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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