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

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

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

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

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

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

Duality observed in all unpolarized structure functions (E94110)

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

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

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”

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

Kinematic coverage

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”

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)

Moments of F 2 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 Q 2 = 2 (GeV/c) 2 30% of M 2 comes from the resonance region

Why large x ? Integral Ratio Res / Scaling

Quantification Large x Structure Functions

Kinematic coverage

“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

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)

LH 2 target Quark-parton prediction

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