== QCD and MC tools for the LHC, Martigano June 2010. ==

5 Lectures are given on QCD and MC's developments for the LHC. at the LHC.

The PDF of the lectures can be found [attachment:maltoni-martignano-2010.pdf here].

The examples and exercises are related to physics at the LHC.
=== Basic aspects of QCD ===
===== Various Tests and exercises =====

A collection of test, exercises, and web applications on pQCD can be found in [attachment:QCD-exercises.pdf QCD-exercises.pdf].

===== Exercise on recursive relations =====

Think about the computation of q \bar q + n \gamma in a recursive way, by trying not calculate the same quantities twice. Show that the complexity of the calculation goes from n! (factorial) to 2^{n-1} (exponential) .
=== Going NLO ===

   1. pp>H at LO (1-loop): details of the calculation (Mathematica Notebook) [attachment:HiggsGG-LO-mtfinite.nb HiggsGG-LO-mtfinite.nb]
   1. pp>H at NLO: details of the calculation (Mathematica Notebook) [attachment:HiggsGG-NLO.nb higgsGG-NLO.nb]
   1. pp>H at NLO: cross section evaluation for the LHC (Mathematica Notebook+PDF libraries to be compiled) [attachment:phenHiggs.tar.gz phenHiggs.tar.gz].

A summary of the results can be found in [attachment:Higgs.pdf Higgs.pdf].

=== Selected exercises on QCD that can be solved with a Matrix Element generator. ===

   * [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 in pp collisions.
   * [wiki:tt top production] : $t \bar t$ production, Tevatron vs LHC.
   * [wiki:WAsymm Drell-Yan]: rapidity asymmetry at the Tevatron and LHC.
   * [wiki:TopDecaySpinCorrelations  Spin correlations in top decay], by [http://www.hep.phy.cam.ac.uk/theory/webber/ Bryan Webber].

=== Monte Carlo integration ===

A short introduction to the techniques of Monte Carlo integration. Exercises proposed during lecture are collected in this Mathematica Notebook: [attachment:mc101.nb mc101.nb].

=== LHC Phenomenology ===

   * [wiki:DiscoverTheHiggs SM Higgs discovery at the LHC]: Three important channels
   * [wiki:WarmingUpChallenge Simple Black Boxes]: New gauge bosons

=== How to familiarize with MadGraph ===

All exercises proposed can be "solved" or checked with MadGraph / MadEvent. Here is how to familiarize with the code.

   * Logon to the MadGraph web site and register.

   * Familiarize with the code by generating a few processes in QED and QCD trying to guess which diagrams appear. What is the minimum number of jets have to be asked for in $e^+e^-$ collisions so that the triple gauge vertex appear?

   * Look at the new physics models and check the particle and interactions content.

   * 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

-- Main.FabioMaltoni - 2010-06-13