Monte Carlo Methods in Particle Physics Bryan Webber University of Cambridge IMPRS, Munich 19-23 November 2007
Monte Carlo Methods 3 Bryan Webber Structure of LHC Events
1. Hard process 2. Parton shower 3. Hadronization 4. Underlying event
Monte Carlo Methods 3 Bryan Webber Lecture 3: Hadronization
Partons are not physical 1. Phenomenological particles: they cannot models. freely propagate. 2. Confinement. Hadrons are. 3. The string model. 4. Preconfinement. Need a model of partons' 5. The cluster model. confinement into 6. Underlying event hadrons: hadronization. models.
Monte Carlo Methods 3 Bryan Webber Phenomenological Models
Experimentally, two jets: Flat rapidity plateau and limited
Monte Carlo Methods 3 Bryan Webber Estimate of Hadronization Effects Using this model, can estimate hadronization correction to perturbative quantities.
Jet energy and momentum:
with mean transverse momentum. Estimate from Fermi motion
Jet acquires non-perturbative mass: Large: ~ 10 GeV for 100 GeV jets.
Monte Carlo Methods 3 Bryan Webber Independent Fragmentation Model (“Feynman—Field”) Direct implementation of the above.
Longitudinal momentum distribution = arbitrary fragmentation function: parameterization of data. Transverse momentum distribution = Gaussian.
Recursively apply Hook up remaining soft and
Strongly frame dependent. No obvious relation with perturbative emission. Not infrared safe. Not a model of confinement. Monte Carlo Methods 3 Bryan Webber 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 Monte Carlo Methods 3 Bryan Webber Interquark potential
Can measure from or from lattice QCD: quarkonia spectra:
String tension
Monte Carlo Methods 3 Bryan Webber String Model of Mesons Light quarks connected by string. L=0 mesons only have ‘yo-yo’ modes:
t
x
Obeys area law:
Monte Carlo Methods 3 Bryan Webber 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.
Monte Carlo Methods 3 Bryan Webber Lund Symmetric Fragmentation Function
String picture constraints on fragmentation function: • Lorentz invariance • Acausality • Left—right symmetry
adjustable parameters for quarks and
Fermi motion Gaussian transverse momentum. Tunnelling probability becomes
and = main tuneable parameters of model
Monte Carlo Methods 3 Bryan Webber Baryon Production Baryon pictured as three quarks attached to a common centre:
At large separation, can consider two quarks tightly bound: diquark
diquark treated like antiquark.
Two quarks can tunnel nearby in phase space: baryon—antibaryon pair Extra adjustable parameter for each diquark!
Alternative “popcorn” model:
Monte Carlo Methods 3 Bryan Webber 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. Monte Carlo Methods 3 Bryan Webber String Model Summary
• String model strongly physically motivated. • Very successful fit to data. • Universal: fitted to , little freedom elsewhere.
• How does motivation translate to prediction? ~ one free parameter per hadron/effect!
• Blankets too much perturbative information?
• Can we get by with a simpler model?
Monte Carlo Methods 3 Bryan Webber 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
Monte Carlo Methods 3 Bryan Webber Cluster mass distribution • Independent of shower scale Q – depends on Q 0 and Λ
Monte Carlo Methods 3 Bryan Webber The Naïve 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. Shower cutoff becomes parameter of model.
Monte Carlo Methods 3 Bryan Webber The Cluster Model
Although cluster mass spectrum peaked at small m, broad tail at high m. “Small fraction of clusters too heavy for isotropic two-body decay to be a good approximation” Longitudinal cluster fission:
Rather string-like. Fission threshold becomes crucial parameter. ~15% of primary clusters get split but ~50% of hadrons come from them.
Monte Carlo Methods 3 Bryan Webber The Cluster Model
“Leading hadrons are too soft”
‘perturbative’ quarks remember their direction somewhat
Rather string-like.
Extra adjustable parameter.
Monte Carlo Methods 3 Bryan Webber Strings Clusters “Hadrons are produced by “Get the perturbative phase hadronization: you must right and any old get the non-perturbative hadronization model will dynamics right” be good enough” Improving data has meant Improving data has meant successively refining successively making non- perturbative phase of perturbative phase more evolution… string-like…
???
Monte Carlo Methods 3 Bryan Webber The Underlying Event
• Protons are extended objects • After a parton has been scattered out of each, what happens to the remnants?
Two models: Soft parton—parton cross section is so large that the remnants • Non-perturbative: always undergo a soft collision.
• Perturbative: ‘Hard’ parton—parton cross section huge at low pt, high energy, dominates inelastic cross section and is calculable. Monte Carlo Methods 3 Bryan Webber Soft Underlying Event Model (HERWIG)
Compare underlying event with ‘minimum bias’ collision (‘typical’ inelastic proton—proton collision)
Parametrization of (UA5) data + model of energy dependence
Monte Carlo Methods 3 Bryan Webber Multiparton Interaction Model (PYTHIA/JIMMY)
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 Monte Carlo Methods 3 Bryan Webber Double Parton Scattering
• CDF Collaboration, PR D56 (1997) 3811
σγjσjj σDPS = σeff
+1.7 σeff = 14 1.7 2.3 mb ± −
Monte Carlo Methods 3 Bryan Webber Some Warnings • Not everyone means same thing by “underlying event” – Remnant—remnant interaction – Everything except hard process final state • Separation into components is model dependent – Operational definition (R Field): “transverse” regions
Monte Carlo Methods 3 Bryan Webber Tuning PYTHIA to the Underlying Event
• Rick Field (CDF): keep all parameters that can be fixed by LEP or HERA at their default values. What’s left? • Underlying event. Big uncertainties at LHC...
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Monte Carlo Methods 3 Bryan Webber Summary
• Hard Process is very well understood: firm perturbative basis • Parton Shower is fairly well understood: perturbative basis, with various approximations • Hadronization is less well understood: modelled, but well constrained by data. Extrapolation to LHC fairly reliable. • Underlying event least understood: modelled and only weakly constrained by existing data. Extrapolation?
• Always ask “What physics is dominating my effect?”
Monte Carlo Methods 3 Bryan Webber