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LHC Phenomenology

LHC Phenomenology. Peter Richardson IPPP, Durham University. Summary. Introduction Example: Drell Yan Other Processes Conclusion. Introduction. LHC phenomenology is a very broad topic.

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LHC Phenomenology

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  1. LHC Phenomenology Peter Richardson IPPP, Durham University UCL 30th March

  2. Summary • Introduction • Example: Drell Yan • Other Processes • Conclusion UCL 30th March

  3. Introduction • LHC phenomenology is a very broad topic. • I could have chosen to talk about just about anything from underlying event physics to black hole production. • Given we will hopefully start seeing 7 TeV collisions today I’ll concentrate on: • Standard Model physics; • Theoretical Calculations; • Monte Carlo simulations. UCL 30th March

  4. Standard Model Physics • While 7 TeV isn’t the 14 or even 10 TeV we were hoping for the cross sections for many important Standard Model processes, e.g. • W/Z production, • top production, • High pT jet production, are significantly higher than those at the Tevatron. Taken from Rept.Prog.Phys.70:89,2007 Campbell, Huston, Stirling UCL 30th March

  5. Theoretical Tools • There are three main theoretical approaches used to study hadron collider phenomenology: • Fixed order perturbation theory Calculate relatively inclusive quantities at a given order in the perturbative expansion. • Resummation techniques Take into account the most important terms in the perturbative expansion to all orders, analytically still for fairly inclusive quantities, or in • Monte Carlo Simulations Combine resummation techniques and hadronization models to give an exclusive simulation of events. UCL 30th March

  6. 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. UCL 30th March

  7. Example: Drell-Yan • I won’t talk about the different techniques in an abstract way. • Instead I’ll talk about the recent progress in the various approaches for the production of electroweak vector bosons. • This is a very important process at the LHC for both searches for new physics and as the background to many BSM signals. UCL 30th March

  8. Fixed Order Calculations • In recent years there has been a lot of progress in calculating the next-to-leading, and in some cases even the next-to-next-to-leading, order corrections, e.g. e+e-g3 jets: • LO Ellis, Gallard, Ross 1974 • NLO Ellis, Ross, Terrano 1980 • NNLOGehrmann-De Ridder, Gehrmann, Glover, Heinrich 2007. • Calculating NNLO corrections is still extremely challanging in hadron collisions, only Drell-Yan and gggH are known. UCL 30th March

  9. Fixed Order Calculations • The NLO cross section is putting all the pieces together the answer is finite. • Problem at NLO is calculating loop diagrams with more external particles. • At NNLO its putting everything together. UCL 30th March

  10. NNLO Drell-Yan Taken from Anastasiou, Dixon, Melnikov, Petriello, Phys.Rev.D69:094008,2004 UCL 30th March

  11. PDF Uncertainties Taken from Martin, Stirling, Thorne, Watt Eur.Phys.J.C63:189-285,2009. UCL 30th March

  12. Weak Corrections • Normally we only worry about the strong corrections to processes. • However if we are doing NNLO calculations its possible the NLO electromagnetic and weak corrections are comparable. Taken from Baur Phys.Rev.D75:013005,2007 UCL 30th March

  13. Fixed Order Calculations • However there have been a number of breakthroughs in calculating processes at NLO with higher jet multiplicities. • V+0 jets 1978 • V+1 jet 1981 • V+2 jets 2002 • V+3 jets 2009 • This is becoming more and more automated so there will be many more results for high multiplicity jet cross sections in the near future. UCL 30th March

  14. W+jets Cross Sections Taken from Berger et. al. Phys.Rev.D80:074036,2009 UCL 30th March

  15. W+jets Cross Sections Taken from Berger et. al. Phys.Rev.D80:074036,2009 UCL 30th March

  16. Simulations • At the same time the Monte Carlo simulations of hadron collisions have become more and more sophisticated. • After early improvements to describe one additional hard jet a number of approaches are now available: • NLO to improve the overall normalisation and description of the hardest jet in the event; • Leading order to matrix elements with higher multiplicities to improve the simulation of events with many hard jets. UCL 30th March

  17. NLO Simulations • NLO simulations rearrange the NLO cross section formula. • Either choose C to be the shower approximation MC@NLO (Frixione, Webber) UCL 30th March

  18. NLO Simulations • Or a more complex arrangement POWHEG(Nason) where • Looks more complicated but has the advantage that it is independent of the shower and only generates positive weights. UCL 30th March

  19. Improved simulations of Drell-Yan Herwig++ POWHEG MC@NLO CDF Run I Z pT D0 Run II Z pT JHEP 0810:015,2008 Hamilton, PR, Tully CERN 29th March

  20. Resummed Calculations • Monte Carlo simulations only resum the leading QCD logarithms with some approximate treatment of some sub-leading effects. • For inclusive observables it is possible to calculate the next-to-leading logarithms. Taken from Papaefstathiou, Smillie, Webber, arXiv:1002.4375 UCL 30th March

  21. 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. • The most sophisticated approaches are variants of the CKKW method (Catani, Krauss, Kuhn and Webber JHEP 0111:063,2001) • Recent new approaches in SHERPA( Hoeche, Krauss, Schumann, Siegert, JHEP 0905:053,2009) and Herwig++(JHEP 0911:038,2009 Hamilton, PR, Tully) UCL 30th March

  22. CKKW Procedure • Catani, Krauss, Kuhn and Webber JHEP 0111:063,2001. • In order to match the ME and PS we need to separate the phase space: • one region contains the soft/collinear region and is filled by the PS; • the other is filled by the matrix element. • In these approaches the phase space is separated using in kT-type jet algorithm. Cambridge 2nd Feb

  23. CKKW Procedure • Catani, Krauss, Kuhn and Webber JHEP 0111:063,2001. • In order to match the ME and PS we need to separate the phase space: • one region contains the soft/collinear region and is filled by the PS; • the other is filled by the matrix element. • In these approaches the phase space is separated using in kT-type jet algorithm. Cambridge 2nd Feb

  24. CKKW Procedure • Radiation above a cut-off value of the jet measure is simulated by the matrix element and radiation below the cut-off by the parton shower. • Select the jet multiplicity with probability where is the n-jet matrix element evaluated at resolution using as the scale for the PDFs and aS, n is the number of jets • Distribute the jet momenta according the ME. Cambridge 2nd Feb

  25. CKKW Procedure • Cluster the partons to determine the values at which 1,2,..n-jets are resolved. These give the nodal scales for a tree diagram. • Apply a coupling constant reweighting. Cambridge 2nd Feb

  26. CKKW Procedure • Reweight the lines by a Sudakov factor • Accept the configuration if the product of the aS and Sudakov weight is less than otherwise return to step 1. Cambridge 2nd Feb

  27. CKKW Procedure • Generate the parton shower from the event starting the evolution of each parton at the scale at which it was created and vetoing emission above the scale . Recent improvements use an idea from POWHEG to simulate soft radiation from the internal lines giving improved results. Cambridge 2nd Feb

  28. Jet Multiplicity in Z+jets at the Tevatron Herwig++ compared to data from CDF Phys.Rev.Lett.100:102001,2008 UCL 30th March

  29. pT of the Z in Z+jets at the Tevatron Herwig++ compared to data from D0 Phys.Rev.Lett.100:102002,2008 UCL 30th March

  30. pT of jets in Z+jets at the Tevatron Herwig++ compared to data from CDF Phys.Rev.Lett.100:102001,2008 CERN 29th March

  31. pT of jets in W+jets at the Tevatron All Jets 3rd Hardest Jet Herwig++ compared to data from CDF Phys.Rev.D77:011108,2008 UCL 30th March

  32. Drell-Yan • So everything looks very good. We have a range of techniques to describe various different properties of vector boson production. • However further work is still needed in order to put all the tools together to study the phenomenology and compare with experimental results. UCL 30th March

  33. Other Processes • Unfortunately Drell-Yam is the one process for which we know the: • NNLO cross section; • the NLO +1,2,3-jet cross sections; • and for which combining fixed order calculations and Monte Carlo simulations is easiest and best tested. • For many other processes the accuracy of the theoretical calculations and simulations isn’t as good. UCL 30th March

  34. Top Quark Production • The physics of top quark production is interesting in both its own right and as a major background in many new physics models. • The next-to-leading order calculation and its combination with the shower has been available for some time. • However while we believe we understand QCD radiation top quark event. UCL 30th March

  35. MC@NLO HERWIG NLO Top Production at the LHC S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/0305252. UCL 30th March

  36. Top Quark Production Taken from Frixione, Nason, Ridolfi JHEP 0709:126,2007. UCL 30th March

  37. Top Quark Mass • The issue of the top quark mass has attracted a lot attention as the experimental uncertainty has reduced 171.3 ±1.1± 1.2 GeV (PDG). • Question is what is this mass? • Pole Mass? • Mass is a given renormalisation scheme? • PMASS(6,1) parameter of PYTHIA? • Almost certainly the PYTHIA parameter. • How does this relate to the mass in a well defined scheme, probably a potential subtracted mass but the exact scheme is undefined. UCL 30th March

  38. Jets • Inclusive jet production is important for the: • measurement of aS; • measurement of the parton distribution functions; • search for new physics, e.g. compositeness. • The NLO corrections to di-jet production (early 1990s)and 3-jet production (late 1990’s) are known. • The NNLO matrix elements are all known still need to put them together with the real pieces to calculate the cross section. • However still only leading-order Monte Carlo simulations and matching to hard emissions is very complicated. UCL 30th March

  39. Conclusions • Even in the Standard Model there’s a lot of interesting phenomenology to study at the LHC. • We will need many experimental analyses and theoretical calculations before we can hope to understand all the Standard Model processes. • It’s important to measure Standard Model parameters and make sure we understand the backgrounds to potential new physics signals. • We’ve all been waiting for the LHC to take data for a long time in the near future we will finally be able to test our predictions against data. UCL 30th March

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