Quark-Hadron Duality

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Quark-Hadron Duality

• Science Driving the 12 GeV Upgrade

Cynthia Keppel for Jefferson Lab PAC 23
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QCD and the Strong Nuclear ForceQCD has the
most bizarre properties of all the forces in
nature

• Asymptotic freedom
• quarks feel almost no strong force when close
  together
• Confinement
• restoring force between quarks at large distances
  equivalent to 10 tons, no matter how far apart

• QCD in principle describes all of nuclear physics
  - at all distance scales - but how does it work?

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Quark-Hadron Dualitycomplementarity between
quark and hadron descriptions of observables
At high enough energy

• Hadronic Cross Sections
• averaged over appropriate energy range
• Shadrons

• Perturbative
• Quark-Gluon Theory

Squarks
Can use either set of complete basis states to
describe physical phenomena
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Example ee- hadronslim s(ee-
X) NC S eq2 E ? s(ee-
mm-) q
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• At high energies interactions between quarks and
  gluons become weak
• (asymptotic freedom)
• efficient description of phenomena afforded in
  terms of quarks
• At low energies effects of confinement make
  strongly-coupled QCD highly non-perturbative
• collective degrees of freedom (mesons and
  baryons) more efficient
• Duality between quark and hadron descriptions
• reflects relationship between confinement and
  asymptotic freedom
• intimately related to nature and transition from
  non-perturbative to perturbative QCD

Duality defines the transition from soft to hard
QCD.
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Deep Inelastic Scattering ds ?
sMott S ei2xqi(x,Q2) qi(x,Q2)dWdE

• Bjorken Limit Q2, n ? ?
• Empirically, DIS region is where logarithmic
  scaling is observed Q2 gt 5 GeV2, W2 gt 4 GeV2
• Duality Averaged over W, logarithmic scaling
  observed to work also for Q2 gt 0.5 GeV2, W2 lt 4
  GeV2, resonance regime

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Observed for all unpolarized structure functions
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Quark-hadron duality in nuclei

• If we had used only scintillators, scaling would
  be thought to hold down to low Q2!

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Duality in QCD

• Moments of the Structure Function
• Mn(Q2) S dx xn-2F(x,Q2)
• If n 2, this is the Bloom-Gilman duality
  integral.
• Operator Product Expansion
• Mn(Q2) ? (nM02/ Q2)k-1 Bnk(Q2)
• higher twist logarithmic dependence
• Duality is described in the Operator Product
  Expansion as higher twist effects being small or
  cancelling DeRujula, Georgi, Politzer
  (1977)
• Duality violations are not easily interpretable
  by lattice QCD calculations!

1
0
?
k1
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Separated Unpolarized Structure Functions at 11
GeV
Hall C
x 0.8
De gt 0.3
SHMS
HMS
Also necessary for polarized structure function
measurements...
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Polarized Structure Functions at 11 GeV
Hall C
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Neutron Structure Functions at 11 GeV
to CLAS
BONUS
D
e,
n
p
to recoil detector
e

• Detect 60-100 MeV/c
• spectator protons at large angles
• Map large region in Bjorken x
• and Q2 (up to 10 GeV2)
• 1st time rigorous p n moments!
• Proton-Neutron difference is acid
• test of quark-hadron duality

(7.5 atm thin deuterium target, radial TPC, DVCS
solenoid)
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Applications of Quark-Hadron Duality

• Allows for direct comparison to QCD Moments
• CTEQ currently considering the use of duality for
  large x parton distribution modeling
• Neutrino community planning to test duality
• Neutrino community using duality to predict low
  energy (1 GeV) regime
• New Bodek model successfully uses duality to
  extend pdf-based parameterization to the
  photoproduction limit successfully
• Spin structure at HERMES
• Duality provides extended access to large x regime

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A1n from 3He(e,e)
?
?
Hall A
2
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Duality in Meson ElectroproductionDuality and
factorization possible for Q2,W2 ? 3 GeV2 (Close
and Isgur, Phys. Lett. B509, 81 (2001))
hadronic description quark-gluon description
Requires non-trivial cancellations of decay
angular distributions If duality is not observed,
factorization is questionable
ds/dz ? ?iei2?qi(x,Q2)Dqim(z,Q2)
qi(x,Q2)Dqim(z,Q2)?
On to the next universal function
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(Semi-)Exclusive Meson Electroproduction

• Large z Eh/n to emphasize duality and
  factorization (Berger criterion)
• Meson electroproduced along q, i.e. emphasize
  forward angles
• SHMS in Hall C well suited to detect these mesons
  (cf. pion form factor)
• If Berger criterion and duality ? factorization

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Summary

• Quark-hadron duality is a non-trivial property of
  QCD ? Soft-Hard Transition!
• Duality violations obscure comparison with
  lattice QCD through the structure function
  moments
• Duality has a broad interest and application base
• If understood and well-measured, it can provide a
  valuable tool to access the high x regime
• New data at an 11 GeV JLab will allow for a
  complete study of duality in electron scattering,
  including polarized and unpolarized structure
  functions, on the nucleons and in nuclei, and in
  semi-exclusive (and exclusive?) reactions