\) | 0.61 | 0.54 | N/A |

\(c\) | N/A | N/A | 0.01 |

\(f\) | N/A | N/A | 0.21 |

\(N_{\rm steps}\) | N/A | N/A | 10 |

\(\alpha\) | N/A | N/A | 0.66 |

These tunes are implemented in the following input files:

N.B.

- The reference scale] \(E_0\) is set to 7000 GeV.
- Please note that
`LHC-UE-EE-4`

is identical to`LHC-UE-EE-3`

, but uses the value for \(p_{\perp}^{\min}\) from the extrapolation formula also for 900, 1800 and 7000 GeV. There are no significant differences in the observables. The same is true for`LHC-UE-EE-4-CTEQ6L1`

and`LHC-UE-EE-3-CTEQ6L1`

.

### Herwig++ 2.5¶

UE-EE-3 for MRST LO✶✶ (default in Herwig++ 2.5) and CTEQ6L1 PDFs

The third generation of energy-extrapolation tunes for two PDF sets can be obtained here:

- LHC-UE-EE-3.in (MRST LO✶✶)
- LHC-UE-EE-3-CTEQ6L1.in

The tunes provide a better energy-extrapolation and can be used at 14 TeV.

Plots for various analyses are provided Herwig++ 2.5 EE3.

CTEQ6L1 | MRST LO✶✶ | Plots UE-EE-2 vs UE-EE-3 (CTEQ6L1 and MRST LO✶✶) | |

\(\sqrt{s}\) | \(p_\perp^{\min}\) | ||

900 | 1.55 | 1.86 | ATLAS_2010_S8894728 |

1800 | 2.26 | 2.55 | CDF_2001_S4751469 |

2760 | 2.33 | 2.62 | No data |

7000 | 2.752 | 3.06 | ATLAS_2010_S8894728 vs UE-EE-2, vs UE7-2 |

8000 | 2.85 | 3.21 | No data |

14000 | 3.16 | 3.53 | No data |

with these fixed parameters

Parameter | CTEQ6L1 | MRST LO✶✶ |

\(p_{\rm disrupt}\) | 0.75 | 0.80 |

\(\mu^2/{\rm GeV}^2\) | 1.35 | 1.11 |

\(p_{\rm reco}\) | 0.61 | 0.54 |

N.B You have to choose the desired center-of-mass energy in the input files! Please read the instructions inside the files carefully.

#### UE-EE-2¶

\(\mu^2 = 1.1/{\rm GeV}^2\), \(p_{\rm disrupt}=0.15\), \(p_{\rm reco}= 0.55\), (input file: LHC-UE-EE-2.in )

\(\sqrt{s}\) | Name | \(p_\perp^{\min}\) | Plots UE-EE-2 vs UE-EE-1 vs (UE7 and MU900) |

900 | UE-EE-2 | 2.34 | ATLAS_2010_S8894728 900 |

1800 | UE-EE-2 | 3.09 | plots |

7000 | UE-EE-2 | 4.02 | ATLAS_2010_S8894728 7000 |

Based on this results we made interpolation to \(\sqrt(s) = 2.76 {\rm TeV}\) and suggest to use ‘’‘ptMin = 3.31’‘’ for UE studies at this energy (input file: LHC-UE-EE-2.in).

N.B. You have to choose the desired center-of-mass energy at two places in the LHC-UE-EE-2.in file! Please read the instructions inside the file carefully.

#### Minimum Bias and Underlying Event, 900 GeV and 7 TeV¶

Data | Name | Main parameters | Input file | Plots |

7000 ATLAS UE | LHC-UE7-2 | \(p_{\perp}^{\min}=3.36\) \(\mu^2 =0.81 /{\rm GeV}^2\), \(p_{\rm disrupt}=0.35\), \(p_{\rm reco}=0.616\) | LHC-UE7-2.in | LHC-MU900-2.in | |

900 ATLAS UE&MB(Nch >=6) | MU900-2 | \(p_{\perp}^{\min}=2.60\) \(\mu^2 =1.15 /{\rm GeV}^2\), \(p_{\rm disrupt}=0.298\), \(p_{\rm reco}=0.41\) | UE7-2 vs UE7-1, UE plots | MU900-2 vs MU900-1, MB and UE plots |

**Note about deprecated tunes**

**The first generation of MB and UE tunes (LHC-MU900-1, LHC-UE7-1, LHC-UE-EE-*-1) overestimated
the production of strange hadrons and the b-fragmentation function was also not described properly. Therefore, we discourage the use of the
first generation of MB and UE tunes for production runs. This problem was fixed
in the second generation of tunes, which you can obtain here.**

##### How to use these tunes¶

To generate minimum-bias events, the provided run cards can be used as is. To generate hard processes with one of the tunes provided above, follow these steps in your run card.

Set the colour reconnection, colour disrupt and MPI parameters as found in the respective input file (e.g. LHC-UE7-1.in). The following example uses the parameters from the LHC-UE7-1 tune

# Colour reconnection settings set /Herwig/Hadronization/ColourReconnector:ColourReconnection Yes set /Herwig/Hadronization/ColourReconnector:ReconnectionProbability 0.6165547 # Colour Disrupt settings set /Herwig/Partons/RemnantDecayer:colourDisrupt 0.3493643 # inverse hadron radius set /Herwig/UnderlyingEvent/MPIHandler:InvRadius 0.81 # Min KT parameter set /Herwig/UnderlyingEvent/KtCut:MinKT 3.36 # This should always be 2*MinKT!! set /Herwig/UnderlyingEvent/UECuts:MHatMin 6.72

Adopt these MPI settings:

set /Herwig/UnderlyingEvent/MPIHandler:softInt Yes set /Herwig/UnderlyingEvent/MPIHandler:twoComp Yes set /Herwig/UnderlyingEvent/MPIHandler:DLmode 3

Select the matrix element for the hard subprocess, e.g.

cd /Herwig/MatrixElements/ insert SubProcess:MatrixElements[0] MEqq2gZ2ff

Optional: select kinematic cuts to be applied for the hard subprocess, e.g.

cd /Herwig/Cuts set LeptonKtCut:MinKt 10.0*GeV

Specify which of the hard processes (selected above in SubProcess:MatrixElements) is identical to the UE one, i.e. QCD dijets.

# -1 means, none of the matrix elements is QCD dijet production set /Herwig/UnderlyingEvent/MPIHandler:IdenticalToUE -1

The main difference of these instructions to the ready-to-use minimum bias run cards is that the minimum-bias-specific settings are dropped:

```
set JetKtCut:MinKT 0.0*GeV
set Cuts:MHatMin 0.0*GeV
set Cuts:X1Min 0.055
set Cuts:X2Min 0.055
```

[1] | In the near future we also plan to provide tunes using CT14 and NNPDF3.0 parton distribution functions. |