UCL 30 th March1 LHC Phenomenology Peter Richardson IPPP, Durham University

Summary Introduction Example: Drell Yan Other Processes Conclusion UCL 30 th March2

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 Ill concentrate on: –Standard Model physics; –Theoretical Calculations; –Monte Carlo simulations. UCL 30 th March3

Standard Model Physics While 7 TeV isnt 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 p T jet production, are significantly higher than those at the Tevatron. UCL 30 th March4 Taken from Rept.Prog.Phys.70:89,2007 Campbell, Huston, Stirling

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 30 th March5

6 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.

Example: Drell-Yan I wont talk about the different techniques in an abstract way. Instead Ill 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 30 th March7

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 - 3 jets: –LO Ellis, Gallard, Ross 1974 –NLO Ellis, Ross, Terrano 1980 –NNLO Gehrmann-De Ridder, Gehrmann, Glover, Heinrich Calculating NNLO corrections is still extremely challanging in hadron collisions, only Drell-Yan and gg H are known. UCL 30 th March8

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 30 th March9

NNLO Drell-Yan UCL 30 th March10 Taken from Anastasiou, Dixon, Melnikov, Petriello, Phys.Rev.D69:094008,2004

PDF Uncertainties UCL 30 th March11 Taken from Martin, Stirling, Thorne, Watt Eur.Phys.J.C63: ,2009.

Weak Corrections UCL 30 th March12 Taken from Baur Phys.Rev.D75:013005,2007 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.

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 jets2002 –V+3 jets2009 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 30 th March13

W+jets Cross Sections UCL 30 th March14 Taken from Berger et. al. Phys.Rev.D80:074036,2009

W+jets Cross Sections UCL 30 th March15 Taken from Berger et. al. Phys.Rev.D80:074036,2009

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 30 th March16

NLO Simulations NLO simulations rearrange the NLO cross section formula. Either choose C to be the shower approximation (Frixione, Webber) UCL 30 th March17

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 30 th March18

CERN 29 th March19 Improved simulations of Drell- Yan CDF Run I Z p T D0 Run II Z p T Herwig++ POWHEG JHEP 0810:015,2008 Hamilton, PR, Tully

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. UCL 30 th March20 Taken from Papaefstathiou, Smillie, Webber, arXiv:

UCL 30 th March21 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 )

Cambridge 2 nd Feb22 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 k T -type jet algorithm.

Cambridge 2 nd Feb23 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 k T -type jet algorithm.

Cambridge 2 nd Feb24 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. 1)Select the jet multiplicity with probability where is the n-jet matrix element evaluated at resolution using as the scale for the PDFs and S, n is the number of jets 2)Distribute the jet momenta according the ME.

Cambridge 2 nd Feb25 CKKW Procedure 3)Cluster the partons to determine the values at which 1,2,..n-jets are resolved. These give the nodal scales for a tree diagram. 4)Apply a coupling constant reweighting.

Cambridge 2 nd Feb26 CKKW Procedure 5)Reweight the lines by a Sudakov factor 6)Accept the configuration if the product of the S and Sudakov weight is less than otherwise return to step 1.

Cambridge 2 nd Feb27 CKKW Procedure 7)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.

Jet Multiplicity in Z+jets at the Tevatron UCL 30 th March28 Herwig++ compared to data from CDF Phys.Rev.Lett.100:102001,2008

p T of the Z in Z+jets at the Tevatron UCL 30 th March29 Herwig++ compared to data from D0 Phys.Rev.Lett.100:102002,2008

p T of jets in Z+jets at the Tevatron CERN 29 th March30 Herwig++ compared to data from CDF Phys.Rev.Lett.100:102001,2008

p T of jets in W+jets at the Tevatron UCL 30 th March31 Herwig++ compared to data from CDF Phys.Rev.D77:011108,2008 All Jets 3 rd Hardest Jet

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 30 th March32

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 isnt as good. UCL 30 th March33

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 30 th March34

UCL 30 th March35 Top Production at the LHC S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/ HERWIG NLO

Top Quark Production UCL 30 th March36 Taken from Frixione, Nason, Ridolfi JHEP 0709:126,2007.

Top Quark Mass The issue of the top quark mass has attracted a lot attention as the experimental uncertainty has reduced ±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 30 th March37

Jets Inclusive jet production is important for the: –measurement of S ; –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 1990s) 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 30 th March38

Conclusions Even in the Standard Model theres 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. Its important to measure Standard Model parameters and make sure we understand the backgrounds to potential new physics signals. Weve 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 30 th March39