Introduction to Monte Carlo Event Generators Peter Richardson

Introduction to Monte Carlo Event Generators Peter Richardson IPPP, Durham University Yeti 09 12 th 1

Plan • Introduction – Basic principles of event generation • Parton Showers – Parton Shower Approach – CKKW and MC@NLO, POWHEG • Hadronization and Underlying Event – Hadronization Models – Underlying Event Modelling (Mike Seymour) Yeti 09 12 th 2

Plan • I will concentrate on hadron collisions. • There are many things I will not have time to cover – – – Heavy Ion physics B Production BSM Physics Diffractive Physics Underlying Event (Mike Seymour) • I will concentrate on the basic aspects of Monte Carlo simulations which are essential for the Tevatron and LHC. Yeti 09 12 th 3

Other Lectures and Information • Unfortunately there are no good books or review papers on Event Generator physics. • However many of the other generator authors have given similar lectures to these which are available on the web • Torbjorn Sjostrand at the Durham MCnet school http: //conference. ippp. dur. ac. uk/conference. Other. Views. py? view=stand ard&conf. Id=3 • Mike Seymour at the CTEQ-MCnet school http: //conference. ippp. dur. ac. uk/conference. Other. Views. py? view=ippp& amp; conf. Id=156 Yeti 09 12 th 4

Monte Carlo Event Generators • At the most basic level a Monte Carlo event generator is a program which simulates particle physics events with the same probability as they occur in nature. • In essence it performs a large number of integrals and then unweights to give the momenta of the particles which interact with the detector. Yeti 09 12 th 5

A Monte Carlo Event Hard Perturbative scattering: Modelling of the soft underlying event Multiple perturbative scattering. Usually calculated at leading order in QCD, electroweak theory or some BSM model. Perturbative Decays calculated QCD, State EW or Initial andin. Final parton showers resum the Finally the unstable hadrons are some theory. large. BSM QCD logs. of the Non-perturbative modelling decayed. hadronization process. Yeti 09 12 th 6

Monte Carlo Event Generators • All the event generators split the simulation up into the same phases: – – – Hard Process; Parton Shower; Secondary Decays; Hadronization; Multiple Scattering/Soft Underlying Event; Hadron Decays. • I will discuss the different models and approximations in the different programs as we go along. • I will try and give a fair and objective comparision, but bear in mind that I’m one of the authors of HERWIG. Yeti 09 12 th 7

Monte Carlo Event Generators • • There a range of Monte Carlo simulation programs. In general there are two classes of programs. 1) General Purpose Event Generators Does everything 2) Specialized Programs Just perform part of the process • Often need to use both types of program. Yeti 09 12 th 8

Monte Carlo Event Generators General Purpose Specialized Hard Processes HERWIG/Herwig++ Many Resonance Decays ISAJET HDECAY, SDECAY Parton Showers PYTHIA/Pythia 8 Ariadne/LDC, NLLJet Underlying Event SHERPA DPMJET, PHOJET Hadronization None? Hadron Decays TAUOLA/Evt. Gen Yeti 09 12 th 9

Hard Processes • Traditionally all the hard processes used were in the event generators. • These are normally 2 g 2 scattering processes. • There a vast range of processes in both HERWIG and PYTHIA. • However for the LHC we are often interested in higher multiplicity final states. • For these need to use specialized matrix element generators, for example SHERPA has its own matrix element generator built in. Yeti 09 12 th 10

QCD Radiation • It is impossible to calculate and integrate the matrix elements for large numbers of partons. • Instead we treat the regions where the emission of QCD radiation is enhanced. • This is soft and collinear radiation. Yeti 09 12 th 11

Collinear Singularities • In the collinear limit the cross section for a process factorizes – Pji(z) is the DGLAP splitting function. • The splitting function only depends on the spin and flavours of the particles Yeti 09 12 th 12

Collinear Singularities • This expression is singular as qg 0. • What is a parton? (or what is the difference between a collinear pair and a parton) • Introduce a resolution criterion, e. g. • Combine the virtual corrections and unresolvable emission Resolvable Emission Finite Unresolvable Emission Finite • Unitarity: Unresolved + Resolved =1 Yeti 09 12 th 13

Monte Carlo Procedure • The key difference between the different Monte Carlo simulations is in the choice of the evolution variable. • Evolution Scale – – Virtuality, q 2 Transverse Momentum, k. T. Angle, q. …. • Energy fraction, z – Energy fraction – Light-cone momentum fraction – …. • All are the same in the collinear limit. Yeti 09 12 th 14

Soft Emission • We have only considered collinear emission. What about soft emission? • In the soft limit the matrix element factorizes but at the amplitude level. • Soft gluons come from all over the event. • There is quantum interference between them. • Does this spoil the parton shower picture? Yeti 09 12 th 15

Angular Ordering • There is a remarkable result that if we take the large number of colours limit much of the interference is destructive. • In particular if we consider the colour flow in an event. • QCD radiation only occurs in a cone up to the direction of the colour partner. • The best choice of evolution variable is therefore an angular one. Yeti 09 12 th Colour Flow Emitter Colour Partner 16

Colour Coherence • Angular Ordering and Colour Coherence are often used interchangeably in talks etc. . • However there is a difference. • Colour Coherence is the phenomena that a soft gluon can’t resolve a small angle pair of particles and so only sees the colour charge of the pair. • Angular Ordering is a way of implementing colour coherence in parton shower simulations. Yeti 09 12 th 17

Running Coupling • It is often said that Monte Carlo event generators are leadinglog. • However they include many effects beyond leading log, e. g. • Momentum Conservation • Running Coupling Effects – Effect of summing higher orders is absorbed by replacing as with as(k. T 2). – Gives more soft gluons, but must avoid the Landau pole which makes the cut-off a physical parameter. Yeti 09 12 th 18

The Colour Dipole Model • The standard parton shower approach starts from the collinear limit and makes changes to include soft gluon coherence. • The Colour Dipole Model starts from the soft limit. • Emission of soft gluons from the colour-anticolour dipole is universal. i • After emitting a gluon, the colour dipole splits into two new dipoles Yeti 09 12 th 19

Parton Shower • ISAJET uses the original parton shower algorithm which only resums collinear logarithms. • PYTHIA originally used the collinear algorithm with an angular veto to try to reproduce the effect of the angular ordered shower. • HERWIG uses the angular ordered parton shower algorithm which resums both soft and collinear singularities. • SHERPA uses the PYTHIA algorithm. • ARIADNE uses the colour dipole model. Yeti 09 12 th 20

Parton Shower • Recently there as been a lot of work on new parton shower algorithms. • Later versions of PYTHIA and Pythia 8 use a p. T order shower. • SHERPA now includes two alternative dipole based shower modules. • Other approaches are being studied. Yeti 09 12 th 21

LEP Event Shapes Yeti 09 12 th 22

Energy Dependence Yeti 09 12 th 23

Hard Jet Radiation • The parton shower is designed to simulate soft and collinear radiation. • While this is the bulk of the emission we are often interested in the radiation of a hard jet. • This is not something the parton shower should be able to do, although it often does better than we except. • If you are looking at hard radiation HERWIG/PYTHIA will often get it wrong. Yeti 09 12 th 24

Hard Jet Radiation • Given this failure of the approximations this is an obvious area to make improvements in the shower and has a long history. • You will often here this called: – – Matrix Element matching; Matrix Element corrections; Merging matrix elements and parton shower; MC@NLO/POWHEG. • I will discuss all of these and where the different ideas are useful. Yeti 09 12 th 25

Hard Jet Radiation: General Idea • Parton Shower (PS) simulations use the soft/collinear approximation: – Good for simulating the internal structure of a jet; – Can’t produce high p. T jets. • Matrix Elements (ME) compute the exact result at fixed order: – Good for simulating a few high p. T jets; – Can’t give the structure of a jet. • We want to use both in a consistent way, i. e. – – ME gives hard emission PS gives soft/collinear emission Smooth matching between the two. No double counting of radiation. Yeti 09 12 th 26

Matching Matrix Elements and Parton Shower • The oldest approaches are usually called matching matrix elements and parton showers or the matrix element correction. HERWIG phase • Slightly different for HERWIG and space for Drell. PYTHIA. Yan • In HERWIG Dead Zone – Use the leading order matrix element to fill the dead zone. – Correct the parton shower to get the leading order matrix element in the already filled region. • PYTHIA fills the full phase space so only the second step is needed. Yeti 09 12 th 27

Matrix Element Corrections W q. T distribution from D 0 Z q. T distribution from CDF G. Corcella and M. Seymour, Nucl. Phys. B 565: 227 -244, 2000. Yeti 09 12 th 28

Recent Progress • In the last few years there has been a lot of work addressing both of these problems. • Two types of approach have emerged 1) NLO Simulation • • NLO normalization of the cross section Gets the hardest emission correct 2) Multi-Jet Leading Order • • Still leading order. Gets many hard emissions correct. Yeti 09 12 th 29

NLO Simulation • There has been a lot of work on NLO Monte Carlo simulations. • The MC@NLO approach of Frixione, Nason and Webber and the POWHEG approach of Nason are the only techniques which have been shown to work in practice. Yeti 09 12 th 30

MC@NLO • The basic idea of MC@NLO is: – work out the shower approximation for the real emission; – subtract it from the real emission; – add it to the virtual piece. • This cancels the singularities and avoids double counting. • It’s a lot more complicated than it sounds. Yeti 09 12 th 31

MC@NLO • For each new process the shower approximation must be worked out, which is often complicated. • While the general approach works for any shower it has to be worked out for a specific case. • So for MC@NLO only works with the HERWIG shower algorithm, an implementation for Herwig++ is in progress. • It could be worked out for other algorithms but this remains to be done. Yeti 09 12 th 32

Top Production MC@NLO HERWIG NLO S. Frixione, P. Nason and B. R. Webber, JHEP 0308(2003) 007, hep-ph/0305252. Yeti 09 12 th 33

POWHEG • Alternative approach POsitive Weight Hardest Emission Generator of Nason et. al. . • Here: – Generate the kinematical variables for the leading order process with Next-to-leading order accuracy; – Generate the hardest emission by exponentiating the real emission matrix element ordering in p. T; – Some modifications needed if shower not p. T ordered. • Has NLO accuracy but different sub-leading corrections to MC@NLO. Yeti 09 12 th 34

Top Production Taken from JHEP 0709: 126, 2007 Frixione et. al. Yeti 09 12 th 35

Multi-Jet Leading Order • While the NLO approach is good for one hard additional jet and the overall normalization it cannot be used to give many jets. • Therefore to simulate these processes use matching at leading order to get many hard emissions correct. • I will briefly review the general idea behind these approaches and then show some results. Yeti 09 12 th 36

Two approaches CKKW MLM • Simulate N jet partonic state. • Apply weight factors for probability that no jets emitted above matching scale. • Generate shower vetoing radiation above the matching scale. • The weight factors ensure the different samples can be added. • Simulate partonic N jet state. • Generate parton shower. • Require that all the jets above the matching scale after the shower have an associated pre-shower parton. • For each N the shower doesn’t add any more jets. • Rejection ensures that samples with different numbers of jets can be summed Yeti 09 12 th 37

Two approaches • While the CKKW approach is more rigorous the approaches are similar and the MLM method is easier to implement. • The rejection of events without a match between the pre- and post-shower jets in the MLM approach plays the same role as the weight factors and veto in the CKKW approach. Yeti 09 12 th 38

CKKW results for Z +jets Yeti 09 12 th 39

CKKW results for Z +jets Yeti 09 12 th 40

CKKW results for Z +jets Yeti 09 12 th 41

MLM Method for W+jets Yeti 09 12 th 42

Hadronization • Partons aren’t physical particles: they can’t propagate freely. • We therefore need to describe the transition of the quarks and gluons in our perturbative calculations into the hadrons which can propagate freely. • We need a phenomenological model of this process. • There are three models which are commonly used. – Independent Fragmentation – Lund String Model – Cluster Model Yeti 09 12 th 43

Independent Fragmentation Model “Feynman-Field” • The longitudinal momentum distribution is given by an arbitrary fragmentation function which is a parameterization of data. • The transverse momentum distribution is Gaussian. • The algorithm recursively splits qgq’+hadron. • The remaining soft quark and antiquark are connected at the end. • The model has a number of flaws – – – Strongly frame dependent No obvious relation with the perturbative physics. Not infrared safe Not a confinement model Wrong energy dependence. Yeti 09 12 th 44

Confinement • We know that at small distances we have asymptotic freedom and the force between a quark-antiquark pair is like that between an e+e- pair. QED + - • But at long distances the self interactions of the gluons make the field lines attract each other. QCD • A linear potential at long distances and confinement. Yeti 09 12 th 45

Lund String Model • In QCD the field lines seem to be compress into a tubelike region, looks like a string. • So we have linear confinement with a string tension. • Separate the transverse and longitudinal degrees of freedom gives a simple description as a 1+1 dimensional object, the string, with a Lorentz invariant formalism. Yeti 09 12 th 46

Intraquark potential • In the real world the string can break non-perturbatively by producing quark-antiquark pairs in the intense colour field. i Quenched QCD Full QCD i • This is the basic physics idea behind the string model and is very physically appealing. Yeti 09 12 th 47

Preconfinement • In the planar approximation, large number of colours limit Gluon= colour-anticolour pair • We can follow the colour structure of the parton shower. • At the end colour singlet pairs end up close in phase space. • Non-perturbatively split the gluons into quark-antiquark pairs. Yeti 09 12 th 48

Preconfinement • The mass spectrum of colour-singlet pairs is asymptotically independent of energy and the production mechanism. • It peaks at low mass, of order the cut-off Q 0. Yeti 09 12 th 49

The Cluster Model • Project the colour singlet clusters onto the continuum of high-mass mesonic resonances (=clusters). • Decay to lighter well-known resonances and stable hadrons using – Pure 2 body phase-space decay and phase space weight • The hadron-level properties are fully determined by the cluster mass spectrum, i. e. by the properties of the parton shower. • The cut-off Q 0 is the crucial parameter of the model. Yeti 09 12 th 50

The ‘Beliefs’ • There are two main schools of thought in the event generator community. PYTHIA • “Hadrons are produced by hadronization. You must get the nonperturbative dynamics right. ” • Better data has required improvements to the perturbative simulation. HERWIG • “Get the perturbative physics right and any hadronization model will be good enough” • Better data has required changes to the cluster model to make it more string-like • There ain’t no such thing as a good parameter-free description. Yeti 09 12 th 51

Identified Particle Spectra Yeti 09 12 th 52

The facts? • Independent fragmentation doesn’t describe the data, in particular the energy dependence. • All the generators give good agreement for event shapes • HERWIG has less parameters to tune the flavour composition and tends to be worse for identified particle spectra. • Baryon Production is often a problem. Yeti 09 12 th 53

Hadron Decays • The final step of the event generation is to decay the unstable hadrons. • This is unspectacular/ungrateful but necessary, after all this is where most of the final-state particles are produced. • There’s a lot more to it than simply typing in the PDG. • Normally use dedicated programs with special attention to polarization effects: – EVTGEN: B Decays – TAUOLA: t decays – PHOTOS: QED radiation in decays. • Herwig++ and SHERPA now include their own sophisticated internal models. Yeti 09 12 th 54

The Future • Most of the work in the generator community is currently devoted to developing the next generation of C++ generators. • We needed to do this for a number of reasons: – Code structures needed rewriting; – Experimentalists don’t understand FORTRAN any more; – Couldn’t include some of the new ideas in the existing programs. Yeti 09 12 th 55

The Future • A number of programs – – The. PEG Herwig++ SHERPA PYTHIA 8 • While it now looks likely that C++ versions of HERWIG and PYTHIA won’t be used for early LHC data this is where all the improvements the experimentalists want/need will be made and will have to be used in the long term. Yeti 09 12 th 56

Outlook • The event generators are in a constant state of change, in the last 5 years: – Better matrix element calculations; – Improved shower algorithms; – Better matching of matrix elements and parton showers; – First NLO processes; – Improvements to hadronization and decays; – Improved modelling or the underlying event; – The move to C++. • Things will continue to improve for the LHC. Yeti 09 12 th 57

Summary • Hopefully these lectures will help you understand the physics inside Monte Carlo event generators. • If nothing else I hope you knew enough to start think about what you are doing when running the programs and questions like – Should the simulation describe what I’m looking for? – What is the best simulation for my study? – What physics in the simulation affects my study? – Is what I’m seeing physics or a bug? Yeti 09 12 th 58