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Quark-Hadron Duality

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:

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Quark-Hadron Duality

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  1. Science Driving the 12 GeV Upgrade Quark-Hadron Duality Cynthia Keppel for Jefferson Lab PAC 23

  2. 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 matterhow far apart QCD in principle describes all of nuclear physics - at all distance scales - but how does it work?

  3. Hadronic Cross Sections averaged over appropriate energy range Shadrons Perturbative Quark-Gluon Theory Quark-Hadron Dualitycomplementarity between quark and hadron descriptions of observables At high enough energy: = Squarks Can use either set of complete basis states to describe physical phenomena

  4. Example: e+e- hadronslim s(e+e- X) = NC S eq2E  s(e+e- m+m-) q

  5. 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.

  6. Deep Inelastic Scattering ds  sMott Sei2x[qi(x,Q2) + qi(x,Q2)]dWdE’ • 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

  7. Observed for all unpolarized structure functions

  8. Quark-hadron duality in nuclei If we had used only scintillators, scaling would be thought to hold down to low Q2!

  9. Duality in QCD 1 0 • Moments of the Structure Function Mn(Q2) = S dxxn-2F(x,Q2) If n = 2, this is the Bloom-Gilman duality integral. • Operator Product Expansion Mn(Q2) = (nM02/Q2)k-1Bnk(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!  k=1

  10. Separated Unpolarized Structure Functions at 11 GeV Hall C x = 0.8 De > 0.3 SHMS HMS Also necessary for polarized structure function measurements...

  11. Polarized Structure Functions at 11 GeV Hall C

  12. 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)

  13. 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

  14.  Hall A A1n from 3He(e,e’) 2

  15. 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…

  16. (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

  17. 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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