GIF 2007

Three lectures are given on:

1. Basic aspects of pQCD
2. Accurate predictions: NLO and NNLO calculations
3. Matrix element techniques

The PDF of the lectures can be found here​.

Most of 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 QCDGIF.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 \cdot n!$% (factorial) to %$n \cdot 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 - 22 Sep 2007