UCL 30th March 1

LHC Phenomenolog

yPeter Richardson

IPPP, Durham University

Summary• Introduction• Example: Drell Yan• Other Processes• Conclusion

UCL 30th March 2

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 3

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.

UCL 30th March 4

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 techniquesTake into account the most important terms in the perturbative expansion to all orders, analytically still for fairly inclusive quantities, or in

– Monte Carlo SimulationsCombine resummation techniques and hadronization models to give an exclusive simulation of events.

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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 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 7

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 2007.

• Calculating NNLO corrections is still extremely challanging in hadron collisions, only Drell-Yan and ggH are known.UCL 30th March 8

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.

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( ) ( ( ) ( , ) )

( ( , ) ( , ))

v r v

v r

d B v d V v C v r d d

R v r C v r d d

NNLO Drell-Yan

UCL 30th March 10

Taken from Anastasiou, Dixon, Melnikov, Petriello, Phys.Rev.D69:094008,2004

PDF Uncertainties

UCL 30th March 11

Taken from Martin, Stirling, Thorne, Watt Eur.Phys.J.C63:189-285,2009.

Weak Corrections

UCL 30th March 12

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 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.

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W+jets Cross Sections

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Taken from Berger et. al. Phys.Rev.D80:074036,2009

W+jets Cross Sections

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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.

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NLO Simulations• NLO simulations

rearrange the NLO cross section formula.

• Either choose C to be the shower approximation

MC@NLO (Frixione, Webber)

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shower

shower

( ) ( ( ) ( , ) )

( ( , ) ( , ))

v r v

v r

d B v d V v C v r d d

R v r C v r d d

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.

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CERN 29th March 19

Improved simulations of Drell-Yan

CDF Run I Z pT D0 Run II Z pT

Herwig++

POWHEG

MC@NLO

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 30th March 20

Taken from Papaefstathiou, Smillie, Webber, arXiv:1002.4375

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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 2nd Feb 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.

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.

N

kk

nnP

0

n

inid inid

Cambridge 2nd Feb 25

CKKW Procedure3) 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.

1)(

)()...()(

ini

321 n

S

SSS

d

ddd

Cambridge 2nd Feb 26

CKKW Procedure5) 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.

),(

),(

ini

ini

k

j

dd

dd

]1,0[R

Cambridge 2nd Feb 27

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.

inid

Jet Multiplicity in Z+jets at the Tevatron

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Herwig++ compared to data from CDF Phys.Rev.Lett.100:102001,2008

pT of the Z in Z+jets at the Tevatron

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Herwig++ compared to data from D0 Phys.Rev.Lett.100:102002,2008

pT of jets in Z+jets at the Tevatron

CERN 29th March 30

Herwig++ compared to data from CDF Phys.Rev.Lett.100:102001,2008

pT of jets in W+jets at the Tevatron

UCL 30th March 31

Herwig++ compared to data from CDF Phys.Rev.D77:011108,2008

All Jets3rd 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.

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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 33

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.

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Top Production at the LHC

S. Frixione, P. Nason and B.R. Webber, JHEP 0308(2003) 007, hep-ph/0305252.

MC@NLO

HERWIG

NLO

Top Quark Production

UCL 30th March 36

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 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.

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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.

• However still only leading-order Monte Carlo simulations and matching to hard emissions is very complicated.

UCL 30th March 38

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 39