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11. generate a specific decay process

chapter ten

11.1 the production of top quark pairs at the LHC

  • top quark pairs are abundantly produced at the Large Hadron Collider
    • a top quark, once produced, decays into a W boson and a b quark
    • the W boson then in turn disintegrates in a lepton-neutrino pair or in a quark pair
  • the production of a pair of undecayed top quarks is coded as follows: 
    generate p p > t t~

11.2 the particle decay syntax

  • instructions on how to use the generate instruction can be obtained from MG itself: 
    generate p p > t t~
  • this will produce an ouptut, where the section concerning the decay chains is the following, where in particular the example for the top quark pairs is reported, for the semi-leptonic decay when the top quark decays leptonically, while the anti-top decays hadronically: 
    ./bin/mg5_aMC 
MG5_aMC>help generate
[...]
Decay chain syntax:
 o core process, decay1, (decay2, (decay2', ...)), ...  etc
 o Example: generate p p > t~ t QED=0, (t~ > W- b~, W- > l- vl~), t > j j b @2
 > Note that identical particles will all be decayed.
[...]

11.2 the possible decay chains

11.2.1 the fully leptonic decay

  • assuming the multi-particle definitions of Chapter 3, the fully leptonic case happens when the W bosons produced in both top and anti-top quark decays disintegrate into lepton-neutrino: 
    generate p p > t~ t, (t~ > W- b~, W- > l- vl~), (t > W+ b, W+ > l+ vl)
  • the generated decays can be inspected within MG: 
    MG5_aMC>display processes
Process: g g > t~ t WEIGHTED<=2 @1
Process: u u~ > t~ t WEIGHTED<=2 @1
Process: c c~ > t~ t WEIGHTED<=2 @1
Process: d d~ > t~ t WEIGHTED<=2 @1
Process: s s~ > t~ t WEIGHTED<=2 @1
Decays:
  Process: t~ > w- b~ WEIGHTED<=2
  Decays:
    Process: w- > e- ve~ WEIGHTED<=2
    Process: w- > mu- vm~ WEIGHTED<=2
  Process: t > w+ b WEIGHTED<=2
  Decays:
    Process: w+ > e+ ve WEIGHTED<=2
    Process: w+ > mu+ vm WEIGHTED<=2

11.2.2 the fully hadronic decay

  • still assuming the multi-particle definitions of Chapter 3, the fully hadronic case happens when the W bosons produced in both top and anti-top quark decays disintegrate into quarks: 
    generate p p > t~ t, (t~ > W- b~, W- > j j), (t > W+ b, W+ > j j)

11.2.3 the semi-leptonic decay

  • always assuming the multi-particle definitions of Chapter 3, the semi-leptonic case happens when one W boson produced in either the top or the anti-top quark decay disintegrates into a lepton-neutrino pair, while the other one into quarks.
  • in this situation, either the W+ or the W- may decay leptonically, therefore two processes have to be considered: 
    generate p p > t~ t, (t~ > W- b~, W- > j j), (t > W+ b, W+ > l+ vl) @1
add process p p > t~ t, (t~ > W- b~, W- > l- vl~), (t > W+ b, W+ > j j) @2
  • the @ symbol indicates the identification of the process

11.3 requesting the presence of intermediate particles in the process

11.3.1 forcing an s-channel particle

  • it is possible to ask Madgraph to generate only a sub-set of diagrams that originate from a given process
  • the following process generates all possible diagrams with one w+ boson and one z boson present anywhere in the diagram in the s-channel: 
    generate p p > w+ z > e+ e- mu+ vm j j

11.4 exercises

  • generate the fully-leptonic top pair production charaterised by two leptons of different flavour in the final state
  • generate the same final state without specifying any intermediate particles or decay paths:
    • what is the difference with respect to the previous generation?
    • when is it appropriate to use one or the other generation?

chapter twelve