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Jump to first page Quark-Hadron Duality Science Driving the 12 GeV Upgrade Cynthia Keppel for Jefferson Lab PAC 23
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Jump to first page QCD and the Strong Nuclear Force QCD has the most bizarre properties of all the forces in nature n Asymptotic freedom: u quarks feel almost no strong force when close together n Confinement: u 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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Jump to first page 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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Jump to first page Example: e + e - hadrons lim ( e + e - X) = N C e q 2 E ( e + e - + - ) q
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Jump to first page n At high energies: interactions between quarks and gluons become weak (“asymptotic freedom”) ä efficient description of phenomena afforded in terms of quarks n At low energies: effects of confinement make strongly-coupled QCD highly non-perturbative ä collective degrees of freedom (mesons and baryons) more efficient n Duality between quark and hadron descriptions u reflects relationship between confinement and asymptotic freedom u 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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Jump to first page Deep Inelastic Scattering d Mott e i 2 x[q i (x,Q 2 ) + q i (x,Q 2 )] d dE’ Bjorken Limit: Q 2, n Empirically, DIS region is where logarithmic scaling is observed: Q 2 > 5 GeV 2, W 2 > 4 GeV 2 n Duality: Averaged over W, logarithmic scaling observed to work also for Q 2 > 0.5 GeV 2, W 2 < 4 GeV 2, resonance regime
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Jump to first page Observed for all unpolarized structure functions
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Jump to first page Quark-hadron duality in nuclei If we had used only scintillators, scaling would be thought to hold down to low Q 2 !
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Jump to first page Duality in QCD n Moments of the Structure Function M n (Q 2 ) = S dx x n-2 F(x,Q 2 ) If n = 2, this is the Bloom-Gilman duality integral. n Operator Product Expansion M n (Q 2 ) = (nM 0 2 / Q 2 ) k-1 B nk (Q 2 ) higher twist logarithmic dependence n 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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Jump to first page 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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Jump to first page Polarized Structure Functions at 11 GeV Hall C
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Jump to first page Neutron Structure Functions at 11 GeV “BONUS” Detect 60-100 MeV/c spectator protons at large angles Map large region in Bjorken x and Q 2 (up to 10 GeV 2 ) 1 st time: rigorous p – n moments! Proton-Neutron difference is acid test of quark-hadron duality to recoil detector D to CLAS++ e e,e, p n (7.5 atm thin deuterium target, radial TPC, DVCS solenoid)
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Jump to first page Applications of Quark-Hadron Duality n Allows for direct comparison to QCD Moments n CTEQ currently considering the use of duality for large x parton distribution modeling n Neutrino community planning to test duality n 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 n Spin structure at HERMES n Duality provides extended access to large x regime
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Jump to first page A 1 n from 3 He(e,e’) Hall A 2
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Jump to first page Duality in Meson Electroproduction Duality and factorization possible for Q 2,W 2 3 GeV 2 (Close and Isgur, Phys. Lett. B509, 81 (2001)) d /dz i e i 2 q i (x,Q 2 )D qi m (z,Q 2 ) + q i (x,Q 2 )D qi m (z,Q 2 ) Requires non-trivial cancellations of decay angular distributions If duality is not observed, factorization is questionable hadronic descriptionquark-gluon description On to the next universal function…
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Jump to first page (Semi-)Exclusive Meson Electroproduction Large z = E h / to emphasize duality and factorization (Berger criterion) n Meson electroproduced along q, i.e. emphasize forward angles n SHMS in Hall C well suited to detect these mesons (cf. pion form factor) n If Berger criterion and duality factorization
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Jump to first page Summary n Quark-hadron duality is a non-trivial property of QCD Soft-Hard Transition! n Duality violations obscure comparison with lattice QCD through the structure function moments n Duality has a broad interest and application base n 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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