Event Simulation at the LHC

Event Simulation at the LHC
Peter Richardson IPPP, Durham University Higgs-Maxwell Meeting 7th Feb

Higgs-Maxwell Meeting 7th Feb
Summary Introduction From LEP/Tevatron to LHC Underlying event Parton Showers Hard Radiation Conclusions Higgs-Maxwell Meeting 7th Feb

Introduction Monte Carlo event generators are essential for experimental particle physics. They are used for: Comparison of experimental results with theoretical predictions; Studies for future experiments. Often these programs are ignored by theorists and treated as black boxes by experimentalists. It is important to understand the assumptions and approximations involved in these simulations. Higgs-Maxwell Meeting 7th Feb

Introduction Experimental physicists need to be able to answer the following questions Is the effect I’m seeing due to different models, or approximations, or is it a bug? Am I measuring a fundamental quantity or merely a parameter of the simulation code? Theorists need to understand enough to be able ask Have the experimentalists misused the Monte Carlo giving incorrect results? Higgs-Maxwell Meeting 7th Feb

Introduction In this talk I will start by describing the ideas behind Monte Carlo simulations. Recently there has been a lot of progress in two related areas: Next-to-leading order simulation; Matching leading-order matrix elements; which are aimed at improving the treatment of hard radiation. I will go on to discuss these and where they are of use at the LHC. Higgs-Maxwell Meeting 7th Feb

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. Higgs-Maxwell Meeting 7th Feb

Monte Carlo Event Generators
The different event generators ISAJET PYTHIA HERWIG SHERPA use different approximations or models for the different stages of the event. However the overall strategy is the same. Higgs-Maxwell Meeting 7th Feb

From LEP/Tevatron to LHC
Some of these programs have been in use for the last years. They have been very successful in describing data from LEP, HERA and the Tevatron. However getting good agreement with data has required many improvements and developments along the way. For the LHC in order to include all the new theoretical ideas from the last 5 years major changes were needed. Higgs-Maxwell Meeting 7th Feb

In order to be able to maintain and support the simulations for the LHC a major program is underway. Either writing new generators or rewriting existing programs. There are ongoing projects to rewrite HERWIG and PYTHIA in C++. This is essential to include all the new physics ideas. Some of the newer projects, SHERPA, are also in C++. Higgs-Maxwell Meeting 7th Feb

Historically the general purpose event generators have been the workhorses of most experimental analyses. However there are often specific packages that perform one particular part of the simulation better than any general program can hope to. Higgs-Maxwell Meeting 7th Feb

Monte Carlo Event Generators
General Purpose Specialized Hard Processes HERWIG Many, e.g. ALPGEN, MadGraph Resonance Decays PYTHIA HDECAY, SDECAY Parton Showers ISAJET Ariadne/LDC, NLLJet Underlying Event SHERPA DPMJET Hadronization + new C++ versions None? Ordinary Decays TAUOLA/EvtGen Higgs-Maxwell Meeting 7th Feb

The belief when we started 5 years ago was that the new generation of event generators would do less than their predecessors. Rely on external programs for: Hard Processes; BSM physics; Hadron decays. Concentrate on the parton shower and hadronization. However this hasn’t happened. Higgs-Maxwell Meeting 7th Feb

Many of the physics developments require more communication between the different stages of the event generation. New approaches to treating hard QCD radiation require more information to be passed from the hard process to the parton shower. New approaches to spin correlations in decays requires more information to be passed between the hard process, decays and parton shower. Getting the correlations right in tau decays requires information to be passed between the perturbative and non-perturbative decays. In reality the general purpose event generators seem to be doing more. Higgs-Maxwell Meeting 7th Feb

All the programs involve a large number of parameters. We use the parton shower to evolve from the high energy of the collision to a low energy where we use the non-perturbative models. This should ensure the universality of the parameters just like the PDFs. In general if the parameters are energy dependent then there is some missing physics in the evolution. Higgs-Maxwell Meeting 7th Feb

However at the LHC we are entering a new energy regime for the first time. May be effects in the evolution that are missing. For some non-perturbative physics that does change with energy we don’t understand the evolution Underlying Event Intrinsic pT Higgs-Maxwell Meeting 7th Feb

The higher energy means that the rate for the production of events with high pT jets and leptons is significantly higher. While the parton shower describes soft and collinear emission it can not simulate the emission of high pT jets. There has been a lot of progress over the last 5 years to improve the simulation of hard jets by using more information from both higher order and higher multiplicity matrix elements. Higgs-Maxwell Meeting 7th Feb

Underlying Event The cross-section for 2g2 scattering is dominated by t-channel gluon exchange. It diverges like This must be regulated used a cut of pTmin. For small values of pTmin this is larger than the total hadron-hadron cross section. More than one parton-parton scattering per hadron collision Higgs-Maxwell Meeting 7th Feb

Multiparton Interaction Models
If the interactions occur independently then follow Poissonian statistics However energy-momentum conservation tends to suppressed large numbers of parton scatterings. Also need a model of the spatial distribution of partons within the proton. Higgs-Maxwell Meeting 7th Feb

Multiparton Interaction Models
In general there are two options for regulating the cross section. where or are free parameters of order 2 GeV. Typically 2-3 interactions per event at the Tevatron and 4-5 at the LHC. However tends to be more in the events with interesting high pT ones. Higgs-Maxwell Meeting 7th Feb

Data There have been a lot of studies at the Tevatron of the underlying event. Define three regions Toward near the leading jet Away near the second jet Transverse to both jets Expect the underlying event in the transverse region. Higgs-Maxwell Meeting 7th Feb

Data Higgs-Maxwell Meeting 7th Feb

and for the LHC? Higgs-Maxwell Meeting 7th Feb

and for the LHC? Problem is that unlike the PDFs and the parton shower we don’t know what the energy dependence should be. Makes it hard to extrapolate to the LHC as the lever arm in energy we have from CERN experiments and the Tevatron isn’t large enough. Higgs-Maxwell Meeting 7th Feb

Parton Showers The parton shower is designed to simulate QCD radiation in the: Collinear limit; Soft limit. These are the most important regions of phase space. The different algorithms differ in the sophistication of their treatment of different effects. Higgs-Maxwell Meeting 7th Feb

Parton Showers In the parton shower per se there have been two recent advances. New Herwig++ shower Based on massive splitting functions. Better treatment of radiation from heavy quarks. More Lorentz invariant. New PYTHIA pT ordered shower Order shower in pT, should be coherent. Easier to include new underlying event models. Easier to match to matrix elements Higgs-Maxwell Meeting 7th Feb

Herwig++ for tgbW+g hep-ph/ , Keith Hamilton, Peter Richardson based on the formalism of S. Gieseke, P. Stephens and B.R. Webber, JHEP 0312:045,2003. Improvement on the previous FORTRAN version. Higgs-Maxwell Meeting 7th Feb

PYTHIA pT ordered Shower
Higgs-Maxwell Meeting 7th Feb

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 expect. If you are looking at hard radiation HERWIG/PYTHIA will often get it wrong. Higgs-Maxwell Meeting 7th Feb

Hard Jet Radiation There has been a lot of work in this area in the last 5 years. In order to test the new approaches and tune new parameters we must compare and tune with Tevatron data. The conventional approaches give good agreement with LEP data. It is only in hadron collisions where it is possible to have a lot of additional hard radiation that these techniques are needed. Higgs-Maxwell Meeting 7th Feb

Hard Jet Radiation There have been a number of developments NLO Simulation, Multi-Jet matching MLM procedure CKKW and variants For many of these, particularly NLO simulation, there are a lot of theoretical ideas. However the true test of a Monte Carlo algorithm is comparing an implementation with data. Higgs-Maxwell Meeting 7th Feb

NLO Simulation There has been a lot of work on NLO Monte Carlo simulations. However apart from some early work by Dobbs the only Frixione, Nason and Webber have produced code which can be used to generate results. I will therefore only talk about the work of Frixione, Nason and Webber. Most of this is taken from Bryan Webber’s talk at the YETI meeting in Durham. Higgs-Maxwell Meeting 7th Feb

S. Frixione and B.R. Webber JHEP 0206(2002) 029, hep-ph/ , hep-ph/ S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/ Higgs-Maxwell Meeting 7th Feb

was designed to have the following features. The output is a set of fully exclusive events. The total rate is accurate to NLO NLO results for observables are recovered when expanded in as. Hard emissions are treated as in NLO calculations. Soft/Collinear emission are treated as in the parton shower. The matching between hard emission and the parton shower is smooth. MC hadronization models are used. Higgs-Maxwell Meeting 7th Feb

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 only works with the HERWIG shower algorithm. It could be worked out for PYTHIA or Herwig++ but this remains to be done. Higgs-Maxwell Meeting 7th Feb

Top Production HERWIG NLO S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/ Higgs-Maxwell Meeting 7th Feb

Top Production at the LHC
HERWIG NLO S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/ Higgs-Maxwell Meeting 7th Feb

B Production at the Tevatron
S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/ Higgs-Maxwell Meeting 7th Feb

NLO Simulation is the most sophisticated implementation of a NLO Monte Carlo simulation. There have been some ideas by Paulo Nason JHEP 0411:040,2004 and recent results. In this approach there are no negative weights but more terms would be exponentiated beyond leading log. Higgs-Maxwell Meeting 7th Feb

Nason Approach to MC@NLO
hep-ph/ Oluseyi Latunde-Dada, Stefan Gieseke, Bryan Webber Higgs-Maxwell Meeting 7th Feb

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 this approach and then show some results. Higgs-Maxwell Meeting 7th Feb

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 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 pT scale. Higgs-Maxwell Meeting 7th Feb

Two approaches CKKW 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 Higgs-Maxwell Meeting 7th Feb

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. Higgs-Maxwell Meeting 7th Feb

CKKW results for Z +jets
Higgs-Maxwell Meeting 7th Feb

MLM Method for W+jets Higgs-Maxwell Meeting 7th Feb

LHC ET of the 4th jet from HERWIG
ME HW 0 jets 1 jets 2 jets 3 jets 4 jets Higgs-Maxwell Meeting 7th Feb

LHC We need to use these new tools for the simulation of multi-jet final states. Important for a more realistic estimate of LHC backgrounds. Higgs-Maxwell Meeting 7th Feb

Conclusions There have been a lot of new developments in: new parton shower algorithms; improved treatment of hard QCD radiation. There have been other developments: improved simulation of perturbative and non-perturbative decays; better simulation of radiation from heavy particles. Everything should be ready in time for the LHC Higgs-Maxwell Meeting 7th Feb

Event Simulation at the LHC

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