1. Event generators for the LHC
Mike Seymour
University of Manchester
LNF Spring Institute
16th May 2012, Frascati

2. Event Generators “Current” general purpose event generators:
Pythia8
Herwig++
Sherpa
“Legacy” support for previous generation:
Pythia6
HERWIG(+Jimmy)
Many specialized codes
Powheg
VINCIA, Ariadne, HEJ, Cascade, PhoJet, …
LNF

3. Related programs Matrix element tools Secondary decay packages
Madgraph, ALPGEN, HELAC, CompHEP, …
SanC, Grace, …
MCFM, NLOJET++, BlackHat, Rocket, …
PowHEG Box, …
Secondary decay packages
TAUOLA, PHOTOS, EvtGen, …
Validation/tuning/visualization tools
Rivet, Professor, mcplots
LNF

4. Structure of LHC Events
Hard process
Parton shower
Hadronization
Underlying event
Unstable particle decays
LNF

5. Introduction to Parton Showers
QED: accelerated charges radiate.
QCD identical: accelerated colours radiate.
gluons also charged.
 cascade of partons.
= parton shower.
QCD emission matrix elements diverge
The collinear limit
The soft limit
Hard scattering
LNF

6. QCD emission matrix elements diverge
e.g. e+e–  3 partons:
Divergent in collinear limit   0, (for massless quarks)
and soft limit zg  0
e+e–  2 partons
“quark charge squared”
QCD running coupling ~ 0.1
Eg/Eg,max
LNF

7. Collinear Limit Universal:
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi splitting kernel: dependent on flavour and spin
LNF

8. Multiple Collinear Emission
Formulated as evolution in
opening angle 2
virtuality q2 ~ z(1–z)E2 2
transverse momentum k2 ~ z2(1–z)2E2 2
Sums leading logarithms (slog(Q/Q0))n to all orders
where Q0 is parton resolution criterion i.e. infrared cutoff
“Leading log parton shower algorithm”
LNF

9. Soft limit Also universal. But at amplitude level…
soft gluon comes from everywhere in event.
Quantum interference.
Spoils independent evolution picture?
LNF

10. Angular ordering
NO:
outside angular ordered cones, soft gluons sum coherently: only see colour charge of whole jet.
Soft gluon effects fully incorporated by using as evolution variable: angular ordering
First gluon not necessarily hardest!
LNF

11. Hard Scattering Sets up initial conditions for parton showers.
Colour coherence important here too.
Emission from each parton confined to cone stretching to its colour partner
Essential to fit Tevatron data…
LNF

12. Distributions of third-hardest jet in multi-jet events
LNF

13. Distributions of third-hardest jet in multi-jet events
HERWIG has complete treatment of colour coherence,
PYTHIA+ has partial
LNF

14. Parton showers Crucial role of colour structure of hard process
e.g. qq~->qq~
Corrections suppressed by ~1/Nc2 interjet region
shouldn’t we worry about them too?
LNF

15. New approaches
HEJ (Andersson & Smillie) resums rapidity-enhanced (i.e. small-x) terms
Can be combined with dipole shower (+Lönnblad)
LNF

16. New approaches
HEJ (Andersson & Smillie) resums rapidity-enhanced (i.e. small-x) terms
important for Higgs production [Andersen, Campbell & Höche, arXiv: ]
mean no. of jets as a function of rapidity distribution between most forward and most backward
c.f. VBF cuts/rapidity veto
LNF

17. Hard process generation
Tree-level matrix element automation: a solved problem
But efficiency improvements and generalizations always being made
Matching to parton showers without double-counting
MLM built in to Madgraph, Alpgen
CKKW-L automated in Sherpa, Herwig++
Crucial role of colour structure
Large Nc description good enough for precision physics?
FeynRules
Towards automated loop calculation
LNF

18. NLO hard process generation
How to combine NLO calculation with parton shower without double-counting real emission?
Solved by method:
Carefully extract analytical expression for parton shower emission
Use it as subtraction term for NLO calculation
Gives finite (but not positive definite) weights for “real” and “virtual” phase space points
LNF

19.
Available for a wide variety of processes and very successfully used
But…
Negative weights
Tied to a specific event generator algorithm
Inclusively corrects an emission to the next-order tree level matrix element (not necessarily hardest)
Is not able to correct major deficiencies in hard emission distribution of parton shower
LNF

20.
Is not able to correct major deficiencies in hard emission distribution of parton shower
Alioli, Nason, Oleari & Re, ggH, JHEP 0904(2009)002
LNF

21. MC@NLO Is guaranteed to reproduce next-order tree-level matrix element
Alioli, Nason, Oleari & Re, ggH, JHEP 0904(2009)002
LNF

22. MC@NLO Is guaranteed to reproduce next-order tree-level matrix element
Alioli, Nason, Oleari & Re, ggH, JHEP 0904(2009)002
LNF

23. POWHEG Born configurations with NLO weight
Nason, JHEP 0411 (2004) 040
Born configurations with NLO weight
Hardest emission: exponentiated tree level ME
(Almost always) positive weight
Independent of shower algorithm
Hardest emission always given by ME
times inclusive K factor
LNF

24. Truncated shower Self-consistent implementation requires either
shower is kt ordered (so POWHEG emission would have been first anyway)
or truncated shower is added (giving emission off internal lines ‘before’ hardest one)
Herwig++ status:
Working implementation for internal Powheg processes
General implementation exists in principle but not released
LNF

25. POWHEGs POWHEG method has become the method of choice in Herwig++
pp → γ/W/Z/H/WH/ZH/WW/WZ/ZZ
DIS, pp → VBF → Hjj
POWHEG BOX ( Alioli, Hamilton, Nason, Oleari and Re) is a standalone implementation for even more processes, incl.
pp → dijets, ttbar
LNF

26. MENLOPS
Hamilton & Nason, JHEP 1006 (2010) 039
Höche et al, JHEP 1104 (2011) 024
Giele, Kosower & Skands, Vincia…
Combines multi-jet matching with NLO matrix elements normalization from lowest-multiplicity cross section
Step towards NLO multi-jet matching
LNF

27. Structure of LHC Events
Hard process
Parton shower
Hadronization
Underlying event
Unstable particle decays
LNF

28. Confinement
Asymptotic freedom: becomes increasingly QED-like at short distances.
QED:
but at long distances, gluon self-interaction makes field lines attract each other:
QCD:
linear potential  confinement + + – –
LNF

29. Interquark potential Can measure from quarkonia spectra:
or from lattice QCD:
 String tension
LNF

30. The Lund String Model Start by ignoring gluon radiation:
annihilation = pointlike source of pairs
Intense chromomagnetic field within string  pairs created by tunnelling. Analogy with QED:
Expanding string breaks into mesons long before yo-yo point.
LNF

31. Three-jet Events
So far: string model = motivated, constrained independent fragmentation!
New feature: universal
Gluon = kink on string  the string effect
Infrared safe matching with parton shower: gluons with
inverse string width irrelevant.
LNF

32. Preconfinement Planar approximation: gluon = colour—anticolour pair.
Follow colour structure of parton shower: colour-singlet pairs end up close in phase space
Mass spectrum of colour-singlet pairs asymptotically independent of energy, production mechanism, …
Peaked at low mass
LNF

33. Cluster mass distribution
Independent of shower scale Q
depends on Q0 and 
LNF

34. The Cluster Model
Project colour singlets onto continuum of high-mass mesonic resonances (=clusters). Decay to lighter well-known resonances and stable hadrons.
Assume spin information washed out:
decay = pure phase space.
 heavier hadrons suppressed
baryon & strangeness suppression ‘for free’ (i.e. untuneable).
Hadron-level properties fully determined by cluster mass spectrum, i.e. by perturbative parameters.
crucial parameter of model.
LNF

35. Hadronization Basic string and cluster models ~ unchanged in 25 years
Many small improvements motivated by deeper understanding/better data
e.g. baryon production models
Pythia 8: BSM hadronization scenarios
R-hadrons (confined long-lived spartons)
Hidden sector hadronization
LNF

36. Torbjörn Sjöstrand
LNF

37. Torbjörn Sjöstrand
LNF

38. Structure of LHC Events
Hard process
Parton shower
Hadronization
Underlying event
Unstable particle decays
LNF

39. Secondary particle decays
Previous generations typically used external packages, e.g. TAUOLA, PHOTOS, EVTGEN
Sherpa & Herwig++ contain at least as complete a description in all areas…
without interfacing issues (c.f. τ spin)
LNF

40. Tau Decays
Mass spectrum of pp in tgppnt for various models and example of mass distribution in tg5pnt comparing Herwig++ and TAUOLA.
LNF

41. LNF

42. DgKpp
Comparison of Herwig++ and EvtGen implementations of the fit of Phys. Rev. D63 (2001) (CLEO).
LNF

43. LNF

44. Structure of LHC Events
Hard process
Parton shower
Hadronization
Underlying event
Unstable particle decays
LNF

45. The Basics: event classes
‘Soft inclusive’ events and the underlying event
How similar are they?
Fluctuations and correlations play crucial role
LNF

46. The Basics: Multiparton Interaction Model
For small pt min and high energy inclusive parton—parton cross section is larger than total proton—proton cross section.
LNF

47. The Basics: Multiparton Interaction Model
For small pt min and high energy inclusive parton—parton cross section is larger than total proton—proton cross section.
More than one parton—parton scatter per proton—proton
Need a model of spatial distribution within proton
 Perturbation theory gives you n-scatter distributions
Sjöstrand, van Zijl, Phys. Rev. D36 (1987) 2019
LNF

48. Matter Distributions Usually assume x and b factorize ( see later)
and n-parton distributions are independent ( see soon)
 scatters Poissonian at fixed impact parameter
LNF

49. Colour correlations Can have a big influence on final states
 see later
LNF

50. Herwig++ colour reconnection model
Röhr, Siodmok and Gieseke have implemented a new model based on momentum structure
Refit LEP-I and LEP-II data
Conclusion: hadronization parameters correlated with reconnection probability, but good fit can be obtained for any value of preco
LNF

51. LNF

52. Parameter tuning Procedure:
fix parton shower and hadronization parameters to LEP data, as a function of colour reconnection preco
choose a total cross section and elastic slope parameter  Asoft,inc(b) and σtot,inc
fit Ahard,inc(b), pt,min ( σhard,inc and σsoft,inc) and preco to minimum bias and underlying event data
LNF

53. Colour reconnection model/MPI tuning
LNF

54. Underlying event at 900 GeV
LNF

55. Underlying event at 1800 GeV
LNF

56. Underlying event at 7000 GeV
LNF

57. x-dependent matter distributions
Most existing models use factorization of x and b
or (Herwig++) crude separation into hard and soft components (simple hot-spot model)
R.Corke and T.Sjöstrand, arXiv: consider Gaussian matter distribution with width
LNF

58. x-dependent matter distributions
Most existing models use factorization of x and b
or (Herwig++) crude separation into hard and soft components (simple hot-spot model)
R.Corke and T.Sjöstrand, arXiv: consider Gaussian matter distribution with width
for a10.15, matter distribution can be E-indep
LNF

59. x-dependent matter distributions
(My) conclusion: for soft inclusive and jet underlying event data compatible with data but not required, but sheds interesting light on energy dependence
Interesting correlation with hardness of hard scatter, e.g. less underlying event in 1 TeV Z’ events than in Z events
LNF

60. Conclusions on UE/MB
Despite ~25 year history, multi-parton interaction models are still in their infancy
LHC experiments’
step up in energy
high efficiency, purity and phase space coverage
emphasis on physical definition of observables
have given us a huge amount of useful data
existing models describe data well with tuning
need more understanding of correlations/corners of phase space/relations between different model components
LNF

61. Conclusions
Modern event generators are extremely well developed and tested
Step up to LHC opens up phase space enormously – lots of scope for multiple hard emission and lots of different logs
matrix element matching mandatory
Multiple-interaction physics entering quantitative phase
LNF