Last modified 5 years ago Last modified on 04/13/12 10:36:53

Monte Carlo Event Generators at NLO and Jet Physics

School of the Think Tank on Physics@LHC initiative.

5-9 December 2011 Sariska Palace, Rajasthan, India

Preparatory Material

The school is meant to introduce to young researchers in phenomenology and experimental LHC physics the MC tools necessary to perform accurate simulations and analyses. Particular emphasis will be given to NLO calculations, their interface to the shower programs, and applications to jet physics. While the basics will be reviewed during the lectures, the school assume basic knowledge of perturbative QCD concepts and methods.

We invite the students to study the excellent introductory lectures:
Elements of QCD for hadron colliders.
Gavin P. Salam (CERN)
e-Print: arXiv:1011.5131 [hep-ph]

These lecture notes cover all the basic concepts assumed in our lectures.

In order to develop an hand-on experience on QCD calculation, we propose the students to calculate the pp>H+X cross section at NLO in the HEFT. The full computation is described here. Mathematica Notebooks are provided below which contain all the details of the calculation and the implementation in a simple Notebook which can calculate cross section production at NLO at the LHC.

  • pp>H at LO (1-loop): details of the calculation (Mathematica Notebook) HiggsGG-LO-mtfinite.nb
  • pp>H at NLO: details of the calculation (Mathematica Notebook) higgsGG-NLO.nb
  • pp>H at NLO: cross section evaluation for the LHC (Mathematica Notebook+PDF libraries to be compiled) phenHiggs.tar.gz .

LHC Phenomenology with MadGraph


Find the pdf of the 4 x 1 hour lectures and the tutorials:(available after lectures)

  • Lectures (mornings) :
    • Basics of QCD
    • NLO
    • NLO+PS
    • Jets


MadGraph and Pheno Exercises

A summary of advanced QCD and pheno exercises can be found here.

Tutorial 1: Familiarize with MadGraph

  • Logon to the MadGraph web site and register:
  • Register with a valid e-mail address
  • Feynman diagrams. Generate a few processes (with different QED + QCD couplings) trying to guess which diagrams appear:
    • u u~ > t t~
    • g g > t t~
    • g g > t t~ h
    • u u~ > t t~ b b~
  • Subprocess identification. List all subprocesses contributing to:
    • p p > h > t t~ b b~
    • p p > t t~ b b~
    • p p > t t~ j j
  • Look at the new physics models and check the particle and interactions content.
  • Advanced: Download the MadGraph 5 package from launchpad and play with the standalone version.
  • Kinematics at the LHC: refresh the kinematics of an hadron collider.

Tutorial 2: Calculate cross sections and generate events

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

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

Some phenomenological applications (at the parton level):

  • Jets : Di-jet kinematics and rates in pp collisions.
  • 3 Jets : Energy distributions in 3-jet events.
  • Drell-Yan : Study the rapidity asymmetry at the Tevatron.
  • top production : $t \bar t$ production, Tevatron vs LHC.
  • t' production : $t'$ production at the LHC.

Tutorial 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: $pp \to H\to W^+ W^- \to e^- \bar \nu_e \mu^+ \nu_\mu$
  2. Top associated production $pp \to t\bar tH$ with $H \to b \bar b$

Tutorial 4: The MadGraph BlackBox Challenge

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 $H_T=\sum |p_T^{vis}| + E_T^{miss}$.
  • 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 -> n particles
  • Vegas
  • Top decay : comparison among the various methods
  • qq -> tt production

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