HEPTOOLS 2008 <BR> Graduate School in Physics at Colliders : <BR> "From twistors to Monte Carlos"

Lectures

Find here​ the pdf of the 4 hour lecture on "Monte Carlo's for the LHC" by Fabio Maltoni.
Find ​here a very nice course on QCD and MC by Stefano Frixione.

MC101

A short introduction to the techniques of Monte Carlo integration. Exercises include:

• 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

Exercises

All exercises proposed here can be "solved" or checked with Software.MadGraph / Software.MadEvent. To familiarize with the code click here.

• Radiation from heavy quarks: the dead cone in $e^+e- \to Q \bar Q g$.
• Spin of the gluon: Vector vs scalar in the angular correlations of $ e^{+ e}- \to$ 4 jets.
• Jets : Di-jet kinematics and rates in pp collisions.
• 3 Jets : Energy distributions in 3-jet events.
• Spin correlations in top decay.
• top production : $t \bar t$ production, Tevatron vs LHC.
• Kinematics at the LHC: single particle quantities.

Reference: ​QCD and Collider Physics

by Keith Ellis, James Stirling, Bryan Webber (Cambridge Monographs, 1996).

Discover the 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 -->

1. 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 -->

1. 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​

Discover New gauge bosons at the LHC

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.

Analysis Tools

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

-- Main.FabioMaltoni - 03 Jan 2008