# 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
wmath: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 rangw 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.

### Herwig 7.1. Baryonic Reconnection Tune¶

This tuned set of parameters is recommended for usage when running the baryonic colour reconnection model for high LHC energies. It was tuned to minimum bias data at $$\sqrt{s}=7\,\mathrm{TeV}$$ and $$\sqrt{s}=13\,\mathrm{TeV}$$, with a heavy focus on particle flavours and multiplicity distributions.

Parameter H7.1-BaryonicReconnection
$$p_{\perp,0}^{\min}$$ 3.053252
$$\mu^2/{\rm GeV}^2$$ 1.282032
$$p_{\rm reco}$$ 0.772606
$$p_{\rm recoB}$$ 0.477612
$$p_{\rm PwtSquark}$$ 0.291717
$$p_{\rm SplitPwtSquark}$$ 0.824135

In addition to the baryonic reconnection model the non-perturbative splitting of gluons into all light quark flavours (u,d,s) is allowed by:

set /Herwig/Hadronization/PartonSplitter:Split uds


and setting the constituent mass of the s-quark to:

set /Herwig/Particles/s:ConstituentMass 0.45*GeV
set /Herwig/Particles/sbar:ConstituentMass 0.45*GeV


The rate where a gluon splits into up, down and strange quarks is given by:

set /Herwig/Hadronization/PartonSplitter:SplitPwtSquark 0.824135


These parameters and options are all set in the snippet BaryonicReconnection.in which can be used by making it available in LHC-MB.in with:

read snippets/BaryonicReconnection.in


## 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:

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

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

 PDF 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

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.

1. 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

# Colour Disrupt settings
set /Herwig/Partons/RemnantDecayer:colourDisrupt 0.3493643

# Min KT parameter
set /Herwig/UnderlyingEvent/KtCut:MinKT 3.36

# This should always be 2*MinKT!!
set  /Herwig/UnderlyingEvent/UECuts:MHatMin 6.72


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

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

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

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

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

5. 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.