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July 20-25, 2009N u F a c t 0 9 IIT, Chicago 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 -Nucleon/Nucleus Scattering?

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July 20-25, 2009N 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/ nucleus scattering (rather short review) the duality in neutrino interactions a promising phenomenon?

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago Bloom-Gilman duality ep eX 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 Q2. E.D. Bloom, F.J. Gilman, Phys. Rev.D4, 2901 for m=2 Bloom-Gilman high-Q2: =2 (LT) dominates weakly depends on Q2 describes scaling behavior Low-Q2 Strong Q2 dependence duality suppression of higher twists De Rujula et al.. Ann. Phys. 103, 315 Parton Model High Q2, low s (Q2) Collective degrees of freedom (Mesons Baryons) Low Q2, high s (Q2) Quark-Hadron Duality

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

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago duality application to interactions duality is observed in electron- nucleon scattering, for F2, FL g1 and g2 structure functions Does duality appear in the neutrino-nucleon scattering? –phenomenological indications assuming that the Bloom-Gilman duality exists in neutrino-nucleon interactions: useful tool for construction of the neutrino structure functions in the transition region RES+DIS additional constrain for fitting the electromagnetic, and axial nucleon form factors (see: De Rujula et al..). construction of the nonresonant background Niculescu et al..Phys. Rev. Lett. 85, 1186 Q2 MRS(G) CTEQ4 1.9

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

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago duality in neutrino scattering off nucleon Sato-Lee model PRC 72, 025204 (1232) resonance region Excellent agreement for the electroproduction data Dortmund isobar model (O.Lalakulich et al..) PRC 75, 015202 P33(1232), P11(1440), D13(1520), S11(1535) Giesen group approach (O.Lalakulich Nuint09 present.) MAID description of the resonance region duality in the Rein-Seghal model (NPA 781,227) A main ingredient of the Monte Carlo Generators After updating vector contribution reasonable fits to the MiniBooNE data (but larger M A ) J. Nowak (NuInt09) However, (nowadays) rather instructive toy model for study of the neutrino interactions Quark Model Indications for duality Close et al. (PRD6, 2533; PRD7, 2258, PLB509, 81; PRC68, 035210) the quark-model arguments for the duality appearance magnetic dominance mechanism K. Matsui,T. Sato,T.S. H. Lee, Phys. Rev. C 72, 025204

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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.D77:053001,2008 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 Original form factors underestimated vector contribution!

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

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only resonance-like contribution! local duality on quantitative level saturation for W max around 2.0 GeV violation of BD duality below Q 2 =0.3 Close&Isgur explanation? (PLB509, 81) summing over 56 and 70 SU(6) multiplets underestimated predictions above 1.8 GeV! problems of the FKR formalism at low Q2 Q 2 DIS =10 Lalakulich et al.. W<1.6

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago I. Niculescu, et al., Phys. Rev. Lett. 85, 1182 Valence-like behavior of F2(proton) electroproduction Quark exchange Gluon exchange Generalization of s- and t- channel duality (Harari & Freund) Resonance dual to the nodifferactive Regge pole Nonresonant background is dual to Pomeron exchange Two Component Quark-Hadron Duality

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

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data from I. Niculescu et al., Phys. Rev. Lett. 85, 1186 very naive construction but effective More ambitious idea: Nonresonantt background described by the Pomeron-like amplitudes (e.g. see: Jenkovszky et al.. EPA12, 361) may be useful for neutrino scattering the BG duality Modelin nonresbackground By DIS NuWro MC Generator GENI MC Generator

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

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KMG, C.Juszczak, J.T.Sobczyk, Nucl. Phys. A781, 227 BG duality? Duality for the Isoscalar like (deuteron like) target if appears then duality for neutrino-nucleon scattering simultaneous duality for both proton and neutron targets is impossible to observe For P33(1232) resonance!

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago Comparable resultsDuality is rather seen for W<1.8! 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)

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago nonres. background Duality: Charge Current = Neutral Current 11 Based on: arXiv:0907.1886

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago higher moments higher moments in saturates rather for W max <1.8

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July 20-25, 2009N 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? 0.8
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July 20-25, 2009N u F a c t 0 9 IIT, Chicago nuclear effects in RES region off shell nucleons –Fermi monition –binding energy, –local density distributions of the nucleon momentum –Pauli blocking in-medium modifications –resonance form factors? –resonance widths (reduction by about 5-10% Athar et al..EPJA24, 459; 20 % Leitner et al..PRC73, 065502) –Does re-interaction change the total cross section? A. Ankowski NuInt09 proceedings (1232) Spectral function+MAID07 Quasi-elastic peak

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July 20-25, 2009N 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 PRC55, 253 W.B.Atwood, G.B.West, PRD7, 773 A.Bodek, J.L.Ritchie, PRD23, 427 Single free nucleon structure function with modification due to off shell effects O. Lalakulich et al..PRC79, 015206 duality in lepton off nucleus scattering Independent particle-shell model The Dortmund resonance model Lack of the nonresonant background Z or W N

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July 20-25, 2009N u F a c t 0 9 IIT, Chicago A need to consider larger number of resonances Nonresonant background Inclusion of the tail from Quasielastic contribution Compared with the DIS data sets for Q2=12.59, 19.95 (CCFR, NuTeV) Compared with the DIS data for Q2=30, 50, 45 (BCDMS) Taken from: O. Lalakulich et al...PRC79, 015206

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July 20-25, 2009N 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 GeV 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 GeV xF1 and xF3 (with 1 level of accuracy), for the F2 (with 2 level of accuracy) violation below Q 2 =0.3 GeV the experimental verification is required (waiting for Miner a measurements) duality in neutrino scattering off nucleus waits for more comprehensive studies

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