The First run

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A First Herwig Run: Z Production at the LHC

In the first part of this tutorial, we will simulate the process pp -> Z -> e+e- at sqrt(s) = 13 TeV at the LHC. We will focus on the different components of the event generator - we will start by simulating the hard process and then include parton shower and hadronisation components.

Please start by creating a work directory in your preferred path:

mkdir Herwig_tutorial
cd Herwig_tutorial

For this part of the tutorial, you will need to download this file:

You can do this manually or using the following terminal command:

wget https://phab-files.hepforge.org/file/download/v4xwihvtrkawxvwazfpg/PHID-FILE-iyegxl2qznfz5wyptfkq/LHC.in

Step 1: Hard Process Generation

Look inside the LHC.in input file. This is where we specify the details of our simulation. For our case, we need to specify the following:

• This is a proton-proton collision
• We want sqrt(s) = 13000 GeV
• We want to generate Drell-Yan Z/gamma
• We just want e+ e- (no other pairs)

This is also the place to specify any cuts on the events we want to generate. To make things efficient, we can specify cuts of the combined mass of the electrons to be around the Z boson mass.

Running Herwig

Simulating events in Herwig involves two steps:

DRH Herwig read LHC.in

will generate the LHC.run file (combines all the requested settings with integrated MEs, ready for the simulation). This can then be run with

DRH  Herwig run LHC.run -N 10000 -j 8

which generates 10000 events, parallelised into 8 separate jobs. The results will be 8 distinct sets of output files

LHC-1.log  LHC-1.out  LHC-1.tex  LHC-1.yoda

to

LHC-8.log  LHC-8.out  LHC-8.tex  LHC-8.yoda

Here, .log files contain details of the first few events. The cross-section calculated from these simulated events is also provided at the end. Useful analyses of the event and the electron pair are done using Rivet and stored as histograms in .yoda files. These files can be merged back together and combined using

DRH yodamerge LHC-*.yoda -o LHC.yoda

Now, you can plot these histograms using

DRH rivet-mkhtml --mc-errs LHC.yoda

This will create histograms in a folder called rivet-plots. For now, focus on the MC_ZINC folder, which has observables for the Z.

(Careful - every time this folder is overwritten, you can specify a different folder name using -o)

Monte Carlo and Convergence

Now try simulating 1, 10, 100, 1000, 10000 and 100000 events. What happens to the cross-section and its uncertainty as you increase the number of events? Does this agree with what we talked about in the lectures?

(You should achieve results like this GIF)

Step 2: The Parton Shower

You will notice in your plots that while the Z mass and rapidity show interesting distributions, the famously used Z p_T distribution is empty. This is because the quarks from our protons collide face-to-face. Gluon/Photon emissions from these quarks would offset their path, leading to the Z gaining transverse momentum. Similarly, the electron pair can emit photons, changing their trajectory.

Additionally, the emitted gluons can emit more gluons and decay into quark-antiquark pairs. This leads to a chain reaction/cascade, giving rise to jets.

Parton Showers Choices

Let's stick to QCD for now - In LHC.in, you will find the options for two parton shower models:

• The Angular Ordered Shower: The default shower in Herwig. This shower orders emissions by the angle generated between the emitter and the emission.

• The Dipole Shower: The alternate shower. This model includes a third spectator parton, which is involved in maintaining colour flows and taking recoil from the emission.

Turn on one shower at a time and see what the Z p_T distribution looks like. You can now also have a look inside the MC_ZJETS folder, which does jet clustering with the quarks and gluons in the system.

You can now start renaming LHC.yoda and store the results of your different simulations. Multiple histograms can be plotted by the command

DRH rivet-mkhtml --mc-errs LHC-Angular.yoda LHC-Dipole.yoda ...

What immediate differences do you notice from before? Do the two showers agree with each other, or differ? If so, discuss the differences with your peers and the tutorial hosts.

Why is MPI off? We want to study the effect of the parton shower in isolation in this step. Additionally, we have a complete tutorial on Soft QCD that covers MPI in detail, which you can do after.

Step 3: Hadronisation

Due to confinement, all our quarks and gluons need to be converted into hadrons. While we don't have a full theory of this hadronisation process, we have models informed by the physical phenomena that we understand. There are two popular models of hadronisation used today, the string model and the cluster model.

In Herwig, use the cluster model. We start by forcing all gluons to split into quark-antiquark pairs, as well as the remnant of the proton into quarks and diquarks. These particles are paired up by their colour to form colourless pseudoparticles called clusters. These clusters then decay into unstable hadrons, which decay into stable ones. This model is based on the pre-confinement theory of quarks and relies on the parton shower to provide it with accurate momenta and colour.

Turning on Hadronisation

Enable Hadronisation by uncommenting the lines. What differences do you see? How do the two showers behave with the hadronisation model? Which areas of the histograms are affected most?

End of First Tutorial

Now you know how to generate an LHC Event in Herwig! We looked at each event generator component's contributions to the simulated results. You can now proceed to the second tutorial.

Next Steps: There are two tutorials you may be interested in looking into

• Second Run: NLO Processes, Matching and Merging
• Third Run: MPI, Diffraction, Colour Reconnection