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Basics of QCD for the LHC, Cern School 2011

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

The PDF of the lectures can be found here:

QCD1 : Intro and QCD fundamentals

QCD2: QCD in the final state

QCD3: QCD in the initial state

QCD4: From accurate QCD to useful QCD

QCD5: Advanced QCD with applications to the LHC

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

A summary of the results can be found in Higgs.pdf.

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

  • [:DeadCone:Radiation from heavy quarks]: the dead cone in %$e^+e^- \to Q \bar Q g$%.
  • [:GluonSpin:Spin of the gluon]: Vector vs scalar in the angular correlations of %$ e^+ e^- \to$% 4 jets.
  • [:2Jets:Jets] : Di-jet kinematics and rates in pp collisions.
  • [:3Jets:3 Jets] : Energy distributions in 3-jet events in pp collisions.
  • [:tt:top production] : %$t \bar t$% production, Tevatron vs LHC.
  • [:WAsymm:Drell-Yan]: rapidity asymmetry at the Tevatron and LHC.
  • [:TopDecaySpinCorrelations: Spin correlations in top decay], by 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: mc101.nb.

LHC Phenomenology

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

How to familiarize with Software.MadGraph

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

  • Logon to the Software.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 - 2011-09-09

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