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9. generation with intermediate particles in the process

chapter eight

9.1 gauge invariant processes

  • The perturbative calculation of a scattering process is gauge invariant when stable particles are considered in the initial and final states of the interaction, and all possible Feynman diagrams that can be drawn from the initial to the final state are considered in the calculation.
  • A particle is typically considered stable when its lifetime is significantly longer that the time scale of the interaction. Therefore, muons, tau leptons, b quarks are considered stable to this extent, as well as light quarks and gluons, before they shower.

9.2 generation with intermediate particles

  • MG allows to generate processes where specific intermediate particles are required to be present: * to allow for a study of the impact of the various components (for example in the case of the Drell Yan process at LEP) * to simplify the generation, which would otherwise become computationally too expensive (for example for the case of high final state particle multiplicity) * to target a specific physics case (for example the Higgs boson physics)
  • There exist different ways to obtain this objective:
    • the concatenated decay
      • the comma notation
      • the use of an external tool

9.2.1 the gauge invariant reference

As a comparison, the full process generation is the following:

generate p p > e+ e-
  • say here how Madspin works

9.2.2 the concatenated decay

Describe the decay chain as a sequence of decays, as if a specific Feynman diagram is being drawn.

generate p p > z > e+ e-
  • down to which depth can one go?
  • what are the approximations present here in the calculation?
    • what are the corresponding parameters in the run_card.dat

9.2.2 the comma notation

Generate an intermediate particle, and then describe how the generated particle may decay.

generate p p > z, z > e+ e-
  • what is the difference wrt the previous one?
    • more sophisticated example: ttbar
    • can one indicate separate decays of the two top quarks?
      • how deep can one go in the chain? May one let decay the top, and then the W bosons, in specific ways?

9.2.3 the use of an external tool

Generate the intermediate particle and let other programs (for example Pythia generate the decay

generate p p > z

This last approach is not considered in the tutorial.

9.3 exercises

  • generate events with the first three techniques listed:
    • are there differences in the total cross-sections?
      • are there differences in the invariant mass shapes?
      • are there differences in the number and type of diagrams generated in the three cases?
      • are the effects of cutoffs introduced in the run_card.dat visible?

chapter ten