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            |  | 3 | == GIF 2007 == | 
          
            |  | 4 |  | 
          
            |  | 5 | Three lectures are given on: | 
          
            |  | 6 |  | 
          
            |  | 7 | 1. Basic aspects of pQCD | 
          
            |  | 8 | 1. Accurate predictions: NLO and NNLO calculations | 
          
            |  | 9 | 1. Matrix element techniques | 
          
            |  | 10 |  | 
          
            |  | 11 | The PDF of the lectures can be found [attachment:maltoni-gif-2007.pdf here]. | 
          
            |  | 12 |  | 
          
            |  | 13 | Most of the examples and exercises are related to physics at the LHC. | 
          
            |  | 14 |  | 
          
            |  | 15 | === Basic aspects of QCD  === | 
          
            |  | 16 |  | 
          
            |  | 17 | ===== Various Tests and exercises ===== | 
          
            |  | 18 | A collection of test, exercises,  and web applications on pQCD can be found  in | 
          
            |  | 19 | [attachment:QCDGIF.pdf QCDGIF.pdf]. | 
          
            |  | 20 |  | 
          
            |  | 21 | ===== Exercise on recursive relations ===== | 
          
            |  | 22 | Think about the computation of %$ q \bar q + n \gamma$% in a recursive way, by | 
          
            |  | 23 | trying not calculate the same quantities twice. Show that the complexity of the calculation goes | 
          
            |  | 24 | from %$n \cdot n!$% (factorial) to %$n \cdot 2^{n-1} $%  (exponential) . | 
          
            |  | 25 |  | 
          
            |  | 26 | === Going NLO  === | 
          
            |  | 27 |  | 
          
            |  | 28 | 1. pp>H at LO (1-loop):  details of the calculation (Mathematica Notebook) [attachment:HiggsGG-LO-mtfinite.nb HiggsGG-LO-mtfinite.nb] | 
          
            |  | 29 | 1. pp>H at NLO: details of the calculation (Mathematica Notebook) [attachment:HiggsGG-NLO.nb higgsGG-NLO.nb] | 
          
            |  | 30 | 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]. | 
          
            |  | 31 |  | 
          
            |  | 32 | A summary of  the results  can be found in [attachment:Higgs.pdf Higgs.pdf]. | 
          
            |  | 33 |  | 
          
            |  | 34 | === Selected exercises on QCD that can be solved with a Matrix Element generator. === | 
          
            |  | 35 |  | 
          
            |  | 36 | * [:DeadCone:Radiation from heavy quarks]:  the dead cone in %$e^+e^- \to Q \bar Q g$%. | 
          
            |  | 37 | * [:GluonSpin:Spin of the gluon]:  Vector vs scalar in the  angular correlations of %$ e^+ e^- \to$% 4 jets. | 
          
            |  | 38 | * [:2Jets:Jets] : Di-jet kinematics and rates in pp collisions. | 
          
            |  | 39 | * [:3Jets:3 Jets] : Energy distributions in 3-jet events in pp collisions. | 
          
            |  | 40 | * [:tt:top production] : %$t \bar t$% production, Tevatron vs LHC. | 
          
            |  | 41 | * [:WAsymm:Drell-Yan]: rapidity asymmetry at the Tevatron and LHC. | 
          
            |  | 42 | * [:TopDecaySpinCorrelations: Spin correlations in top decay], by [http://www.hep.phy.cam.ac.uk/theory/webber/ Bryan Webber]. | 
          
            |  | 43 |  | 
          
            |  | 44 | === Monte Carlo integration === | 
          
            |  | 45 |  | 
          
            |  | 46 | A short introduction to the techniques of Monte Carlo integration. Exercises proposed during lecture | 
          
            |  | 47 | are collected in this Mathematica Notebook:  [attachment:mc101.nb mc101.nb]. | 
          
            |  | 48 |  | 
          
            |  | 49 | === LHC Phenomenology === | 
          
            |  | 50 |  | 
          
            |  | 51 | * [:DiscoverTheHiggs:SM Higgs discovery at the LHC]: Three important channels | 
          
            |  | 52 | * [:WarmingUpChallenge:Simple Black Boxes]: New gauge bosons | 
          
            |  | 53 |  | 
          
            |  | 54 | === How to familiarize with Software.MadGraph === | 
          
            |  | 55 |  | 
          
            |  | 56 | All exercises proposed can be "solved" or checked with Software.MadGraph / Software.MadEvent. | 
          
            |  | 57 | Here is how to familiarize with the code. | 
          
            |  | 58 |  | 
          
            |  | 59 | * Logon to the Software.MadGraph web site and register. | 
          
            |  | 60 |  | 
          
            |  | 61 | * 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? | 
          
            |  | 62 |  | 
          
            |  | 63 | * Look at the new physics models and check the particle and interactions content. | 
          
            |  | 64 |  | 
          
            |  | 65 | * Generate events for a few selected processes and look at the plots: | 
          
            |  | 66 | * ttbar production with decays: pp>tt~>bb~mu+e-ve~vm | 
          
            |  | 67 | * VV production: pp>VV> leptons, with V=Z,W. | 
          
            |  | 68 | * Single top + Higgs: pp>tHj  (QCD=0, QED=3, j=gudsc,p=gudscb). Show that there is a large negative interference between the diagrams | 
          
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            |  | 79 | -- Main.FabioMaltoni - 22 Sep 2007 | 
          
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