LHC Phenomenology with MadGraph

Universita' di Milano, May 25-26, 2010

Authors

• Fabio Maltoni (lecturer)

Lectures

An abstract and plan is available here​.

Find the pdf of the 3 x 1h+1h hours lecture:

• 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.

References

• ​QCD and Collider Physics by Keith Ellis, James Stirling, Bryan Webber (Cambridge Monographs, 1996).
• [:FurtherReading:Perspectives on LHC physics, Ed. by G. Kane and A. Pierce].

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 Software.MadGraph

• Logon to the Software.MadGraph web site and register: ​http://madgraph.hep.uiuc.edu.
• 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.
• [:SimpleKinematics: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):

• [:2Jets:Jets] : Di-jet kinematics and rates in pp collisions.
• [:3Jets:3 Jets] : Energy distributions in 3-jet events.
• ​Drell-Yan : Study the rapidity asymmetry at the Tevatron.
• [:tt:top production] : %$t \bar t$% production, Tevatron vs LHC.
• [:tprime:t' production] : %$t'$% production at the LHC.

Lecture 3: The full simulation chain and advanced features

Try out the Analysis Tools:

• a Fortran-based package: Software.MadAnalysis (​Download it here)
• a Mathematica-based package: ​Chameleon.

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 4 lepton final state: %$pp \to H\to Z Z \to e^+e- \mu^{+ \mu}-$%
   • Signal
     • Events: ​Parton Level ​Detector Level
     • Plots: ​Parton Level ​Detector Level
   • Background
     • Events: ​Parton Level ​Detector Level
     • Plots: ​Parton Level ​Detector Level
2. The 2 lepton + missing Et final state: %$pp \to H\to W^{+ W}- \to e^{- \bar \nu_e \mu}+ \nu_\mu $
   • Signal
     • Events: ​Parton Level ​Detector Level
     • Plots: ​Parton Level ​Detector Level
   • Background
     • Events: ​Parton Level ​Detector Level
     • Plots: ​Parton Level ​Detector Level
3. Top associated production %$pp \to t\bar tH$% with %$H \to b \bar b$%
   • Signal + Background samples:
     • Events: ​Parton Level ​Detector Level
     • Plots: ​Parton Level ​Detector Level

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:

• Box A : ​Events Plots: ​Parton level ​Detector level
• Box B : ​Events Plots: ​Parton level ​Detector level
• Box C : ​Events Plots: ​Parton level ​Detector level

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

Animations

• ​Interactive Flash version Note you may want to zoom in!
• ​Fast movie (.avi) of collision
• ​Guided movie (.mov) of collision
• ​LHC_Rap

-- Main.FabioMaltoni - 2010-05-23