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Quark-Hadron Duality in lepton scattering off nucleons/nuclei from the nucleon to the nucleus

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## Quark-Hadron Duality in lepton scattering off nucleons/nuclei from the nucleon to the nucleus

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**Quark-Hadron Duality in lepton scattering off**nucleons/nucleifrom the nucleon to the nucleus Krzysztof M. Graczyk Institute of Theoretical Physics Wrocław University Do We See the Duality in n-Nucleon/Nucleus Scattering? 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? N u F a c t 0 9 IIT, Chicago**E.D. Bloom, F.J. Gilman, Phys. Rev.D4, 2901**Quark-Hadron Duality Bloom-Gilman duality epeX • Collective degrees of freedom (Mesons Baryons) • Low Q2, highas(Q2) • Parton Model • High Q2, lowas(Q2) • The resonance region data oscillate around the scaling curve. • The resonance data are on average equivalent to the scaling curve. • The resonance region data “slide” along the deep inelastic curve with increasing Q2. • for m=2 Bloom-Gilman • high-Q2: t=2 (LT) dominates • weakly depends on Q2 • describes scaling behavior • Low-Q2 • Strong Q2 dependence • duality suppression ofhigher twists De Rujula et al.. Ann. Phys. 103, 315 N u F a c t 0 9 IIT, Chicago**Niculescu et al..Phys. Rev. Lett. 85, 1186**threshold RES xmax Nachtman Variable consumes target mass corrections Quantitative study of BG duality N u F a c t 0 9 IIT, Chicago**Niculescu et al..Phys. Rev. Lett. 85, 1186**Q2 duality application to n interactions CTEQ4 MRS(G) • 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 1.3<W2<1.9 1.9<W2<2.5 N u F a c t 0 9 IIT, Chicago**Searching for duality in neutrino-nucleon scattering**phenomenological models indications N u F a c t 0 9 IIT, Chicago**K. Matsui,T. Sato,T.S. H. Lee, Phys. Rev. C 72, 025204**duality in neutrino scattering off nucleon • Sato-Lee model PRC 72, 025204 • D(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 MA) • 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 N u F a c t 0 9 IIT, Chicago**Nonresonant background**• added noncoherently to get • ½ isospin character • represented by P11-like amplitude • multiplied by constant to get agreement ANL datasee: D. Rein, L. Seghal, Ann. Phys.133, 79 Relativistic Harmonic Oscillator Quark Model (FKR) basis for the Rein Seghal approach for neutrino scattering Simultaneous fit to ANL and BNL data Updated to recent fits obtained by Dortmund group See: KMG, J.T.Sobczyk, Phys.Rev.D77:053001,2008 electron/neutrino-nucleon scattering Original form factors underestimated vector contribution!**Resonances wave functions for third and fourth level of the**oscillator based on Hey et al. Phys. Rept. 96 (1983) 71. Does not contribute N u F a c t 0 9 IIT, Chicago**only resonance-like contribution!**Q2DIS=10 • local duality on quantitative level • saturation for Wmax around 2.0 GeV • violation of BD duality below Q2=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 Lalakulich et al.. W<1.6**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 Quark exchange Gluon exchange I. Niculescu, et al., Phys. Rev. Lett. 85, 1182 electroproduction Valence-like behavior of F2(proton) N u F a c t 0 9 IIT, Chicago**Valence like behavior of the resonance contribution!**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 NuWro 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.. EPA12, 361) • may be useful for neutrino scattering**n-N scattering**scalar transverse (magnetic-like)**KMG, C.Juszczak, J.T.Sobczyk, Nucl. Phys. A781, 227**simultaneous duality for both proton and neutron targets is impossible to observe BG duality? For P33(1232) resonance! 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 P33(1232), P11(1440),D13(1520), S11(1535) N u F a c t 0 9 IIT, Chicago**nonres. background**1s Duality: Charge Current = Neutral Current Based on: arXiv:0907.1886 N u F a c t 0 9 IIT, Chicago**higher moments in x saturates rather for Wmax<1.8**higher moments N u F a c t 0 9 IIT, Chicago**electron-nucleus scattering**Taken from: J. Arrington et al..PRC73, 035205 • 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<Q2<3.3 Q2<5.0 Scaling curve EMC corrected! elastic and quasielastic data are removed N u F a c t 0 9 IIT, Chicago**D(1232)**A. Ankowski NuInt09 proceedings 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 • 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? Spectral function+MAID07 N u F a c t 0 9 IIT, Chicago**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 p N From the nucleon to nucleus structure function N u F a c t 0 9 IIT, Chicago**Taken from: O. Lalakulich et al...PRC79,015206**Compared with the DIS data for Q2=30, 50, 45 (BCDMS) Compared with the DIS data sets for Q2=12.59, 19.95 (CCFR, NuTeV) • A need to consider • larger number of resonances • Nonresonant background • Inclusion of the tail from Quasielastic contribution 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 Q2=0.3 GeV2 • BG duality can help to fine tune the magnitude of nonresonant contribution • Neutrino-nucleon • phenomenological models suggest appearance of the duality in neutrino scatteringoff deuteron-like target • for charged current and neutral current structure functions with W < 1.6/1.8 GeV • xF1 and xF3 (with 1s level of accuracy), for the F2 (with 2s level of accuracy) • violation below Q2=0.3 GeV • the experimental verification is required (waiting for Minerna measurements) • duality in neutrino scattering off nucleus waits for more comprehensive studies N u F a c t 0 9 IIT, Chicago