quark-hadron duality
DESCRIPTION
Science Driving the 12 GeV Upgrade. Quark-Hadron Duality. Cynthia Keppel for Jefferson Lab PAC 23. QCD and the Strong Nuclear Force QCD has the most bizarre properties of all the forces in nature. Asymptotic freedom: quarks feel almost no strong force when close together Confinement: - PowerPoint PPT PresentationTRANSCRIPT
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Quark-Hadron DualityScience 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 Duality
complementarity between quark and hadron descriptions of observables
Hadronic Cross Sections
averaged over appropriate energy range
hadrons
Perturbative
Quark-Gluon Theory
=
At high enough energy:
quarks
Can use either set of complete basis states to describe physical phenomena
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Example: e+e- hadrons
lim (e+e- X) = NC eq2
E (e+e- +-) 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
dMott ei2x[qi(x,Q2) +
qi(x,Q2)]ddE’ Bjorken Limit: Q2, Empirically, DIS region is
where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2
Duality: Averaged over W, logarithmic scaling observed to work also for Q2 > 0.5 GeV2, W2 < 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!
0
1
k=1
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Separated Unpolarized Structure Functions at 11 GeV
Also necessary for polarized structure function measurements...
x = 0.8
HMS
SHMS
Hall C
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Polarized Structure Functions at 11 GeV
Hall C
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Neutron Structure Functions at 11 GeV
“BONUS”
• 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
to recoil detector
Dto CLAS++
e
e,
p
n
(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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A1
n from 3He(e,e’) Hall A
2
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Duality in Meson Electroproduction
Duality and factorization possible for Q2,W2 3 GeV2
(Close and Isgur, Phys. Lett. B509, 81 (2001))
d/dz iei2qi(x,Q2)Dqi
m(z,Q2) + qi(x,Q2)Dqim(z,Q2)
Requires non-trivial cancellations of decay angular distributions
If duality is not observed, factorization is questionable
hadronic description quark-gluon description
On to the next universal function…
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(Semi-)Exclusive Meson Electroproduction
Large z = Eh/ 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