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Duality: Recent and Future Results Ioana Niculescu James Madison University Hall C “Summer” Workshop

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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+gluons Can use either set of complete basis states to describe physical phenomena

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Q 2 : Four-momentum transfer x : Bjorken variable (=Q 2 /2Mn) n : Energy transfer M : Nucleon mass W : Final state hadronic mass L T U Inclusive Electron Scattering

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Duality in Inclusive electron scattering Duality in Inclusive electron scattering Elastic Resonance Deep Inelastic Where : flux of transversely polarized virtual photons : relative longitudinal polarization F L = F 2 – 2xF 1 + 2M p F 2 F 2 L + T R = L / T = F L / 2xF 1

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Duality in F 2 Structure Function ’ = 1+W 2 /Q 2 First observed ~1970 by Bloom and Gilman at SLAC by comparing resonance production data with deep inelastic scattering data Integrated F 2 strength in Nucleon Resonance region equals strength under scaling curve. Shortcomings: Only a single scaling curve and no Q 2 evolution (Theory inadequate in pre-QCD era) No L / T separation F 2 data depend on assumption of R = L / T Only moderate statistics

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Now can obtain “true” F 2 data Compare with DIS fits or QCD calculations/fits (CTEQ/MRST) Bjorken x instead of ’ Empirically, DIS region is where logarithmic scaling is observed: Q 2 > 5 GeV 2, W 2 > 4 GeV 2 Duality: Averaged over W, log scaling observed to work also for Q 2 > 0.5 GeV 2, W 2 < 4 GeV 2 JLab results (E94110): Works quantitatively to better than 10% Duality in the F 2 Structure Function

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Duality observed in all unpolarized structure functions (E94110)

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p Fe d = 2x [ 1 + (1 + 4M 2 x 2 /Q 2 ) 1/2 ] …and in Nuclei (F 2 )

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Where we are now… Experimentally, duality holds in all unpolarized structure functions, in nuclei, and in tested spin structure functions down to surprisingly low Q 2 Apparently a non-trivial property of nucleon structure

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What is new… E00-002: “F 2 N at Low Q 2 ” E00-116: “Duality at Intermediate Q 2 ” E00-108: “Duality in Meson Electroproduction”

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Low Q 2 duality in inclusive electron-nucleon scattering Measure F 2 (p and n) in the region where it drops off Study F 2 at low Q 2 as a function of x

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Kinematic coverage

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Duality at Intermediate Q 2 “proposed measurements will help answering the question of the nature of power corrections in hard processes as fundamental components in understanding the transition between pQCD and non-pQCD”

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Cornwall-Norton moments Logarithmic dependence Higher twists. Duality is described in the Operator Product Expansion as higher twist effects being small or canceling DeRujula, Georgi, Politzer (1977)

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Moments of F 2 p @ Low Q 2 Proton Charge (Coulomb Sum Rule) Elastic contribution n = 2 n = 4 n = 6 n = 8 50% of momentum carried by quarks (Momentum Sum Rule) total n = 2 elastic -region W 2 > 4 GeV 2 (“DIS”) S 11 -region @ Q 2 = 2 (GeV/c) 2 30% of M 2 comes from the resonance region

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Why large x ? Integral Ratio Res / Scaling

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Quantification Large x Structure Functions

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Kinematic coverage

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“Explore the extent to which the electroproduction of mesons exhibits the same dual behavior between resonance region scattering and scaling region” At high energies: factorization (pQCD) quark hadronizationhard quark-photon interaction If duality holds: may see behavior consistent with factorization even at lower energies. Duality in Meson Electroproduction

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Spectra in z at low Q 2 and W average to scaling curve (high Q 2 and W)? Q2 behavior of resonant bumps Relative strength of resonances/ background at different Q 2 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 ) Duality in meson electroproduction: look for duality in f(z)

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LH 2 target Quark-parton prediction

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The future… CTEQ currently planning to use duality for large x parton distribution modeling Neutrino community planning to test duality Neutrino community using duality to predict low energy (~1 GeV) regime Duality provides extended access to large x regime Allows for direct comparison to QCD Moments calculated on the lattice More experiments are planned Neutron Polarized structure functions Neutrino scattering

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