Last modified 5 years ago Last modified on 04/19/12 08:43:13

LHC Phenomenology with MadGraph

Cargese, July 20-31, 2010


  • Tim Stelzer (lecturer)


Find the pdf of the 3 x 1.5 hours lecture:(available after lectures)

  • Lecture 1: The big picture and matrix element generators.
  • Lecture 2: Cross sections and parton level event generation.
  • Lecture 3 : Simulation of a complex final state.


MadGraph Exercises

Here we present simple exercises to familiarize with MadGraph software and also for more interesting applications to LHC phenomenology.

A summary of the pheno exercises can be found here.

---+++ Lecture 1: Familiarize with MadGraph

  • Logon to the MadGraph web site and register:
  • Register with a valid e-mail address
  • Feynman diagrams. Generate a few processes (with different QED + QCD couplings) trying to guess which diagrams appear:
    • uu~>tt~
    • gg>tt~
    • gg>tt~h
    • uu~>tt~bb~
  • Subprocess identification. List all subprocesses contributing to:
    • pp>h>tt~bb~
    • pp>tt~bb~
    • pp>tt~jj
  • Look at the new physics models and check the particle and interactions content.
  • Advanced: Download the MG/ME package and play with the standalone version.
  • Kinematics at the LHC: refresh the kinematics of an hadron collider.

Lecture 2: Calculate cross sections and generate events

Generate events for a few selected processes and look at the plots:

  • ttbar production with decays: pp>tt~>bb~mu+e-ve~vm
  • VV production: pp>VV> leptons, with V=Z,W.
  • Single top + Higgs: pp>tHj (QCD=0, QED=3, j=gudsc,p=gudscb). Show that there is a large negative interference between the diagrams.
  • gg>H>WW
  • Weak boson fusion

Some phenomenological applications (at the parton level):

  • Jets : Di-jet kinematics and rates in pp collisions.
  • 3 Jets : Energy distributions in 3-jet events.
  • Drell-Yan : Study the rapidity asymmetry at the Tevatron.
  • top production : $t \bar t$ production, Tevatron vs LHC.
  • t' production : $t'$ production at the LHC.

Lecture 3: The full simulation chain and advanced features

Try out the Analysis Tools:

Study what is known of a SM Higgs at the LHC:

  • Find the best prediction for Higgs production at the LHC here.
  • Find the Higgs branching ratios here.

Choose a channel and investigate signal and background:

  1. The 2 lepton + missing Et final state: $pp \to H\to W^+ W^- \to e^- \bar \nu_e \mu^+ \nu_\mu $
  2. Top associated production $pp \to t\bar tH$ with $H \to b \bar b$

MadGraph BlackBox Challenge

Three "black boxes" are given, in the form of event files in the LHC Olympics format and a series of selected plots:

Black boxes contain only signal events. The students are asked to pair up the boxes above with the following models and also answer to the questions:

  • Model 1 : Extra Z (zp) : What its mass? Does it have Standard Model couplings to fermions?
  • Model 2 : Heavy Scalar (h): What its mass? Is it a SM Higgs?
  • Model 3 : Extra W (wp+ or wp-) : What its mass? Does it have Standard Model couplings to fermions?

Useful extra information:

  • In the plots $H_T=\sum ||p_T^{vis}|| + E_T^{miss}$.
  • A SM-like Z' would decay (more or less democratically) into: jet jet (uu~,cc~,dd~,ss~,bb~), t tbar (tt~), lept+lept- (e+e-,mu+mu-,ta+ta-), neutrino anti-neutrino (ve ve~,vm vm~,vt vt~). It could also have couplings to SM W and Z, and in that case would decay in to ZZ and W+W-.
  • An Higgs couple to particles with a strength which is proportional to the particle masses. A SM-like heavy H would decay in to t tbar (tt~), W+W-, ZZ.
  • A SM-like W'+ would decay into: jet jet (ud~,cs~), t b (tb~), lept neutrino (e+ ve , mu+ vm, ta+ vt). It could also have couplings to SM W and Z, and in that case would decay in to ZW.

Monte Carlo's

For those interested in getting deeper into Monte Carlo techniques, here are some more exercises:

  • Write the simplest integration function based on the definition of average and error
  • Importance sampling via an analytic transformation
  • Von Neumann's rejection method : plain and improved
  • Phase space for 1 -> n particles
  • Vegas
  • Top decay : comparison among the various methods
  • qq -> tt production

All exercises are presented and solved this Mathematica Notebook: mc101.nb. Reference: Introduction to MC methods, by Stefan Weinzierl


-- Main.TimStelzer - 2010-07-19