QuarkHadron Duality in lepton scattering off nucleonsnuclei from

Quark-Hadron Duality in lepton scattering off nucleons/nuclei from the nucleon to the nucleus Krzysztof M. Graczyk Institute of Theoretical Physics Wrocław University Do We See the Duality in n-Nucleon/Nucleus Scattering? July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

outline • the Bloom-Gilman duality - general idea • duality in electron-nucleon scattering • searching for duality in neutrino-nucleon scattering – study with phenomenological models (most popular) which are applied to neutrino-nucleon scattering – duality vs. nonresonant contribution • duality in electron/n-nucleus scattering (rather short review) • the duality in neutrino interactions a promising phenomenon? July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

• Collective degrees Parton Model of freedom • High Q 2, low Quark-Hadron Duality (Mesons Baryons) as(Q 2) • Low Q 2, high as(Q 2) Bloom-Gilman duality ep e. X E. D. Bloom, F. J. Gilman, Phys. Rev. D 4, 2901 1. The resonance region data oscillate around the scaling curve. 2. The resonance data are on average equivalent to the scaling curve. 3. The resonance region data “slide” along the deep inelastic curve with increasing Q 2. • for m=2 Bloom-Gilman • high-Q 2: t=2 (LT) dominates • weakly depends on Q 2 • describes scaling behavior • Low-Q 2 • Strong Q 2 dependence • duality suppression of higher twists De Rujula et al. . Ann. Phys. 103, 315 July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

Quantitative study of BG duality Niculescu et al. . Phys. Rev. Lett. 85, 1186 threshold xmax RES Nachtman Variable consumes target mass corrections July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

duality application to n interactions CTEQ 4 • • duality is observed in electronnucleon scattering, for F 2, FL g 1 and g 2 structure functions Does duality appear in the neutrino-nucleon scattering? MRS(G) 1. 3<W 2<1. 9 Niculescu et al. . Phys. Rev. Lett. 85, 1186 – phenomenological indications • assuming that the Bloom-Gilman duality exists in neutrino-nucleon interactions: Ø useful tool for construction of the neutrino structure functions in the transition region RES+DIS Ø additional constrain for fitting the electromagnetic, and axial nucleon form factors (see: De Rujula et al. . ). Ø construction of the nonresonant background 1. 9<W 2<2. 5 Q 2 July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

Searching for duality in neutrino-nucleon scattering phenomenological models indications July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

duality in neutrino scattering off nucleon K. Matsui, T. Sato, T. S. H. Lee, Phys. Rev. C 72, 025204 Ø Sato-Lee model PRC 72, 025204 Ø D(1232) resonance region Ø Excellent agreement for the electroproduction data Ø Dortmund isobar model (O. Lalakulich et al. . ) PRC 75, 015202 Ø P 33(1232), P 11(1440), D 13(1520), S 11(1535) Ø Giesen group approach (O. Lalakulich Nuint 09 present. ) Ø MAID description of the resonance region Ø duality in the Rein-Seghal model (NPA 781, 227) Ø A main ingredient of the Monte Carlo Generators Ø After updating vector contribution reasonable fits to the Mini. Boo. NE data (but larger MA) Ø J. Nowak (Nu. Int 09) Ø However, (nowadays) rather instructive toy model for study of the neutrino interactions Ø Quark Model Indications for duality Ø Close et al. (PRD 6, 2533; PRD 7, 2258, PLB 509, 81; PRC 68, 035210) Ø the quark-model arguments for the duality appearance Ø magnetic dominance mechanism July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

electron/neutrino-nucleon scattering Relativistic Harmonic Oscillator Quark Model (FKR) basis for the Rein Seghal approach for neutrino scattering Updated to recent fits obtained by Dortmund group See: KMG, J. T. Sobczyk, Phys. Rev. D 77: 053001, 2008 Original form factors underestimated vector contribution! Simultaneous fit to ANL and BNL data Nonresonant background • added noncoherently to get • ½ isospin character • represented by P 11 -like amplitude • multiplied by constant to get agreement ANL data see: D. Rein, L. Seghal, Ann. Phys. 133, 79

Resonances wave functions for third and fourth level of the oscillator based on Hey et al. Phys. Rept. 96 (1983) 71. July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago Does not contribute

only resonance-like contribution! Q 2 DIS=10 • local duality on quantitative level Lalakulich et al. . W<1. 6 • saturation for Wmax around 2. 0 Ge. V • violation of BD duality below Q 2=0. 3 • Close&Isgur explanation? (PLB 509, 81) summing over 56 and 70 SU(6) multiplets • underestimated predictions above 1. 8 Ge. V! • problems of the FKR formalism at low Q 2

Two Component Quark-Hadron Duality Generalization of s- and t- channel duality (Harari & Freund) • Resonance dual to the nodifferactive Regge pole • Nonresonant background is dual to Pomeron exchange electroproduction I. Niculescu, et al. , Phys. Rev. Lett. 85, 1182 Quark exchange Gluon exchange July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago Valence-like behavior of F 2(proton)

Valence like behavior of the resonance contribution! July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

data from I. Niculescu et al. , Phys. Rev. Lett. 85, 1186 the BG duality Modelin nonresbackground By DIS Nu. Wro MC Generator GENI MC Generator very naive construction but effective More ambitious idea: • Nonresonantt background described by the Pomeron-like amplitudes (e. g. see: Jenkovszky et al. . EPA 12, 361) • may be useful for neutrino scattering

n-N scattering scalar transverse (magnetic-like) July 20 -25, 2009

KMG, C. Juszczak, J. T. Sobczyk, Nucl. Phys. A 781, 227 BG duality? For P 33(1232) resonance! simultaneous duality for both proton and neutron targets is impossible to observe Duality for the Isoscalar like (deuteron like) target if appears then duality for neutrino-nucleon scattering

Duality is rather seen for W<1. 8! Comparable results W<1. 6 O. Lalakulich, W. Melnitchouk, E. A. Paschos, Phys. Rev C 75, 015202 Model with P 33(1232), P 11(1440), D 13(1520), S 11(1535) July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

nonres. background 1 s Based on: ar. Xiv: 0907. 1886 July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago Duality: Charge Current = Neutral Current

higher moments in x saturates rather for Wmax<1. 8 July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

electron-nucleus scattering • Fermi motion smears the resonance structure and elastic peak • data is naturally averaged • scaling behavior (duality) is observed even better than for proton • Is the nuclear DIS correction of the same order as the nuclear reduction in RES region? July 20 -25, 2009 Taken from: J. Arrington et al. . PRC 73, 035205 0. 8<Q 2<3. 3 Q 2<5. 0 Scaling curve EMC corrected! N u F a c t 0 9 IIT, Chicago elastic and quasielastic data are removed

nuclear effects in RES region Quasi-elastic peak • off shell nucleons – Fermi monition – binding energy, – local density distributions of the nucleon momentum – Pauli blocking • in-medium modifications D(1232) A. Ankowski Nu. Int 09 proceedings – resonance form factors? – resonance widths • (reduction by about 5 -10% Athar et al. . EPJA 24, 459; 20 % Leitner et al. . PRC 73, 065502) – Does re-interaction change the total cross section? Spectral function+MAID 07 July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

From the nucleon to nucleus structure function • The nucleus hadronic tensor has the same tensor structure as the nucleon one • Ferree, D. S. Koltun PRC 55, 253 • W. B. Atwood, G. B. West, PRD 7, 773 • A. Bodek, J. L. Ritchie, PRD 23, 427 • Single free nucleon structure function with modification due to off shell effects O. Lalakulich et al. . PRC 79, 015206 duality in lepton off nucleus scattering • Independent particle-shell model • The Dortmund resonance model • Lack of the nonresonant background Z or W p. N July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

Taken from: O. Lalakulich et al. . . PRC 79, 015206 Compared with the DIS data for Q 2=30, 50, 45 (BCDMS) Compared with the DIS data sets for Q 2=12. 59, 19. 95 (CCFR, Nu. Te. V) A need to consider • larger number of resonances • Nonresonant background • Inclusion of the tail from Quasielastic contribution July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago

Summary • the Bloom-Gilman duality is confirmed experimentally for the electron scattering off nucleon and nucleus – BG duality is violated below Q 2=0. 3 Ge. V 2 • BG duality can help to fine tune the magnitude of nonresonant contribution • Neutrino-nucleon – phenomenological models suggest appearance of the duality in neutrino scattering off deuteron-like target – for charged current and neutral current structure functions with W < 1. 6/1. 8 Ge. V • x. F 1 and x. F 3 (with 1 s level of accuracy), for the F 2 (with 2 s level of accuracy) • violation below Q 2=0. 3 Ge. V • the experimental verification is required (waiting for Minerna measurements) • duality in neutrino scattering off nucleus waits for more comprehensive studies July 20 -25, 2009 N u F a c t 0 9 IIT, Chicago