1 / 17

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:

ronna
Download Presentation

Quark-Hadron Duality

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related