Bonn 23 rd Feb1 Simulations of BSM Signals Peter Richardson IPPP, Durham University

Bonn 23 rd Feb2 Summary Introduction Basics of Monte Carlo Simulation Processes inside the Generators Cascade decays Conclusions

Bonn 23 rd Feb3 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.

Bonn 23 rd Feb4 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.

Bonn 23 rd Feb5 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.

Bonn 23 rd Feb6 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.

Bonn 23 rd Feb7 Built In Models HERWIGPYTHIA SUSY SUSY+RPV RS Gravitons Z’/W’ Technicolor Left-Right Models Compositeness Excited fermions Leptoquarks Fourth generation

Bonn 23 rd Feb8 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.

Bonn 23 rd Feb9 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.

Bonn 23 rd Feb10 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.

Bonn 23 rd Feb11 Cascade Decays These models were implemented as follows: –implement the production of the new particles in 2  2 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.

Bonn 23 rd Feb12 Cascade Decays There are two ways round these limitations. 1)Calculate the matrix element for the hard scattering as a 2  n 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.

Bonn 23 rd Feb13 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.

Bonn 23 rd Feb14 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.

Bonn 23 rd Feb15 Spin Correlations

Bonn 23 rd Feb16 Spin Correlations

Bonn 23 rd Feb17 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.

Bonn 23 rd Feb18 Off-Shell Effects For example for the decay t  bW + 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.

Bonn 23 rd Feb19 Off-Shell Effects Top Width as a function of top mass. On shell-W Three body matrix element. Approximation retaining W propagator. Approximation with M W replaced by off-shell mass in propagator

Bonn 23 rd Feb20 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.

Bonn 23 rd Feb21 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/ Hagiwara et.al. and more recent work by Dave Rainwater.

Bonn 23 rd Feb22 Off-Shell Effects Taken from D. Rainwater’s seminar at John Hopkins

Bonn 23 rd Feb23 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

Bonn 23 rd Feb24 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.

Bonn 23 rd Feb25 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 2  2 matrix elements based on the spin structures. –Code the 1  2 decays in the same way and use phase space for the 1  3 decays to start with. –Easy to include spin correlations as we have access to the spin unaveraged matrix elements.

Bonn 23 rd Feb26 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.

Bonn 23 rd Feb27 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.

Bonn 23 rd Feb28 Herwig++

Bonn 23 rd Feb29 Herwig++ Unpolarised + Hw++ HERWIG+ TAUOLA

Bonn 23 rd Feb30 Herwig++ Unpolarised + Hw++ HERWIG+ TAUOLA

Bonn 23 rd Feb31 Tau Decays Left Handed stau Right Handed stau Fraction of visible energy carried by the charged pion + Hw++ HERWIG+ TAUOLA

Bonn 23 rd Feb32 Tau Decays followed by Based on hep-ph/ Choi et. al. + Hw++ HERWIG+ TAUOLA

Bonn 23 rd Feb33 Tau Decays Based on hep-ph/ Choi et. al. followed by + Hw++ HERWIG+ TAUOLA

Bonn 23 rd Feb34 Tau Decays Decay of h   +  - generated with SHERPA

Bonn 23 rd Feb35 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.

Bonn 23 rd Feb36 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.

Bonn 23 rd Feb37 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.

Bonn 23 rd Feb38 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.