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).
• 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.
• 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:

• 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