Specialising Generators for High-Performance Monte-Carlo Simulation ... in Haskell
Monte Carlo Generators
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Transcript of Monte Carlo Generators
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Monte Carlo Generators
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Outline
1.Overview2.Event Integrator vs Generator
3.NLO Monte Carlo
4.Parton Showers
1. DGLAP
2. Sudakov Factor
5.Hadronization
1. String Model
2. Cluster Model
6.Lattice QCD
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Overview
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Event Integrator vs Generator
Alex: Monte Carlo numerical integration Histogram each event with a weight
Probability distro. (positive definite function) event generator:
events:
weights:
Occur with the same frequency as in nature
If weight > random number, accept and histogram with weight 1
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Elementary Hard Process
Solutions: Phase space slicing (JETRAD, DYRAD, EERAD)
Subtraction Method (EVENT, DISENT, NLOJET++,MCFM)
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Initial and Final State Parton Showers
Factorize 2 n process to 2 2 process Initial State Radiation (ISR)
Incident parton with low spacelike virtuality can radiatetimelike partons
Final State Radiation (FSR)
Outgoing parton with largetimelike virtuality can generatea shower with lower virtuality
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Parton Showers
Emission rate for branching diverges when the gluonbecomes collinear or when the gluon energy vanishes
qqg
ggg
1.Iterative structure that allows simple expressions forqqg, ggg and gqq branchings to be combinedto build up complex multiparton final states
2.A Sudakov factor that offers a physical way to handlethe cancellation between real and virtual divergences
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DGLAP Equations
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Sudakov (Form) Factor
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Hadronization Process
A specific model used in an event generator for thetransition from the partonic final state to a completerepresentation of the actual hadronic final state.
Two Main Hadronization Classes:
String
transforms partonic systems directly into hadrons
Cluster
Has an intermediate stage of cluster objects (m ~ GeV)
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String Model
Assumes linear confinement Strings
endpoint = quark
kink = gluon
partons ordered in color along the string
Predictive Framework
Space-time motion and breakup energy-momentum
distribution of primary hadrons Parameters related to flavor properties
Need to be taken from data (weakness)
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Cluster Model
Based on the preconfinement property of parton showers
Color-singlet parton clusters with a universal mass distribution at low scales
Gluons split non-perturbatively into quark-antiquark pairs
Color-connected pairs form clusters
Formed clusters undergo quasi-two-body sequential phase-space decay Limited cluster mass spectrum limited transverse momenta and suppression of
heavy flavor, strangeness and baryon production
Quality when combined with angular-ordered parton showers comparable tothe string theory but needs less parameters
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Lattice QCD Non-perturbative
Treats low-energy QCD where analytic and perturbativesolutions are impossible or fail
Discrete rather than continuous spacetime introduces anatural momentum cutoff of 1/a where 'a' is the lattice spacing
Quark fields defined at lattice sites while gluon fields defined onthe links connecting sites
Approximation approaches continuum QCD in the limit a0
(Early Days) Quenched quark fields are frozen (Today) Dynamical - molecular dynamics or microcanonical
ensemble algorithms
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Some Lattice QCD Results:
1.Mass of the proton determined with less than 2percent error
2.Decay process of a kaon into two pions
Calculation took 54 million processor hours on the IBM
BlueGene/P supercomputer at the Argonne NationalLaboratory in the US.
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References
Brian Webber's Presentation Monte Carlo Methods in ParticlePhysics, 19-23 November, 2007,www.hep.phy.cam.ac.uk/theory/webber/MunichPDF/MClecture1.pdf,www.hep.phy.cam.ac.uk/theory/webber/MunichPDF/MClecture2.pdf.
Matt Dobb's Presentation Simulating Hadron Collider Interactions,January 2005, www-atlas.lbl.gov/physics/Matt_MonteCarloTutorial.pdf.
Torbjorn Sjostrand, Monte Carlo Generators, November 2006, hep-ph/0611247.
Buckley et al. General-Purpose Event Generators for LHC Physics, 13January 2011, hep-ph/1101.2599v1.