Monte Carlo Tools Frank Krauss Institute for Particle Physics - PowerPoint PPT Presentation

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University GGI, 24.&26.9.2007 F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Topics of the lectures Lecture 1: Tour through Event Generators 1 Hard physics simulation: Parton Level event generation Dressing the partons: Parton Showers Soft physics simulation: Hadronization Beyond factorization: Underlying Event Lecture 2: Higher Orders in Monte Carlos 2 Some nomenclature: Anatomy of HO calculations Merging vs. Matching Thanks to the other Sherpas: T.Gleisberg, S.H¨ oche, S.Schumann, F.Siegert, M.Sch¨ onherr, J.Winter; other MC authors: S.Gieseke, K.Hamilton, L.Lonnblad, F.Maltoni, M.Mangano, P.Richardson, M.Seymour, T.Sjostrand, B.Webber, . . . . F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Simulation’s paradigm Basic strategy Sketch of an event Divide event into stages, separated by different scales. �� Signal/background: �� Exact matrix elements. �� QCD-Bremsstrahlung: �� Parton showers (also in initial state). �� Multiple interactions: �� Beyond factorization: Modeling. �� Hadronization: �� Non-perturbative QCD: Modeling. F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Today’s lecture: Event Generation in a Nutshell Monte Carlo integration Parton level event generation Parton showers Multiple interactions Hadronization F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo integration Convergence of numerical integration 1 � d x D f ( � Consider I = x ). 0 Convergence behavior crucial for numerical evaluations. For integration ( N = number of evaluations of f ): Trapezium rule ≃ 1 / N 2 / D Simpson’s rule ≃ 1 / N 4 / D √ Central limit theorem ≃ 1 / N . Therefore: Use central limit theorem. F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo integration Monte Carlo integration Use random vectors � x i − → : Evaluate estimate of the integral � I � rather than I . N � I ( f ) � = 1 � f ( � x i ). N i =1 (This is the original meaning of Monte Carlo: Use random numbers for integration.) Quality of estimate given by error estimator (variance) � E ( f ) � 2 = 1 N − 1 [ � I 2 ( f ) � − � I ( f ) � 2 ]. Name of the game: Minimize � E ( f ) � . Problem: Large fluctuations in integrand f Solution: Smart sampling methods F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo integration Importance sampling Basic idea: Put more samples in regions, where f largest = ⇒ improves convergence behavior (corresponds to a Jacobian transformation). Assume a function g ( � x ) similar to f ( � x ); obviously then, f ( � x ) / g ( � x ) is comparably smooth, hence � E ( f / g ) � is small. F. Krauss IPPP Monte Carlo Tools

Monte Carlo Tools Frank Krauss Institute for Particle Physics - PowerPoint PPT Presentation

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University GGI, 24.&26.9.2007 F. Krauss IPPP Monte

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Monte Carlo Tools Frank Krauss Institute for Particle Physics - PowerPoint PPT Presentation

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University GGI, 24.&26.9.2007 F. Krauss IPPP Monte

Monte Carlo Approximation of Monte Carlo Filters Adam M. Johansen et al. Collaborators Include:

Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University

Monte Carlo Methods An introduction to Monte Carlo (MC) methods How to use MC methods

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Draft 1 Density estimation by Monte Carlo and randomized quasi-Monte Carlo (RQMC) Pierre

Chapter 5: Monte Carlo Methods Monte Carlo methods are learning methods Experience

Monte Carlo Methods Guojin Chen Christopher Cprek Chris Rambicure Monte Carlo Methods 1.

4. THE MONTE CARLO METHOD 4.1 I ntroduction This chapter is aimed at describing the Monte Carlo

Monte Carlo Integration Monte Carlo methods use random numbers for sampling Although

Monte Carlo Methods Why Monte Carlo? Computation of number ( 1) n +1 = 1 1 2 + 1

Monte Carlo Control CMPUT 366: Intelligent Systems S&amp;B 5.3-5.5, 5.7 Lecture Outline 1.

Monte Carlo Generators Monte Carlo Generators Monte Carlo Generators QCD Lecture III P .

Linear Regression: Prior Linear Regression: Posterior 4 4 2 2 0 0 2 2 Prior P ( )

Draft 1 Density estimation by Monte Carlo and randomized quasi-Monte Carlo Pierre LEcuyer

Monte Carlo Simulation technique S. B. Santra Department of Physics Indian Institute of

Monte Carlo Generators for International Linear Collider Physics Stefano Moretti NExT Institute

Sensitivity Estimates Using a Toy Monte Carlo Dave Waters, University College London with Sean

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Techniques in Artificial Intelligence - Part I Todd W. Neller Gettysburg College Monte Carlo

Overview of Monte Carlo Generators John Campbell, Fermilab Monte Carlo overview: history

Monte Carlo Simulations and PcNaive Heino Bohn Nielsen 1 of 21 Monte Carlo Simulations MC

Draft Introduction to (randomized) quasi-Monte Carlo Pierre LEcuyer MCQMC Conference,

Basics of Monte Carlo Simulation condensed from a presentation by M. Asai Dennis Wright Geant4

Monte Carlo Control CMPUT 366: Intelligent Systems S&B 5.3-5.5, 5.7 Lecture Outline 1.