CERN-PH-TH-2010-298 KA-TP-40-2010 Cavendish-HEP-10/21 DCPT/10/202 MAN/HEP/2010/23 IPPP/10/101 SLAC-PUB-14333 LU TP 10-28 HD-THEP-10-24 MCnet-11-01

General-purpose generators for LHC physics

Andy Buckleya, Jonathan Butterworthb, Stefan Giesekec, David Grellscheidd, Stefan H¨ochee, Hendrik Hoethd, Frank Kraussd, Leif L¨onnbladf,g, Emily Nurseb, Peter Richardsond, Steffen Schumannh, Michael H. Seymouri, Torbj¨ornSj¨ostrandf, Peter Skandsg, Bryan Webberj aPPE Group, School of Physics & Astronomy, University of Edinburgh, EH25 9PN, UK bDepartment of Physics & Astronomy, University College London, WC1E 6BT, UK cInstitute for Theoretical Physics, Karlsruhe Institute of Technology, D-76128 Karlsruhe dInstitute for , Durham University, DH1 3LE, UK eSLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA fDepartment of Astronomy and Theoretical Physics, Lund University, Sweden gPH Department, TH Unit, CERN, CH-1211 Geneva 23, Switzerland hInstitute for Theoretical Physics, University of Heidelberg, 69120 Heidelberg, Germany iSchool of Physics and Astronomy, University of Manchester, M13 9PL, UK jCavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, UK

Abstract We review the physics basis, main features and use of general-purpose Monte Carlo event generators for the simulation of proton-proton collisions at the Large Collider. Topics included are: the generation of hard- scattering matrix elements for processes of interest, at both leading and next- to-leading QCD perturbative order; their matching to approximate treat- ments of higher orders based on the showering approximation; the parton and dipole shower formulations; parton distribution functions for event gen- erators; non-perturbative aspects such as soft QCD collisions, the underly- ing event and diffractive processes; the string and cluster models for hadron formation; the treatment of hadron and tau decays; the inclusion of QED radiation and beyond-Standard-Model processes. We describe the principal features of the Ariadne, Herwig++, Pythia 8 and Sherpa generators, to- gether with the Rivet and Professor validation and tuning tools, and discuss the physics philosophy behind the proper use of these generators and tools. This review is aimed at phenomenologists wishing to understand better how parton-level predictions are translated into hadron-level events as well as ex- perimentalists wanting a deeper insight into the tools available for signal and background simulation at the LHC.

Preprint submitted to Physics Reports January 14, 2011

Work supported in part by US Department of Energy contract DE-AC02-76SF00515. Keywords: QCD, hadron colliders, Monte Carlo simulation

Contents

1 General introduction 6

I Review of physics behind MC event generators 11

2 Structure of an event 11 2.1 Jets and algorithms ...... 13 2.2 The large-Nc limit ...... 14

3 Hard subprocesses 14 3.1 Factorization formula for QCD cross sections ...... 15 3.2 Leading-order matrix-element generators ...... 17 3.3 Choices for renormalization and factorization scales ...... 17 3.4 Choices for PDFs ...... 18 3.5 Anatomy of NLO cross section calculations ...... 18 3.6 Summary ...... 20

4 Parton showers 21 4.1 Introduction: QED bremsstrahlung in scattering processes . . 21 4.2 Collinear final state evolution ...... 22 4.3 Soft emission ...... 29 4.4 Initial state evolution ...... 31 4.5 Connecting parton showers to the hard process ...... 34 4.6 Quark mass effects ...... 39 4.7 The dipole approach to parton showering ...... 41 4.8 Summary ...... 43

5 ME and NLO matching and merging 44 5.1 Introduction ...... 44 5.2 Correcting the first emission ...... 48 5.2.1 The NLO cross sec