Bonn 23rd Feb 1

Simulations of BSM Signals

Peter Richardson

IPPP, Durham University

Bonn 23rd Feb 2

Summary

• Introduction• Basics of Monte Carlo Simulation• Processes inside the Generators• Cascade decays• Conclusions

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Introduction• Monte Carlo event generators are programs

which, starting with some fundamental process predict the stable particles which will interact with a detector.

• There are a number of Monte Carlo event generators in common use– PYTHIA– HERWIG– SHERPA

• They all split the event generation up into the same pieces.

• The models and approximations they use for the different pieces are of course different.

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A Monte Carlo Event

Initial and Final State parton showers resum the large QCD logs.

Hard Perturbative scattering:

Usually calculated at leading order in QCD, electroweak theory or some BSM model.

Perturbative Decays calculated in QCD, EW or some BSM theory.

Multiple perturbative scattering.

Non-perturbative modelling of the hadronization process.

Modelling of the soft underlying event

Finally the unstable hadrons are decayed.

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Monte Carlo Event Generators

• For BSM physics the main pieces of the event generators are

1) Hard Process• New intermediate particles• New particles produced• Changes to SM distributions

2) Decays• Decays of new particles produced in the hard

process or previous decays.

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Built In Models• Traditionally models of new physics

are built into the event generator.• This will often include hard

processes and decays.• Relatively few models have been

implemented and the sophistication of the simulation varies.

• Each one was hard-coded by an author of the general purpose generator which was very time consuming.

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Built In ModelsHERWIG PYTHIA

SUSY

SUSY+RPV

RS Gravitons

Z’/W’

Technicolor

Left-Right Models

Compositeness

Excited fermions

Leptoquarks

Fourth generation

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Progress• In the last few years things have moved

on.• Less new models are being implemented

inside the event generators.• Relying more on both.

– Matrix element generators for specific processes, interfaced via the Les Houches matrix element accord.

– Matrix element generators which automatically calculate the processes from the Feynman rules and allow the Feynman rules for new models to be implemented.

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Progress

• The four main matrix element generators for BSM physics are:– COMPHEP/CALCHEP;– MadGraph;– Omega/Whizard;– SHERPA.

• All of these have the Feynman rules for a range of models included.

• Can also implement new models relatively easily from either the Feynman rules or Lagrangian.

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BSM Simulation• In general there are two different classes

of models to be simulated.1) Models which only have either new hard

scattering processes, or modifications to the Standard Model ones.

2) Models in which new heavy particles are produced and subsequently decay.

• The first type are relatively simple to simulate.

• The second class, e.g. SUSY, UED, Little Higgs with T-parity are more complicated.

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Cascade Decays• These models were implemented as follows:

– implement the production of the new particles in 22 scatterings;

– recursively decay the new particles using either phase space or the matrix elements.

• This neglects both:– spin correlation effects, which will be important

in determining what a signal is;– some off-shell effects, which may be important

for specific models or values of parameters.

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Cascade DecaysThere are two ways round these limitations.1) Calculate the matrix element for the hard

scattering as a 2n scattering process.• Ensures that both the spin correlations and off-

shell effects are correctly treated.• Can be inefficient for long decay chains or many

decay modes.

2) Still factorize the process into production and decay but include correlations.• Efficient for long decay chains and large numbers

of decay modes. • Only gets the spin correlations right, although

some off-shell effects can in principle be included.

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What is Available• In general a lot more effort has gone into the

simulation of SUSY than everything else put together.

• The simulation of SUSY is very sophisticated including:– simulation of the hard process, matrix elements

for the decays and spin correlations between the production and decay.

– also available in all the matrix element generators.

• In addition various extensions in HERWIG and PYTHIA.

• Some extra dimensions models in HERWIG, PYTHIA and SHERPA.

• A range of model files for COMPHEP.

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Spin Correlations• In order to simulate long decay chains for

the LHC we need to simulate the production and decay separately– Matrix elements for high multiplicity final-states

are complicated to evaluate and integrate.– Many different channels must be simulated.

• In HERWIG we use an algorithm which reproduces the matrix element, in the narrow width limit, for these chains.

• However the algorithm still allows us to generate the production and decay of particles separately.

• Probably the best compromise for models like SUSY with long decay chains.

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Spin Correlations

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Spin Correlations01

01

02

~ llee R

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Off-Shell Effects• In some cases there will be important

interference/off-shell effects which can only can included by using the matrix element.

• Normally in the event generators the masses of the particles are smeared using a Breit-Wigner distribution.

• In some cases we can include some off-shell effects by including the generating of the mass of the decay products when we generated their momenta.

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Off-Shell Effects• For example for the decay tbW+

we can include the effect of the off-shell W by integrating over its off-shell mass m, i.e. performing the integral

when calculating the top decay.

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Off-Shell Effects

Top Width as a function of top mass.On shell-W

Three body matrix element.

Approximation retaining W propagator.

Approximation with MW replaced by off-shell mass in propagator

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Off-Shell Effects• If we consider the

off-shell decay of the stop,

as a function of the stop mass with the top off-shell.

• Have to be very careful about gauge invariance.

Two body matrix element.

Three body matrix element.

Four body matrix element.

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Off-Shell Effects• This is not as good as having the full

matrix element calculation.• There will always be some

interference effects that can only be obtain using the full matrix element.

• See for hep-ph/0512260 Hagiwara et.al.

and more recent work by Dave Rainwater.

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Off-Shell Effects

Taken from D. Rainwater’s seminar at John Hopkins

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Future• The general purpose event generator

community are in the process of writing a new generation of programs.

• The main aim is to incorporate all the new theoretical developments from the last 5-10 years in programs which can be maintained in the long term.

• There are a number of projects– Herwig++– PYTHIA8– SHERPA– ThePEG

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Future• The approach to BSM physics in these

different programs is different– Herwig++ same basic idea as the FORTRAN

but implemented so that new models can be included more easily and the correlations in different stages of the event can be included.

– SHERPA includes a matrix element generator which is used for BSM physics and allows the easy implementation of new models.

– PYTHIA relies on an interface allow external processes to be supplied at the moment.

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Herwig++• In Herwig++ we have adopted the

following approach– A C++ helicity library based on the HELAS

formalism is used for all matrix element and decay calculations.

– Code the hard 22 matrix elements based on the spin structures.

– Code the 12 decays in the same way and use phase space for the 13 decays to start with.

– Easy to include spin correlations as we have access to the spin unaveraged matrix elements.

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Herwig++• Also use the same structure for the

both hadronic decays and the perturbative decays.

• This ensures that – correlations can be passed to the tau

decays which are sometimes important.

– All the new sophistication of the treatment of hadronic decays including off-shell effects, etc can be used in perturbative decays if needed.

– It’s easier to maintain.

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Herwig++• The main aim though is that all the

should need doing is coding of the Feynman rules for new models, rather than all the matrix elements for production and decay.

• So this a step towards a matrix element generator but much more limited.

• Most of the work has been done by my student Martyn Gigg.

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Herwig++lqlqqL~~~ 0

2

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Herwig++

Unpolarised

01

01

02

~ llee RRLee

LRee

+ Hw++

HERWIG+TAUOLA

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Herwig++

Unpolarised

llee LL*

22~~

RLee

LRee

+ Hw++

HERWIG+TAUOLA

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Tau Decays

Left Handed stau Right Handed stau 00

101

01

~~~~

Fraction of visible energy carried by the charged pion

+ Hw++

HERWIG+TAUOLA

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Tau Decays01

02

~~~~ qqqqL followed by

Based on hep-ph/0612237 Choi et. al.

+ Hw++

HERWIG+TAUOLA

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Tau Decays

Based on hep-ph/0612237 Choi et. al.

01

02

~~~~ qqqqL followed by

+ Hw++

HERWIG+TAUOLA

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Tau Decays

Decay of h+- generated with SHERPA

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Tau Decays• This is one major improvement in the

C++.• In both HERWIG++ and SHERPA by

including the tau decays internally, rather than relying on TAUOLA we can get the correlations right.

• In the FORTRAN this is more of a problem, e.g. HERWIG interfaced to TAUOLA can give both effects I’ve shown, but you need two different incompatible interfaces.

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Herwig++• The MSSM is now implemented and

tested.• Work has start on implementing UED,

the strong vertices have been coded and the strong production processes checked against the literature.

• So far the idea seems to work, it took about a week to implement the strong vertices and most of that was checking against the previous results.

• Hopefully a range of new models will be available soon.

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BSM Simulation• In Monte Carlo simulation most of the effort

in the last few years has been in improving the simulation of Standard Model processes.

• In looking at BSM physics getting the backgrounds right is the most important thing anyway.

• Hopefully any discovery will not depend on fine details of the simulation of the signal.

• In the cases where we need more sophisticated efforts, like spin correlations and off-shell effects, we are in good shape.

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Conclusions• The existing HERWIG and PYTHIA programs

will probably remain the workhorses of event simulation in the near future.

• Unlikely to be any new models implemented in them.

• The matrix element generators are essential for some BSM processes and many backgrounds.

• The simulation in the new C++ generators will be different and allow more models to be studied.