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‎_episodes/01-introduction.md

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---
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title: "1 - Introduction"
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teaching: 15
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exercises: 30
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title: "1 - Matrix Element Generator"
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teaching: 20
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exercises: 40
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questions:
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- "What are Monte Carlo Generators?"
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- "Why are we using simulated samples in CMS?"
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- "How are simulated samples created in CMS?"
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objectives:
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- "Use the MadGraph generator in standalone mode and get familiar with the basic syntax"
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- "Analyse the produced LHE files"
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- "Analyze the produced LHE files"
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keypoints:
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- "MadGraph is a widely used tool to generate matrix-element predictions for the hard scatter for SM and BSM processes."
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- "MadGraph can be used interactively, or steered using text-based cards"
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- "Gridpacks are used for large scale productions"
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- "MadAnalysis is a tool that allows for quick checks of kinematic distributions"
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- "Standalone MadGraph can run interactively on-the-fly or by importing the predefined text scripts"
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- "Gridpacks are used for large scale productions with consistency guaranteed"
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- "LHE level information is not physical and parton shower is needed to describe full physics"
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---
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# Introduction and first steps
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Samples of simulated events originating from certain processes are essential in high energy physics.
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They are used for studies of physics objects, background predictions or signal efficiency and acceptance determinations.
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Processes at vastly different energy regimes are involved, from the hard scattering process to hadronization and parton showering.
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Luckily, these different processes factorize which allows us to separate the treatment of processes happening at different momentum transfer scales.
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The hard scatter of the incoming partons happens at the highest involved scale, and can be treated perturbatively.
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Soft processes that finally lead to the formation of the observed final state hadrons cannot yet be calculated from first principles and therefore need to be modeled.
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Secondary interactions of other constituent partons of the colliding hadrons are called underlying event.
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Although the hard and soft process are distinct, they are connected by an evolutionary Markov process that leads to parton showering.
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The partons produced in this process eventually participate in the hadron formation (hadronization) where color singlet states are formed.
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Monte Carlo techniques can be used for simulating the Markov process, efficient integration of the high dimensional hard scatter problem, and the hadronization models.
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## Using Madgraph to simulate the hard scatter process
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In the first part of the exercise, we will use the matrix element generator MadGraph5 _aMC@NLO, or in short MG5.
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MG5 can perform automatic matrix element predictions for many processes at leading and next-to-leading order accuracy in QCD.
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Because of its ease of use for processes both in and beyond the standard model, it is one of the most widely used software tools to model the hard interaction.
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We will first use the interactive prompt of MG5 to generate proton proton collision events that produce W bosons.
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Although quite old, [link](https://arxiv.org/pdf/1304.6677.pdf) is a great reading material to get a general overview of Monte Carlo event generators.
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Monte Carlo event generators are essential components of almost all experimental analyses and are also widely used by theorists and experiments to make predictions and preparations for future experiments.
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It is one of the topics where we CMS experimentalists and theorists have the closest connections to, theorists give us predictions and experimentalists verify them with the actual data.
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Although Monte Carlo event generators are extremely important tools in HEP, they are often used as black boxes which we more or less treat them as "data".
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Our aim is to get the minimal background of how these tools are working and analyze them using the generator level information.
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Samples that are used by CMS experiments go through several steps of simulation :
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1. Monte Carlo event generator
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2. Detector simulation
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3. Pileup mixing
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4. Trigger emulation
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5. Object econstruction
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We focus on "1. Monte Carlo event generator" in this tutorial.
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Monte Carlo event generator can be further divided into several subpieces as each steps can be factorized and can be handled through separate calculations :
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1. Parton distribution function (PDF)
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2. Hard scattering (matrix element calculation)
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3. Parton shower & hadronization
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First of all, LHC is a proton-proton collider, hence we need information on how partons (quarks and gluons) are distributed in the proton (PDF).
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Hard scattering is the part where calculations can be treated perturbatively, interactions of incoming partons with the largest momentum transfer (usually the physics process we are interested in).
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Parton shower & hadronization further describes how the particles involed in the hard scattering evolve, working downwards to lower momentum scales even to a point where perturbative calculations break down.
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## Using Standalone Madgraph
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In the first part of the exercise, we will use the matrix element generator MadGraph5 _aMC@NLO, or in short MadGraph [link](https://launchpad.net/mg5amcnlo).
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MadGraph can perform the calculations for many different physics processes (both SM and BSM) at leading and next-to-leading order (LO & NLO) in QCD.
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Because of its easy user interface and flexibility with UFO models, you can test wide variety of physics modeling.
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We will now first see how MadGraph runs interactively in standalone mode using simple `W+` (wplus) process as an example.
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We will first use the interactive prompt of MadGraph to generate proton proton collision events that produce W bosons.
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First, log in to a new session on the LPC cluster (`ssh -Y <USERNAME>@cmslpc-el8.fnal.gov`).
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Make sure you have completed the <a href="../setup.html">setup</a> steps!
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Then, start the interactive prompt of Madgraph:
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~~~bash
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cd ~/nobackup/cmsdas_2025_gen/MG5_aMC_v2_6_5/
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cd ~/nobackup/cmsdas_2025_gen/MG5_aMC_v3_5_2/
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./bin/mg5_aMC
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~~~
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{: .source}
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Alternatively, remove `-nojpeg` from the output line and look at the diagrams in jpeg format using `display`.
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Now that MG has figured out the feynman diagrams you can start the actual computation within the MG5 prompt with
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Now that Madgraph has figured out the feynman diagrams you can start the actual computation within the MG5 prompt with
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~~~bash
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launch
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~~~
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launch wplustest_4f_LO
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~~~
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{: .source}
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MG will ask you a few more questions. The first one you can just skip by pressing \<RETURN\>.
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Once asked about the `run_card`, one can either use a default run card by just inserting `2` and hitting \<RETURN\> to edit the default `run_card` by hand, or provide a path to a run card of one's choice.
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Please provide the path to the pre-made run_card: `wplustest_4f_LO_run_card.dat`
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Madgraph will ask you a few more questions. Press `tab` to turn off the timer (otherwise, MadGraph will move on by itself after 60 seconds).
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~~~
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/===========================================================================\
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| 1. Choose the shower/hadronization program shower = Not Avail. |
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| 2. Choose the detector simulation program detector = Not Avail. |
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| 3. Choose an analysis package (plot/convert) analysis = Not Avail. |
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| 4. Decay onshell particles madspin = OFF |
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| 5. Add weights to events for new hypp. reweight = Not Avail. |
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\===========================================================================/
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~~~
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{: .output}
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The first one you can just skip by pressing \<RETURN\>. As we did not install any other `shower`, `detector`, `analysis package`, they are in `Not Avail.` state.
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~~~
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Do you want to edit a card (press enter to bypass editing)?
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/------------------------------------------------------------\
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| 1. param : param_card.dat |
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| 2. run : run_card.dat |
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\------------------------------------------------------------/
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you can also
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- enter the path to a valid card or banner.
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- use the 'set' command to modify a parameter directly.
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The set option works only for param_card and run_card.
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Type 'help set' for more information on this command.
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- call an external program (ASperGE/MadWidth/...).
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Type 'help' for the list of available command
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[0, done, 1, param, 2, run, enter path][90s to answer]
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~~~
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{: .output}
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Let's take a look at the `param card` and see how the values are set, press `1` and `ENTER` (\<RETURN\>) to investigate the parameter settings.
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~~~
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###################################
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## INFORMATION FOR MASS
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###################################
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Block mass
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5 4.700000e+00 # MB
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6 1.730000e+02 # MT
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15 1.777000e+00 # MTA
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23 9.118800e+01 # MZ
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25 1.250000e+02 # MH
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...
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###################################
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## INFORMATION FOR DECAY
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###################################
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DECAY 6 1.491500e+00 # WT
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DECAY 23 2.441404e+00 # WZ
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DECAY 24 2.047600e+00 # WW
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DECAY 25 6.382339e-03 # WH
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~~~
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{: .output}
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Let's take a look at the `run card` and see how the values are set, press `2` and `ENTER` (\<RETURN\>) to investigate the run settings.
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~~~
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#*********************************************************************
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# Number of events and rnd seed *
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# Warning: Do not generate more than 1M events in a single run *
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#*********************************************************************
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10000 = nevents ! Number of unweighted events requested
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0 = iseed ! rnd seed (0=assigned automatically=default))
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...
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#*********************************************************************
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# Collider type and energy *
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# lpp: 0=No PDF, 1=proton, -1=antiproton, *
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# 2=elastic photon of proton/ion beam *
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# +/-3=PDF of electron/positron beam *
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# +/-4=PDF of muon/antimuon beam *
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#*********************************************************************
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1 = lpp1 ! beam 1 type
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1 = lpp2 ! beam 2 type
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6500.0 = ebeam1 ! beam 1 total energy in GeV
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6500.0 = ebeam2 ! beam 2 total energy in GeV
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...
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#*********************************************************************
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# Standard Cuts *
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#*********************************************************************
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# Minimum and maximum pt's (for max, -1 means no cut) *
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#*********************************************************************
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10.0 = ptl ! minimum pt for the charged leptons
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-1.0 = ptlmax ! maximum pt for the charged leptons
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{} = pt_min_pdg ! pt cut for other particles (use pdg code). Applied on particle and anti-particle
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{} = pt_max_pdg ! pt cut for other particles (syntax e.g. {6: 100, 25: 50})
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...
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#*********************************************************************
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# Minimum and maximum invariant mass for pairs *
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#*********************************************************************
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0.0 = mmll ! min invariant mass of l+l- (same flavour) lepton pair
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-1.0 = mmllmax ! max invariant mass of l+l- (same flavour) lepton pair
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{} = mxx_min_pdg ! min invariant mass of a pair of particles X/X~ (e.g. {6:250})
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{'default': False} = mxx_only_part_antipart ! if True the invariant mass is applied only
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! to pairs of particle/antiparticle and not to pairs of the same pdg codes.
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...
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#*********************************************************************
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# maximal pdg code for quark to be considered as a light jet *
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# (otherwise b cuts are applied) *
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#*********************************************************************
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4 = maxjetflavor ! Maximum jet pdg code
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~~~
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{: .output}
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Try editting the beam energy (`ebeam1` and `ebeam2`) `6500` to `6800` as we are now running at 13.6TeV beam energy.
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When done with editting, escape after saving the changes in the text file.
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MadGraph allows you to change settings by interactively typing in below as well.
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~~~
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set run_card nevents 5000
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~~~
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{: .output}
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Take a look at the run card again and see if number of events to generate (`nevents`) is changed to `5000`.
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And change it back to `10000` using same command and check again.
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As shown above, there are several phase space cuts set by default (e.g. `10.0 = ptl`).
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There is a handy command that removes all phase space cuts at once (instead of doing `set run_card ptl 0`, `set run_card ptj 0`, ... one by one by hand).
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~~~
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set no_parton_cut
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~~~
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{: .output}
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Take a look at the card again and see if lepton pt cut (`ptl`) is changed to `0`.
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Keep in mind that the cuts you give before doing `set no_parton_cut` will be removed by this command.
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So don't forget to do `set no_parton_cut` before giving the cuts you wish to give.
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Once you are done, please provide the path to the pre-made run_card: `wplustest_4f_LO_run_card.dat`
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What is the cross section determined by Madgraph?
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> > ~~~
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> > === Results Summary for run: run_01 tag: tag_1 ===
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> >
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> > Cross-section : 2.752e+04 +- 36.14 pb
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> > Cross-section : 2.715e+04 +- 39.45 pb
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> > Nb of events : 10000
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> >
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> > INFO: No version of lhapdf. Can not run systematics computation
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> > INFO: Done
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> > ~~~
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> > {: .output}
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> > The cross section calculated by MG is `2.752e+04 +- 36.14 pb`.
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> > The cross section calculated by MG is `2.715e+04 +- 39.45 pb`.
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> {: .solution}
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{: .challenge}
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> {: .solution}
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{: .challenge}
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> ## What does each column mean?
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>
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> > ## Solution
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> > `ID`, `status`, `mother1`, `mother2`, `color`, `anticolor`, `px`, `py`, `pz`, `E`, `mass`, `life time`, and `spin`
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> > ~~~output
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> > -11 1 3 3 0 0 -2.3393803385e+01 -7.4187481776e+00 -1.5274153214e+02 1.5470062541e+02 0.0000000000e+00 0.0000e+00 1.0000e+00
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> > ~~~
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> > {: .output}
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> > This line tells you that a positron (`ID`) is an outgoing particle (`status`) with Z as its mother (`mother1` and `mother2` : 3rd particle is Z which is `ID=23`) with no color (`color` and `anticolor`), ...
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> {: .solution}
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{: .challenge}
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> ## MadGraph syntax
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> If you want to add another process, e.g. production of W- in the above example, you can add another process with `add process p p > w-, w- > ell- vl~`
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>
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> > ~~~
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> > === Results Summary for run: run_01 tag: tag_1 ===
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> >
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> > Cross-section : 4.732e+04 +- 57.08 pb
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> > Cross-section : 4.667e+04 +- 63.91 pb
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> > Nb of events : 10000
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> > ~~~
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> > {: .output}
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> > The cross section calculated by MG is `4.732e+04 +- 57.08 pb`.
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> > The cross section calculated by Madgraph is `4.732e+04 +- 57.08 pb`.
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> > While one would naiively expect the cross section to double by including W- bosons we only get a cross section that is ~40% larger.
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> > The simplified explanation is that the initial state protons contain more up valence quarks than down valence quarks.
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> {: .solution}
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The cards are located in the MG section of the genproductions directory
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~~~bash
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cd ~/nobackup/cmsdas_2025_gen/genproductions_mg265/bin/MadGraph5_aMCatNLO
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cd ~/nobackup/cmsdas_2025_gen/genproductions_mg352/bin/MadGraph5_aMCatNLO
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time ./gridpack_generation.sh wplustest_4f_LO cards/examples/wplustest_4f_LO local
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~~~
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{: .source}
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> For a given process name $NAME, the input cards must be named as $NAME_run_card.dat, $NAME_proc_card.dat, etc...
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{: .callout}
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The cards for Run2 UL samples that were generated with MG can be found in `bin/MadGraph5_aMCatNLO/cards/production/2017/13TeV/` of the [genproductions repo](https://github.com/cms-sw/genproductions/tree/master/bin/MadGraph5_aMCatNLO/cards/production/2017/13TeV).
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<!-- The cards for Run2 UL samples that were generated with MG can be found in `bin/MadGraph5_aMCatNLO/cards/production/2017/13TeV/` of the [genproductions repo](https://github.com/cms-sw/genproductions/tree/master/bin/MadGraph5_aMCatNLO/cards/production/2017/13TeV). -->
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~~~bash
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mkdir work
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cd work
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tar xf ../wplustest_4f_LO_slc7_amd64_gcc700_CMSSW_10_6_19_tarball.tar.xz
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tar xf ../wplustest_4f_LO_el8_amd64_gcc10_CMSSW_12_4_8_tarball.tar.xz
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NEVENTS=10000
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RANDOMSEED=12345
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## Comparing the LHE output
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There are multiple ways of analyzing an LHE file, each of which has its own advantages and disadvantages.
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For the purpose of this exercise, we will use the most straightforward tool: MadAnalysis (MA).
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For the purpose of this exercise, we will use a pre-made pyroot script.
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~~~bash
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cd ~/nobackup/cmsdas_2025_gen/
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cp /eos/uscms/store/user/cmsdas/2025/short_exercises/generators/LHEReader.py .
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~~~
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{: .source}
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#### Convert LHE output to root format
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> ## Make sure the Python virtual environment is deactivated
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> If you are still using the virtual environment, you need to unset it in order to not interfere with the CMSSW environment.
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> {: .source}
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{: .callout}
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~~~bash
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cd CMSSW_12_4_8/src; cmsenv; cd -
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python3.9 LHEReader.py --input MG5_aMC_v3_5_2/wplustest_4f_LO/Events/run_01/unweighted_events.lhe --output standalone.root
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python3.9 LHEReader.py --input genproductions_mg352/bin/MadGraph5_aMCatNLO/work/cmsgrid_final.lhe --output cmsgrid.root
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~~~
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{: .source}
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Feel free to experiment here and plot various quantities. What are the shapes of the lepton pT distributions? What is the shape of the pT distribution of the W system? Are these shapes physical?
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<!-- The most straightforward tool: MadAnalysis (MA).
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MA is a tool designed to be used by theorists to analyze parton-level LHE files, particle-level HEPMC files or even events with DELPHES detector simulation.
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We can install MA directly from the MG5 console.
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~~~bash
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cd $CDGPATH/MG5_aMC_v2_6_5/
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cd ~/nobackup/cmsdas_2025_gen/MG5_aMC_v3_5_2/
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./bin/mg5_aMC
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~~~
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{: .source}
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firefox ANALYSIS_0/Output/HTML/MadAnalysis5job_0/index.html
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What observations do you make? Are the two datasets consistent? What are the shapes of the lepton pT distributions? What is the shape of the pT distribution of the W system? Are these shapes physical?
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Feel free to experiment here and plot other quantities you find interesting. You can refer to the [user manual](https://arxiv.org/pdf/1206.1599.pdf) to learn about the syntax.
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Feel free to experiment here and plot other quantities you find interesting. You can refer to the [user manual](https://arxiv.org/pdf/1206.1599.pdf) to learn about the syntax. -->
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{% include links.md %}
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