== QCD at the LHC, Frascati 2010 ==
Two lectures are given on QCD at the LHC.
1. Accurate QCD : Fixed order calculations from LO to NNLO
1. Useful QCD : Parton Showers
1. Best QCD : Merging FO calculations with PS at LO and NLO.
The PDF of the lectures can be found [attachment:maltoni-frascati-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 - 05 May 2010