== HEPTOOLS 2008 [[br]] Graduate School in Physics at Colliders : [[br]]  "From twistors to Monte Carlos"  ==


=== Lectures ===

Find  [attachment:maltoni_lectures.pdf here] the pdf of the 4 hour lecture on "Monte Carlo's for the LHC" by Fabio Maltoni.[[br]]
Find [http://www.pd.infn.it/~passera/JC_2007-08/frixione.html 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:  [attachment:mc101.nb mc101.nb].
Reference: [http://www.slac.stanford.edu/spires/find/hep/www?eprint=hep-ph/0006269 Introduction to MC methods], by [http://wwwthep.physik.uni-mainz.de/~stefanw/ Stefan Weinzierl]

=== Exercises ===

    All exercises proposed here can be "solved" or checked with MadGraph / MadEvent. To familiarize with the code click [wiki:MGFamiliarize here].


   * [wiki:DeadCone Radiation from heavy quarks]:  the dead cone in $e^+e^- \to Q \bar Q g$.
   * [wiki:GluonSpin Spin of the gluon]:  Vector vs scalar in the  angular correlations of $ e^+ e^- \to$ 4 jets.
   * [wiki:2Jets Jets] : Di-jet kinematics and rates in pp collisions. 
   * [wiki:3Jets 3 Jets] : Energy distributions in 3-jet events.
   * [wiki:TopDecaySpinCorrelations  Spin correlations in top decay].
   * [wiki:Tt top production] : $t \bar t$ production, Tevatron vs LHC. 
   * [wiki:SimpleKinematics Kinematics at the LHC]: single particle quantities.
 
Reference: [http://www.hep.phy.cam.ac.uk/theory/webber/QCDbook.html 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 [http://maltoni.web.cern.ch/maltoni/TeV4LHC/index.html here].
   * Find the Higgs branching ratios [attachment:h-br.pdf 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:  [attachment:h4l-signal.lhe.gz Parton Level] [attachment:h4l-signal.lhco.gz Detector Level] 
{{{
#!comment
<!--         * Plots: [attachment:h4l-signal-lhe.pdf Parton Level] [attachment:h4l-signal-lhco.pdf Detector Level] -->
}}}
      * Background 
         * Events:  [attachment:h4l.lhe.gz Parton Level] [attachment:h4l.lhco.gz Detector Level] 
{{{
#!comment
<!--         * Plots: [attachment:h4l-lhe.pdf Parton Level] [attachment:h4l-lhco.pdf 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:  [attachment:hww-signal.lhe.gz Parton Level] [attachment:hww-signal.lhco.gz Detector Level] 
{{{
#!comment
 <!--        * Plots: [attachment:hww-signal-lhe.pdf Parton Level] [attachment:hww-signal-lhco.pdf Detector Level]  -->
}}}
      * Background 
         * Events:  [attachment:hww-background.lhe.gz Parton Level] [attachment:hww-background.lhco.gz Detector Level] 
{{{
#!comment
<!--         * Plots: [attachment:hww-background-lhe.pdf Parton Level] [attachment:hww-background-lhco.pdf Detector Level]  -->
}}}
   1. Top associated production $pp \to t\bar tH$ with $H \to b \bar b$
      *  Signal + Background samples:
         * Events:  [attachment:ttb.lhe.gz Parton Level] [attachment:ttbb.lhco.gz Detector Level] 
         * Plots: [attachment:ttbb-lhe.pdf Parton Level] [attachment:ttbb-lhco.pdf 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 : [attachment:A.lhco.gz Events]  Plots:  [attachment:A-lhe.pdf Parton level]  [attachment:A.pdf Detector level]
   * Box B : [attachment:B.lhco.gz Events]   Plots:  [attachment:B-lhe.pdf Parton level]   [attachment:B.pdf Detector level]
   * Box C : [attachment:C.lhco.gz Events]  Plots:  [attachment:C-lhe.pdf Parton level]   [attachment:C.pdf 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: MadAnalysis ([http://madgraph.phys.ucl.ac.be/cgi-bin/NewProcess/download.cgi Download it here])
   * a Mathematica-based package: [http://www.jthaler.net/olympics/html Chameleon].



-- Main.FabioMaltoni - 03 Jan 2008