Transcript Quark-Hadron Duality

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 Force
QCD has the most bizarre properties of all the forces in nature
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Asymptotic freedom:
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quarks feel almost no strong
force when close together
Confinement:
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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
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:
lim
E
+
ee
s(e+e s(e+e-
hadrons
X)
m+m-)
= NC S eq2
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 nonperturbative to perturbative QCD
Duality defines the transition from soft to hard QCD.
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Deep Inelastic Scattering
ds
 sMott S ei2x[qi(x,Q2) + qi(x,Q2)]
dWdE’
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Bjorken Limit: Q2, n  
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
1
Mn(Q2) = S dx xn-2F(x,Q2)
0
If n = 2, this is the Bloom-Gilman duality integral.
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Operator Product Expansion

Mn(Q2) =  (nM02/ Q2)k-1 Bnk(Q2)
k=1
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!

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Separated Unpolarized Structure
Functions at 11 GeV
x = 0.8
De > 0.3
Hall C
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
“BONUS”
to CLAS++
D
,
e
e
(7.5 atm thin deuterium target,
radial TPC, DVCS solenoid)
n
to recoil
detector
p
• 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
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Applications of Quark-Hadron Duality
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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
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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))
hadronic description
quark-gluon description
Requires non-trivial cancellations of decay angular distributions
If duality is not observed, factorization is questionable
ds/dz  Siei2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
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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
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