Monte Carlo Generators

8/2/2019 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.

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Monte Carlo Generators