Version 1 (modified by trac, 7 years ago) (diff)

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### Authors

• Tim Stelzer (lecturer)

### Lectures

Find the pdf of the 3 x 1.5 hours lecture:(available after lectures)

• Lecture 1: The big picture and matrix element generators.
• Lecture 2: Cross sections and parton level event generation.
• Lecture 3 : Simulation of a complex final state.

### References

• QCD and Collider Physics by Keith Ellis, James Stirling, Bryan Webber (Cambridge Monographs, 1996).
• [:FurtherReading:Perspectives on LHC physics, Ed. by G. Kane and A. Pierce].

Here we present simple exercises to familiarize with MadGraph software and also for more interesting applications to LHC phenomenology.

A summary of the pheno exercises can be found here.

#### ---+++ Lecture 1: Familiarize with Software.MadGraph

• Register with a valid e-mail address
• Feynman diagrams. Generate a few processes (with different QED + QCD couplings) trying to guess which diagrams appear:
• uu~&gt;tt~
• gg&gt;tt~
• gg&gt;tt~h
• uu~&gt;tt~bb~
• Subprocess identification. List all subprocesses contributing to:
• pp&gt;h&gt;tt~bb~
• pp&gt;tt~bb~
• pp&gt;tt~jj
• Look at the new physics models and check the particle and interactions content.
• [:SimpleKinematics:Kinematics at the LHC]: refresh the kinematics of an hadron collider.

#### Lecture 2: Calculate cross sections and generate events

Generate events for a few selected processes and look at the plots:

• ttbar production with decays: pp&gt;tt~&gt;bb~mu+e-ve~vm
• VV production: pp&gt;VV&gt; leptons, with V=Z,W.
• Single top + Higgs: pp&gt;tHj (QCD=0, QED=3, j=gudsc,p=gudscb). Show that there is a large negative interference between the diagrams.
• gg&gt;H&gt;WW
• Weak boson fusion

Some phenomenological applications (at the parton level):

• [:2Jets:Jets] : Di-jet kinematics and rates in pp collisions.
• [:3Jets:3 Jets] : Energy distributions in 3-jet events.
• Drell-Yan : Study the rapidity asymmetry at the Tevatron.
• [:tt:top production] : %% production, Tevatron vs LHC.
• [:tprime:t' production] : %% production at the LHC.

#### Lecture 3: The full simulation chain and advanced features

Try out the Analysis Tools:

Study what is known of a SM Higgs at the LHC:

• Find the best prediction for Higgs production at the LHC here.
• Find the Higgs branching ratios here.

Choose a channel and investigate signal and background:

1. The 2 lepton + missing Et final state: %
2. Top associated production %% with %%

Three "black boxes" are given, in the form of event files in the LHC Olympics format and a series of selected plots:

Black boxes contain only signal events. The students are asked to pair up the boxes above with the following models and also answer to the questions:

• Model 1 : Extra Z (zp) : What its mass? Does it have Standard Model couplings to fermions?
• Model 2 : Heavy Scalar (h): What its mass? Is it a SM Higgs?
• Model 3 : Extra W (wp+ or wp-) : What its mass? Does it have Standard Model couplings to fermions?

Useful extra information:

• In the plots %%.
• A SM-like Z' would decay (more or less democratically) into: jet jet (uu~,cc~,dd~,ss~,bb~), t tbar (tt~), lept+lept- (e+e-,mu+mu-,ta+ta-), neutrino anti-neutrino (ve ve~,vm vm~,vt vt~). It could also have couplings to SM W and Z, and in that case would decay in to ZZ and W+W-.
• An Higgs couple to particles with a strength which is proportional to the particle masses. A SM-like heavy H would decay in to t tbar (tt~), W+W-, ZZ.
• A SM-like W'+ would decay into: jet jet (ud~,cs~), t b (tb~), lept neutrino (e+ ve , mu+ vm, ta+ vt). It could also have couplings to SM W and Z, and in that case would decay in to ZW.

### Monte Carlo's

For those interested in getting deeper into Monte Carlo techniques, here are some more exercises:

• Write the simplest integration function based on the definition of average and error
• Importance sampling via an analytic transformation
• Von Neumann's rejection method : plain and improved
• Phase space for 1 -&gt; n particles
• Vegas
• Top decay : comparison among the various methods
• qq -&gt; tt production

All exercises are presented and solved this Mathematica Notebook: mc101.nb. Reference: Introduction to MC methods, by Stefan Weinzierl

### Animations

-- Main.TimStelzer - 2010-07-19