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.

• 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 in pp collisions.
• top production : $t \bar t$ production, Tevatron vs LHC.
• Drell-Yan: rapidity asymmetry at the Tevatron and LHC.
• 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

• SM Higgs discovery at the LHC: Three important channels
• 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 - 22 Sep 2007