Jump to first page Quark-Hadron Duality Science Driving the 12 GeV Upgrade Cynthia Keppel for Jefferson Lab PAC 23

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?

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

Jump to first page Example: e + e - hadrons lim  ( e + e - X) = N C  e q 2 E  ( e + e -  +  - ) q

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.

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

Jump to first page Observed for all unpolarized structure functions

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 !

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 

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

Jump to first page Polarized Structure Functions at 11 GeV Hall C

Jump to first page Neutron Structure Functions at 11 GeV “BONUS” Detect 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)

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

Jump to first page   A 1 n from 3 He(e,e’) Hall A 2

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…

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

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