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3. first test

chapter two

3.1 process description

MG is an automatic code generator, hence it's necessary to instruct the program about the process to be generated

3.1.1 elementary particles

Each elementary particle has a name in Madgraph language

particle symbol particle symbol
electron e- positron e+
neutrino-e ve anti-ve ve~
muon mu- anti-muon mu+
neutrino-mu vm anti-vm vm~
tau ta- antitau ta+
neutrino-ta vt anti-vt vt~
quark u u anti-u u~
quark d d anti-d d~
quark c c anti-c c~
quark s s anti-s s~
quark t t anti-t t~
quark b b anti-b b~
photon a gluon g
W- boson w- W+ boson w+
Z boson z higgs boson h
  • more particles defined in the naming scheme
  • one can define new particles:
define j = g u c d s u~ c~ d~ s~
define l+ = e+ mu+
define l- = e- mu-
define vl = ve vm vt
define vl~ = ve~ vm~ vt~
  • some of them are already present in MG:
define p = g u c d s u~ c~ d~ s~

3.1.2 the description of an elementary process

From the initial state to the final state, at LO

  • Z boson at proton colliders:
    • initial state: p p
    • final state: z
p p > z
  • electron-positron pairs at proton colliders:
    • initial state: p p
    • final state: e+ e-
p p > e+ e-

The second process is not equivalent to the first one:

  • the Z boson is not decayed in the first case

  • the second process contains all possible diagrams at LO that can produce a e+ e- pair starting from protons, while the second one has to generate a Z boson

  • W boson pairs with opposite charge at proton colliders:

    • initial state: p p
    • final state: w+ w-
p p > w+ w-
  • charged and neutral lepton pairs at proton colliders:
    • initial state: p p
    • final state: e- ve~ mu+ vm
p p > e- ve~ mu+ vm

3.2 fist test of MG

3.2.1 start an interative session

Start the interative session from the MG folder:

cd MG5_aMC_v2_7_2/
./bin/mg5_aMC

At startup, MG:

  • tries to load LHAPDF and FastJet; in this case it fails, since they have not been installed
  • loads the physics model to be used in the simulation:
Loading default model: sm
INFO: load particles
INFO: load vertices
INFO: Restrict model sm with file models/sm/restrict_default.dat .
INFO: Run "set stdout_level DEBUG" before import for more information.
INFO: Change particles name to pass to MG5 convention
  • defines some collections of particles:
Defined multiparticle p = g u c d s u~ c~ d~ s~
Defined multiparticle j = g u c d s u~ c~ d~ s~
Defined multiparticle l+ = e+ mu+
Defined multiparticle l- = e- mu-
Defined multiparticle vl = ve vm vt
Defined multiparticle vl~ = ve~ vm~ vt~
Defined multiparticle all = g u c d s u~ c~ d~ s~ a ve vm vt e- mu- ve~ vm~ vt~ e+ mu+ t b t~ b~ z w+ h w- ta- ta+

* why is the proton constituted of anti-quarks and gluons as well?
* how does one instruct MG about colliding protons or anti-protons?
* why are charged leptons defined grouping only electrons and muons?

3.2.2 generating a process

  • Z boson production at proton colliders, at LO:
MG5_aMC> generate p p > z
  • MG output: the program identified 4 processes with 4 diagrams:
INFO: Checking for minimal orders which gives processes.
INFO: Please specify coupling orders to bypass this step.
INFO: Trying process: g g > z WEIGHTED<=2 @1  
INFO: Trying process: u u~ > z WEIGHTED<=2 @1  
INFO: Process has 1 diagrams
INFO: Trying process: u c~ > z WEIGHTED<=2 @1  
INFO: Trying process: c u~ > z WEIGHTED<=2 @1  
INFO: Trying process: c c~ > z WEIGHTED<=2 @1  
INFO: Process has 1 diagrams
INFO: Trying process: d d~ > z WEIGHTED<=2 @1  
INFO: Process has 1 diagrams
INFO: Trying process: d s~ > z WEIGHTED<=2 @1  
INFO: Trying process: s d~ > z WEIGHTED<=2 @1  
INFO: Trying process: s s~ > z WEIGHTED<=2 @1  
INFO: Process has 1 diagrams
INFO: Process u~ u > z added to mirror process u u~ > z
INFO: Process c~ c > z added to mirror process c c~ > z
INFO: Process d~ d > z added to mirror process d d~ > z
INFO: Process s~ s > z added to mirror process s s~ > z
4 processes with 4 diagrams generated in 0.045 s
Total: 4 processes with 4 diagrams

3.2.3 check of the generated process

  • list of the sub-processes identified: MG produces the list of elementary processes that can originate the final state required:
MG5_aMC> display processes
Process: u u~ > z WEIGHTED<=2 @1
Process: c c~ > z WEIGHTED<=2 @1
Process: d d~ > z WEIGHTED<=2 @1
Process: s s~ > z WEIGHTED<=2 @1

* the more complex is the final state, the more are the sub-processes
  • drawing the generated diagrams
MG5_aMC> display diagrams
  • MG draws this for each process: Zprod
    • tree level of the interaction for each diagram participating in the process
    • vertices order: QCD=0 means that there are no QCD vertices ,QED=1 means that there is one electroweak vertex
    • this diagram corresponds to the process u u~ > z

3.3 saving of what done so far

  • MG allows to save what it has done in a folder:
MG5_aMC> output test_Z
  • the name test_Z is chosen by the user
  • to exit:
MG5_aMC> quit

3.4 exercises

  • generate the diagrams of the process: p p > e+ e- and compare them to the ones of the processp p > z:
    • what are the differences?
    • did you expect them?
  • generate the diagrams of the processes : p p > w+ w- and p p > e+ ve e- ve~:
    • what are the differences?
    • did you expect them?
  • generate the diagrams of the process: p p > t t~:
    • what's new with respect to the previuos ones?

chapter four