1. Simulating Physics at the LHC
Peter Richardson
IPPP, Durham University
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Outline
Introduction
Particle Physics Simulations
Research in Durham
Conclusions
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Introduction
The main aim of the LHC is to search for new physics by probing higher energies and shorter distances.
When performing calculations of what we’ll see at the LHC can use perturbative calculations due to the property of asymptotic freedom.
This allows us to perform accurate calculations of cross sections and distributions.
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LHC Status
We had all hoped to see collisions at the LHC last year.
Following the “incident” which caused significant damage to many magnets expect to start in late October 2009.
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Introduction
For example the production of the top quark we can calculate the leading (LO)
and next-to-leading (NLO)
order corrections.
In some cases even the next-to-next-to-leading (NNLO) corrections have been calculated.
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Introduction
However these calculations are limited by the number of final state particles, currently the state-of-the-art is 2g4 processes at NLO.
At the LHC typically each interesting event, for example top pair production, will have several hundred final-state particles.
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Tevatron Top Event
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Simulated LHC Event
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Introduction
In order to study the detailed properties of the events we must therefore use a range of techniques to study the physics over a wide range of energy/distance scales
fixed-order perturbative calculations where possible;
approximate perturbative calculations where fixed-order calculations aren’t practical;
non-perturbative models when the couplings are large.
Involves calculations from all areas of phenomenology research.
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Introduction
Naturally leads to the idea of an event generator, a numerical simulation of particle collisions.
In essence these simulations use the Monte Carlo integration technique to perform a high dimensional integral (~3 x number of final-state particles), a Monte Carlo event generator.
Extremely useful as the result is a simulated event with the momenta of the final-state particles which can be directly compared with experimental results.
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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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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.
In these limits cross sections factorize.
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13. Parton Showers This expression is singular as qg0.
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
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Monte Carlo Procedure
Using this approach we can exponentiate the real emission piece.
This gives the Sudakov form factor which is the probability of evolving between two scales and emitting no resolvable radiation.
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Numerical Procedure
Radioactive Decay
Parton Shower
Start with an isotope
Work out when it decays by generating a random number and solving
where t is its lifetime
Generate another random number and use the branching ratios to find the decay mode.
Generate the decay using the masses of the decay products and phase space.
Repeat the process for any unstable decay products.
This algorithm is actually used in Monte Carlo event generators to simulate particle decays.
Start with a parton at a high virtuality, Q, typical of the hard collision.
Work out the scale of the next branching by generating a random number and solving
where q is the scale of the next branching
If there’s no solution for q bigger than the cut-off stop.
Otherwise workout the type of branching.
Generate the momenta of the decay products using the splitting functions.
Repeat the process for the partons produced in the branching.
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Hadronization
We can’t calculate the hadronization process so we use a phenomenological model.
The hadronization model is based on an interesting property of the parton shower.
First split the gluons into quark-antiquark pairs.
Each quark is then uniquely paired with an antiquark in a colour singlet.
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17. Cluster Hadronization Model
The mass spectrum of these colour singlet clusters after gluon splitting is universal.
Called colour pre-confinement.
Assume these clusters are superpositions of the hadron resonances.
Decay according to phase space to hadrons.
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Work in Durham
These simulation projects are large, at least for theoretical physics, projects, with the programs typically several hundred thousand lines long.
There are three major collaborations in the field. Two of which HERWIG and SHERPA are led from Durham.
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Work in Durham
HERWIG
Peter Richardson, Mike Seymour, Bryan Webber, Stefan Gieseke
David Grellscheid, Keith Hamilton
Andrzej Siodmak, Martyn Gigg, Seyi Latunde-Dada, Jonathan Tully, Simon Plaetzer, Manuel Baehr, Luca d’Errico
SHERPA
Frank Krauss
Tanju Gleisberg, Stefan Hoeche, Steffen Schumann, Jan Winter
Frank Siegert, Jennifer Archibald
currently in Durham
previously in Durham
+ one related postdoc Andy Buckley
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Work in Durham
People in Durham are working on a number of different physics projects in this area which are important for the LHC.
Topics include:
Next-to-leading order simulations;
High multiplicity final states;
New physics.
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Hard Jet Radiation
A lot of work recently improving the approximations including more fixed-order perturbative calculations.
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.
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Hard Jet Radiation
Two broad classes of approach
Include the full next-to-leading order calculation
Gets the full fixed order result
Only useful for low multiplicity final-states, i.e. only one additional jet
Use high multiplicity matrix elements
Still a leading-order calculation but can be used for high multiplicity final states, i.e. many additional jets.
Based on original work by Catani, Krauss, Kuhn and Webber (CKKW).
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23. Next-to-leading Order
Herwig++
Herwig++ NLO
Hamilton, PR, Tully JHEP 0810:015,2008
CDF Run I Z pT
D0 Run II Z pT
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24. Leading Order e+e-gjets
Herwig++
SHERPA
Hamilton, PR, Tully arXiv:
Hoeche, Krauss, Schumann, Siegert JHEP 0905:053,2009
Thrust ~ 1
Thrust ~ 1/2
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25. Leading Order qqgZ+jets
SHERPA
Highest pT jet
2nd Highest pT jet
Hoeche, Krauss, Schumann, Siegert JHEP 0905:053,2009
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26. Matrix Element Calculations
For these approaches need to calculate high multiplicity matrix elements.
SHPERA uses recursive techniques, rather than Feynman diagrams, and better phase space integration.
Calculation of higher multiplicty matrix elements with smaller numerical errors.
T.Gleisberg & S.Hoeche,
JHEP 0812 (2008) 039
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BSM Physics
In recent years most of our work in Durham has concentrated on the simulation of Standard Model processes.
These will be things we see first and are the backgrounds for any new physics at the LHC.
However we are still involved in many studies of new physics for the LHC.
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BSM Physics
Example from recent work by G Moortgat-Pick, J Ellis, F Moortgat, K Rolbiecki, J Smillie, J Tattersall.
Looking at triple products of momenta
which are sensitive to CP violation using Herwig++ and analytic calculations
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BSM Physics
Look at the decay
e- near
e- far
q*L
e*R Z* g* q
e- near
e+ far
e+ near
e+ far
Herwig++ compared to hep-ph/ Smillie and Webber
Gigg, Richardson Eur.Phys.J.C51: ,2007
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Black Holes
Original generator C.M. Harris, PR, B.R. Webber JHEP 0308:033,2003.
Subsequent experimental analysis C.M. Harris, M.J. Palmer, M.A. Parker, PR, A. Sabetfakhri, B.R. Webber JHEP 0505:053,2005
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Conclusions
Simulations in particle physics are important for all experimental analysis.
This is an area where the IPPP now plays the world leading role.
We are working on simulations of many things which are important both for early LHC data and later analyses.
This work will enable the IPPP to play in major role in the LHC programme.
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