QM 3 rd April1 Collider Phenomenology Peter Richardson IPPP, Durham University

Summary Introduction Fixed Order Calculations Monte Carlo Simulations Matching Conclusions QM 3 rd April2

Introduction LHC phenomenology is a very broad topic. I could have chosen to talk about just about anything from underlying event physics to SUSY or black hole production. Given that, with the exception of the Higgs boson, there’s no sign of a significant excess in any of the myriad of BSM searches I’ll concentrate on the Standard Model. QM 3 rd April3

Introduction In particular I’ll mainly discuss QCD phenomenology as this is fundamental to all measurements at the LHC. I’ll try and focus on: –Theoretical Calculations; –Monte Carlo simulations; –New techniques. QM 3 rd April4

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. QM 3 rd April5

Fixed Order Calculations The calculation of leading-order cross sections, including very large multiplicities in the final state, has been automated for some time, e.g. MADGRAPH, HELAC- PHEGAS, ALPGEN, SHERPA, CompHep, COMIX,... However in order to get a reliable calculation of the cross section, and in some cases the shape we need (at least) next-to-leading order (NLO) calculations. QM 3 rd April6

NLO Calculations The NLO cross section is putting all the pieces together the answer is finite. We know how to compute the subtraction terms but it becomes more computational intensive for higher multiplicities. Problem at NLO is calculating loop diagrams with more external particles. QM 3 rd April7

NLO Subtraction We understand the (universal) infrared behavior of amplitudes. Allows the construction of subtraction counter terms, Dipole (Catani, Seymour), Antenna (Kosower), FKW (Frixione, Kunszt, Signer) The contribution from real radiation can now be automatically calculated using subtraction techniques for tree-level matrix elements, SHERPA, MadDipole, Helac/Phegas, MadFKS. QM 3 rd April8

NLO Virtual Corrections In principle the loop integrals involved in loop processes with many external particles can be expressed in terms of 4-1 point functions New unitarity based techniques have lead to a revolution in the calculation of these diagrams. Previously 2  3 was state of the art now some 8 point calculations. QM 3 rd April9

Fixed Order Calculations These breakthroughs in calculating processes at NLO mean we can calculate processes with higher jet multiplicities. –V+0 jets 1978 –V+1 jet 1981 –V+2 jets2002 –V+3 jets2009 –V+4 jets2011 More and more automated so there will be many more results for high multiplicity jet cross sections in the near future. QM 3 rd April10

A Selection of recent calculations pp  4 jets Bern et. al. (2011) pp  Z+4 jets Bern et. al. (2011) (leading colour) pp  W+4 jets Bern et. al. (2011) (leading colour) pp  W+2 jets Melia et. al. (2010), Greiner et. al. (2012) pp  ttbb Denner, et.al. (2010) pp  tt+2 jets Bevilacqua, et. al. (2011) … Based on Daniel de Florian’s DIS talk. QM 3 rd April11

W+jets Cross Sections QM 3 rd April12 Taken from Berger et. al. Phys.Rev.D80:074036,2009

W+jets Cross Sections QM 3 rd April13 Taken from Berger et. al. Phys.Rev.D80:074036,2009

W and Z + Jets Results QM 3 rd April14

pp  4 jets QM 3 rd April15 Taken from Bern et. al. arXiv:

Fixed Order Calculations Progress in calculating the next-to-next-to- leading, order corrections is slower, 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. QM 3 rd April16

NNLO Drell-Yan QM 3 rd April17 Taken from Anastasiou, Dixon, Melnikov, Petriello, Phys.Rev.D69:094008,2004

NNLO Bottlenecks Many more combinations of singularities which must be cancelled. Working out a subtraction scheme is much harder even though we know the universal infrared limits. QM 3 rd April18 2 loop 1 loop +real Double Real

NNLO Bottlenecks For general processes antenna subtraction seems to be the most promising and progress is being made on the calculation of jet production at NNLO. For colour singlet systems a simpler subtraction method has allowed the calculation of: –pp  WH Ferrera, Grazzini, Tramontano (2011); –pp   Catani, Cieri, deFlorian, Ferrera, Grazzini (2011). QM 3 rd April19

PDF Uncertainties QM 3 rd April20 Taken from Martin, Stirling, Thorne, Watt Eur.Phys.J.C63: ,2009.

Weak Corrections QM 3 rd April21 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.

QM 3 rd April22 Monte Carlo Simulations 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.

Simulations 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. QM 3 rd April23

NLO Simulations NLO simulations rearrange the NLO cross section formula. Either choose C to be the shower approximation (Frixione, Webber) QM 3 rd April24

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. QM 3 rd April25

QM 3 rd April26 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

Z p T at the LHC QM 3 rd April27

An alternative to the p T QM 3 rd April28 D0 Phys.Rev.Lett.106:122001,2011

W+jets Until recently limited to relatively simple Born processes. Now automated, SHERPA, POWHEGBox. Many more results for more complicated processes. QM 3 rd April29

Different Approaches The two approaches are the same to NLO. Differ in the subleading terms. In particular at large p T QM 3 rd April30 POWHEG JHEP 0904:002,2009 Alioli et. al.

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. QM 3 rd April31 Taken from Papaefstathiou, Smillie, Webber, arXiv:

QM 3 rd April32 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 )

QM 3 rd April33 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.

QM 3 rd April34 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.

QM 3 rd April35 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.

QM 3 rd April36 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.

QM 3 rd April37 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.

QM 3 rd April38 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 W+jets QM 3 rd April39

MELOPS QM 3 rd May40 Combines the POWHEG approach for the total cross section and 1 st emission together with CKKW for higher emissions Hamilton, Nason JHEP06 (2010) 039, Krauss et. al. arXiv:

MENLOPS QM 3 rd May41

Other Processes Unfortunately Drell-Yam is the one process for which we know the: –NNLO cross section; –the NLO +1,2,3,4-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. QM 3 rd April42

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 until recently no measurements. QM 3 rd April43

QM 3 rd April44 Top Production at the LHC S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/ HERWIG NLO

Top Quark Production QM 3 rd April45 Taken from Frixione, Nason, Ridolfi JHEP 0709:126,2007.

Top Quark Production with jet veto QM 3rd April46 ATLAS arXiv:

Rivet QM 3rd April47 The Rivet package has made comparing theoretical calculations and results much easier.

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 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. Recently the first NLO simulations of these processes. QM 3 rd April48

Jet Production QM 3 rd April49

Jet Substructure QM 3 rd April50 ATLAS arXiv:

Conclusions Even in the Standard Model there’s a lot of interesting phenomenology to study at the LHC. We have a lot better theoretical calculations and simulations due recent phenomenological progress. So far very good agreement been theory and experiment, remains to be seen whether this continues as statistical and systematic errors reduce. QM 3 rd April51