Lecture I: pQCD and spectra

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Lecture I pQCD and spectra
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What is QCD?
From T. Schaefer, QM08 student talk
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QCD and hadrons
Quarks and gluons are the fundamental particles
of QCD (feature in the Lagrangian)
However, in nature, we observe hadrons Color-neut
ral combinations of quarks, anti-quarks
Baryon multiplet
Meson multiplet
S strangeness
I3 (u,d content)
I3 (u,d content)
Mesons quark-anti-quark
Baryons 3 quarks
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Seeing quarks and gluons
In high-energy collisions, observe traces of
quarks, gluons (jets)
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How does it fit together?
S. Bethke, J Phys G 26, R27
Running coupling as decreases with Q2
Pole at m L
LQCD 200 MeV 1 fm-1
Hadronic scale
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Asymptotic freedom and pQCD
At large Q2, hard processes calculate free
parton scattering
more subprocesses
But need to add hadronisation (initial state
PDFs)
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Low Q2 confinement
a large, perturbative techniques not suitable
Bali, hep-lat/9311009
Lattice QCD solve equations of motion (of the
fields) on a space-time lattice by MC
Lattice QCD potential
String breaks, generate qq pair to reduce field
energy
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Singularities in pQCD
(massless case)
Soft divergence
Collinear divergence
Closely related to hadronisation effects
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Singularities in phase space
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Hard processes in QCD

• Hard process scale Q gtgt LQCD
• Hard scattering High-pT parton(photon) QpT
• Heavy flavour production m gtgt LQCD

Factorization

• Cross section calculation can be split into
• Hard part perturbative matrix element
• Soft part parton density (PDF), fragmentation
  (FF)

parton density
matrix element
FF
QM interference between hard and soft suppressed
(by Q2/L2 Higher Twist)
Soft parts, PDF, FF are universal independent of
hard process
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Seeing quarks and gluons
In high-energy collisions, observe traces of
quarks, gluons (jets)
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Fragmentation and parton showers
MC event generators implement parton
showers Longitudinal and transverse dynamics
High-energy parton (from hard scattering)
Hadrons
Q mH LQCD
large Q2
Analytical calculations Fragmentation Function
D(z, m) zph/Ejet Only longitudinal dynamics
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Example DIS events
NC
CC
DIS Measured electron/jet momentum fixes
kinematics
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Proton structure F2
Q2 virtuality of the g x Q2 / 2 p q momentum
fraction of the struck quark
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Factorisation in DIS
Integral over x is DGLAP evolution with splitting
kernel Pqq
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Factorisation in pictures
Note DGLAP evolution only keeps track of
leading parton momentum
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Initial state and final state radiation
Final state radiation
Initial state radiation
Fragmentation function evolves
Parton density evolves
Evolution can turn (leading)quarks into
gluons and vice versa
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Parton density distribution
Low Q2 valence structure
Q2 evolution (gluons)
Gluon content of proton risesquickly with Q2
Soft gluons
Valence quarks (p uud) x 1/3
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pQCD illustrated
fragmentation
jet spectrum parton spectrum
CDF, PRD75, 092006
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Note difference pp, ee-
e e- QCD events jetshave p1/2 vs Directly
measure frag function
pp steeply falling jet spectrum Hadron spectrum
convolution of jet spectrum with fragmentation
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Fragmentation function uncertainties
Hirai, Kumano, Nagai, Sudo, PRD75094009
zpT,h / 2vs
zpT,h / Ejet
Full uncertainty analysis being
pursuedUncertainties increase at small and large
z
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Global analysis of FF
proton
anti-proton
pions
De Florian, Sassot, Stratmann, PRD 76074033,
PRD75114010
... or do a global fit, including pp data
Universality still holds
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Heavy quark fragmentation
Heavy quarks
Light quarks
Heavy quark fragmentation leading heavy meson
carries large momentum fraction
Less gluon radiation than for light quarks, due
to dead cone
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Dead cone effect
Radiated wave front cannot out-run source quark
Heavy quark b lt 1
Result minimum angle for radiation ? Mass
regulates collinear divergence
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Heavy Quark Fragmentation II
Significant non-perturbative effects seen even
in heavy quark fragmentation
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Factorisation in perturbative QCD
Parton density function Non-perturbative
distribution of partons in proton Extracted from
fits to DIS (ep) data
Matrix element Perturbative component
Fragmentation function Non-perturbative Measured/e
xtracted from ee-
Factorisation non-perturbative parts
(long-distance physics) can be factored out in
universal distributions (PDF, FF)
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Hard processes in QCD

• Hard process scale Q gtgt LQCD
• Hard scattering High-pT parton(photon) QpT
• Heavy flavour production m gtgt LQCD

Factorization

• Cross section calculation can be split into
• Hard part perturbative matrix element
• Soft part parton density (PDF), fragmentation
  (FF)

parton density
matrix element
FF
QM interference between hard and soft suppressed
(by Q2/L2 Higher Twist)
Soft parts, PDF, FF are universal independent of
hard process
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Two-body kinematics
2 -gt 2 scattering
Massless case
Mandelstam variables
Invariants independent of ref system NB p are
four-vectors
Good approximation if
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Centre-of-mass system
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pp collision
Incoming partons carry momentum fractions x1,
x2 Lab CMS is not parton-parton CMS
See Eskola paper for further practical details
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pQCD matrix elements
Combridge, Kripfganz, Ranft, PLB70, 234
See also e.g. Owens, Rev Mod Phys 59,465
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Key topics today

• pQCD relies on factorization
• Separation of scales
• Parton Density Functions (soft)
• Hard Scattering
• Fragmentation (soft)
• PDFs from DIS
• FF from ee-
• Heavy flavour fragmentation is qualitatively
  different from light