== 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