Qed: accelerated charges radiate. Qed: accelerated charges radiate

QED: accelerated charges radiate.

• QED: accelerated charges radiate.

• QCD identical: accelerated colours radiate.

• gluons also charged.

•  cascade of partons.

• = parton shower.

Partons are not physical particles: they cannot freely propagate.

• Partons are not physical particles: they cannot freely propagate.

• Hadrons are.

• Need a model of partons' confinement into hadrons: hadronization.

Experimentally, two jets:

• Experimentally, two jets:

• Flat rapidity plateau

Using this model, can estimate hadronization correction to perturbative quantities.

• 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.

Direct implementation of the above.

• 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.

Asymptotic freedom: becomes increasingly QED-like at short distances.

• 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

Can measure from quarkonia spectra:

• Can measure from quarkonia spectra:

Light quarks connected by string.

• Light quarks connected by string.

• L=0 mesons only have ‘yo-yo’ modes:

• Obeys area law:

Start by ignoring gluon radiation:

• 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.

String picture  constraints on 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

Baryon pictured as three quarks attached to a common centre:

• 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!

So far: string model = motivated, constrained independent fragmentation!

• 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.

String model strongly physically motivated.

• 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?

Planar approximation: gluon = colour—anticolour pair.

• 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

Independent of shower scale Q

• Independent of shower scale Q

• depends on Q0 and 

Project colour singlets onto continuum of high-mass mesonic resonances (=clusters). Decay to lighter well-known resonances and stable hadrons.

• 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.

Although cluster mass spectrum peaked at small m, broad tail at high m.

• 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.

“Leading hadrons are too soft”

• “Leading hadrons are too soft”

• ‘perturbative’ quarks remember their direction somewhat

• Rather string-like.

• Extra adjustable parameter.

Strings

• Strings

• “Hadrons are produced by hadronization: you must get the non-perturbative dynamics right”

• Improving data has meant successively refining perturbative phase of evolution…

Is guaranteed by preconfinement: do not need to retune at each energy

• Is guaranteed by preconfinement: do not need to retune at each energy

•  Only tune what’s new in hadron—hadron collisions

Often forgotten ingredient of event generators:

• Often forgotten ingredient of event generators:

• String and cluster decay to some stable hadrons but mainly unstable resonances
• These decay further “according to PDG data tables”
• Matrix elements for n-body decays
• But…
• Not all resonances in a given multiplet have been measured
• Measured branching fractions rarely add up to 100% exactly
• Measured branching fractions rarely respect isospin exactly
• So need to make a lot of choices
• Has a significant effect on hadron yields, transverse momentum release, hadronization corrections to event shapes, …
• Should consider the decay table choice part of the tuned set

Previous generations typically used external packages, e.g. TAUOLA, PHOTOS, EVTGEN

• 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)