Simulating Physics at the LHC

1. Simulating Physics at the LHC Peter Richardson IPPP, Durham University Department Research Event 29th May

2. Outline • Introduction • Particle Physics Simulations • Research in Durham • Conclusions Department Research Event 29th May

3. 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. Department Research Event 29th May

4. 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. Department Research Event 29th May

5. 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. Department Research Event 29th May

6. 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. Department Research Event 29th May

7. Tevatron Top Event Department Research Event 29th May

8. Simulated LHC Event Department Research Event 29th May

9. 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. Department Research Event 29th May

10. 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. Department Research Event 29th May

11. 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. Department Research Event 29th May

12. 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. Department Research Event 29th May

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 Department Research Event 29th May

14. Monte Carlo Procedure • Using this approach we can exponentiate the real emission piece. • This gives the Sudakov form factorwhich is the probability of evolving between two scales and emitting no resolvable radiation. Department Research Event 29th May

15. 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. Numerical Procedure Parton Shower Radioactive Decay Department Research Event 29th May

16. 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. Department Research Event 29th May

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. Department Research Event 29th May

18. 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. Department Research Event 29th May

19. 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 Work in Durham currently in Durham previously in Durham + one related postdoc Andy Buckley Department Research Event 29th May

20. 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. Department Research Event 29th May

21. 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. Department Research Event 29th May

22. 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). Department Research Event 29th May

23. Next-to-leading Order Herwig++ Herwig++ NLO MC@NLO Hamilton, PR, Tully JHEP 0810:015,2008 CDF Run I Z pT D0 Run II Z pT Department Research Event 29th May

24. Leading Order e+e-gjets Herwig++ SHERPA Hamilton, PR, Tully arXiv:0905.3072 Hoeche, Krauss, Schumann, Siegert JHEP 0905:053,2009 Thrust ~ 1/2 Thrust ~ 1 Department Research Event 29th May

25. Leading Order qqgZ+jets SHERPA Highest pT jet 2nd Highest pT jet Hoeche, Krauss, Schumann, Siegert JHEP 0905:053,2009 Department Research Event 29th May

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 Department Research Event 29th May

27. 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. Department Research Event 29th May

28. 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 Department Research Event 29th May

29. q e- near q*L Z* e+ far e*R g* BSM Physics Look at the decay e- near e- far e+ near e+ far Herwig++ compared to hep-ph/0507170 Smillie and Webber Gigg, Richardson Eur.Phys.J.C51:989-1008,2007 Department Research Event 29th May

30. 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 Department Research Event 29th May

31. 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. Department Research Event 29th May