1. Monte Carlo Simulations
Peter Richardson
IPPP, Durham University and CERN Theory Group
DESY 5th December

2. Summary Recap of Event Generation Matching Issues
Simulation of Top Production and Decay
New Physics
Summary
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3. A Monte Carlo Event Hard Perturbative scattering:
Usually calculated at leading order in QCD, electroweak theory or some BSM model.
Modelling of the soft underlying event
Multiple perturbative scattering.
Perturbative Decays calculated in QCD, EW or some BSM theory.
Initial and Final State parton showers resum the large QCD logs.
Finally the unstable hadrons are decayed.
Non-perturbative modelling of the hadronization process.
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4. Introduction
In his talk on Monday Torbjorn Sjostrand discussed many of the issues involved.
He mainly concentrated on
The Parton Shower
Hadronization Models
Multiple Interactions
Matching Issues
I will concentrate on
Matching and Shower issues
BSM Physics
Where possible I’ll try and give a slightly different prospective.
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5. Matching There have been a number of approaches to matching suggested.
In practice only ~three of them have been implemented in practice.
CKKW (Catani, Krauss, Kuhn and Webber)
POWHEG (Nason et. al.)
(Webber and Frixione)
MLM Matching (Mangano)
Many other ideas but no code.
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6. LO Matching: General Idea
Parton Shower (PS) simulations use the soft/collinear approximation:
Good for simulating the internal structure of a jet;
Can’t produce high pT jets.
Matrix Elements (ME) compute the exact result at fixed order:
Good for simulating a few high pT 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.
All the schemes involve matching between the matrix element and parton shower at some scale.
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7. 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.
MLM
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
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8. CKKW results for Z +jets
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9. MLM Method for W+jets
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10. NLO Matching Both the MC@NLO and POWHEG approaches aim to give
Correct NLO cross section
NLO result on expansion in aS
Shower Resummation
This is achieved is different ways
Subtract shower result from real emission piece, negative weights.
Exponentiate the full real emission matrix element, (POWHEG), exponentiates non-leading terms.
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11. Top Production MC@NLO HERWIG NLO
S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/
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12. POWHEG
Figures taken from P. Nason’s talk to 3rd MC workshop Frascati Oct. 06.
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13. Matching
The issue of matching cannot be discussed without discussing the underlying shower algorithm.
In order for matching we need to be able to
Work out the shower result and subtract it from matrix element result
Reweight the matrix element result as if it came from the shower (CKKW)
This requires a detailed understanding of the shower algorithm and makes the results shower algorithm dependent.
The POWHEG approach is less algorithm dependent.
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14. Matching
Many of the new shower approaches favour ordering in pT. This is natural for matching as we want to match the hardest emission with the matrix element.
Herwig++ still favours angular ordering. Need to be sure that the pT ordering is implemented in the right way to get the colour coherence effects angular ordering naturally includes.
In the angular ordered approach need the truncated shower of the POWHEG approach in general for matching.
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15. Truncated shower
Part of the approach of POWHEG that Torbjorn didn’t mention is the truncated shower.
This is the radiation of soft gluons in an angular ordered shower before the hardest emission.
Need for matching in the angular ordered shower as the highest pT emission isn’t first.
Has applications in other forms of matching.
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16. Truncated shower CKKW gives the right amount of radiation
But puts some of it in the wrong place with the wrong colour flow
S. Mrenna and PR JHEP 0405: 04 (2004)
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17. Shower Improvements
There have been a number of developments in recent years.
Herwig++ Shower algorithm, improved Lorentz invariance and treatment of mass effects.
PYTHIA pT ordered algorithm allows full ordering of event in pT.
Based on NLO dipole subtraction
SHERPA Krauss and Schumann
VINCIA Giele, Kosower, Skands
Dinsdale, Ternick, Weinzierl.
SCET based (Bauer, Schwartz)
Various forward evolution ideas for initial-state radiation. (Jadach et. al.)
Complex weights (Soper, Nagy) ….
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18. Shower Improvements
Some of these ideas may be useful but we need concrete implementations so they can be compared with data, only the new HERWIG, PYTHIA and SHERPA approaches are at this stage.
The only true test of a Monte Carlo algorithm is comparison with data.
In general the hope is that the new algorithms are under better theoretical control allowing their results to be analytically calculated.
Should make matching easier.
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19. Shower and Matching Issues
The ‘old’ (i.e. FORTRAN) HERWIG and PYTHIA algorithms stood the test of comparison to experimental data.
We need to make sure that both
We haven’t lost the good features, for example colour coherence, of the old algorithms.
The new approaches both give agreement with, and are tuned to, old experimental (in particular LEP) data.
The CEDAR project should provide the tools to do this.
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20. Tuning: Herwig++ All observables Event shapes 4 jet
Identified particle spectra
Multiplicities
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21. Tuning: Herwig++
Before tune After Tune
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22. MCnet The main aims of the network are
MCnet is an EU network consisting of all the general purpose event generator authors.
The projects involved are Herwig++, Pythia, SHERPA, ThePEG.
Nodes are Karlsruhe, CERN, Lund, Durham(+ Cambridge) and UserLink based at UCL.
The main aims of the network are
To train the user community through annual schools and a large visiting students at the nodes.
To train a new generation of event generator authors via a number of postdoc and PhD positions.
To tune, making use of the expertise of the UserLink node, the new Monte Carlo generators.
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23. Shower Issues Some shower issues are
Are the new ideas, SCET etc., of any use in practice?
Need implementations which can be compared with data.
Are the new shower algorithms better for matching?
Need matching implemented.
Is pT a good choice for the evolution variable?
Needs comparison with the observables the persuaded us angle is best.
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24. Shower Issues Some shower issues are
Can we include effects of sub-leading logs, colour?
Ideas welcome, but have to be practical.
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25. Simulation of Top Production and Decay
Given the accuracy of the recent top quark mass measurements we need to seriously consider the theoretical issues.
Given the experimental approaches either the RMASS(6) parameter of HERWIG or PMAS(6,1) parameters of PYTHIA are measured.
Can’t really publish a paper
Measurement of PMASS(6,1) parameter
Should be ~ the pole mass, wasn’t so important when error was larger, but now the difference could be significant.
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26. Simulation of Top Production and Decay
Can we define the a rigourous scheme in which the showers implement the mass?
Issues of soft radiation and non-perturbative effects which may effect the mass measurement.
Some recent work (Skands and Wicke) on non-erturbative effects, much older work (Khoze, Stirling, Orr, Sjostrand) on soft radiation
Also issues about matching in top quark events, particularly related to the hardest jet.
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27. BSM
There are a lot of issues related to the simulation of physics Beyond the Standard Model:
Simulation of the hard scattering process;
Simulation of the decays of any new particles;
Correlation effects between the production and decay;
Simulation of radiation, QCD and QED, from the particles.
A lot of work has gone in this area, until recently much more than into improving the simulation of Standard Model physics.
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28. BSM The main question is how accurate a simulation do we need.
Before we see something I’m not sure we need a really detailed simulation. If a major discovery relies on the fine details of the simulation would we believe it anyway?
After discovery we will need more accurate simulations in order to decide which model it is.
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29. BSM
Traditionally models have been implemented in the general purpose event generators.
We now have a lot of tools in which adding new models is easier, has to be the way forward until we know which model is right.
Issues over whether to use (improved) narrow-width approximations or high multiplicity matrix elements.
Should the event generator simulate everything or use external programs?
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30. Example of BSM Physics in Herwig++
New approach for the implementation of BSM physics.
Rather than hard coding scattering and decay matrix elements have general matrix elements for 2g2 and 1g2 processes based on spins.
Code the Feynman rules for the different models.
Makes adding new models and getting the spin correlations right much easier.
Tools like COMPHEP and MadGraph have allowed this for a long time.
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31. UED Look at the decay e- near e- far q e- near q*L Z* e+ far e+ near
e*R g*
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32. The Future
When we started on the change to C++, 7-8 years ago, we assumed/hoped:
The general purpose event generators would do less;
There would be more specialised programs for individual parts of the process;
It would be possible to exchange parts of the simulation, e.g. run the LUND string model with the Herwig parton shower.
We would concentrate only on showers and hadronization.
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33. The Future
For a variety of reasons, some physics driven and some sociological this hasn’t happened.
It has proven impossible to agree on a common framework making it hard/impossible to interface parts of different programs.
Getting a more accurate description of the physics has required passing more information between the different parts of the process, e.g. matching usually needs to be tuned to the shower.
Interfaces are always problematic and error prone.
In reality the general purpose event generators look like doing even more in C++.
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34. New Generators
So a lot of work has gone into developing the new generators (on Herwig++ alone STFC has invested ~10 man years of postdoc effort.)
It is important that they are used and integrated into experimental frameworks now.
There’s no going back the FORTRAN is finished. Updates, support and maintainance will stop in the near future.
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35. A Word of Warning
A word of caution, it might seem that anyone can write an event generator.
Often the view of experimentalists (and theorists). They believe they understand what is involved and think its easy. It ain’t.
Requires understanding of a large range of theoretical and experimental physics together with an ability to write good code.
The original HERWIG/PYTHIA authors have a vast amount of experience.
The experiment of bringing in new people to write the C++ generators has not been complete success.
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36. Summary
Monte Carlo simulations form the natural interface between the experimental and theoretical communities.
In is important that the simulations are as accurate as possible.
There have been many improvements to the simulation but there are still many interesting problems to work on.
DESY 5th December