July 20-25, 2009 N 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?

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/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

Bloom-Gilman duality epeX

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

,...4,22

2)(1

0

22

2)(2

))((),(

Q

QAQxFxdxM s

mmm

•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

2

21'

Q

M

x

expansion

0|)}0()({|0Im 4

TWISTS

OPE

JxJTxedW iqx

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

July 20-25, 2009 N 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

July 20-25, 2009 N 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<W2<2.5

1.3<W2<1.9

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

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

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

K. Matsui,T. Sato,T.S. H. Lee, Phys. Rev. C 72, 025204

electron/neutrino-nucleon scattering

Relativistic Harmonic Oscillator Quark Model (FKR)basis for the Rein Seghal approach for neutrino scattering

)2/1(

2

222

41),()(

N

VV M

QQWGQG

Updated to recent fitsobtained by Dortmund groupSee: KMG, J.T.Sobczyk,

Phys.Rev.D77:053001,2008

)2/1(

2

222

41),()(

N

RSAA M

QQWGQG

Simultaneous fit to ANL and BNL data

Nonresonant background•added noncoherently to get•½ isospin character

•represented by P11-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!

July 20-25, 2009 N 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

only resonance-like contribution!

•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

Q2DIS=10

Lalakulich et al.. W<1.6

July 20-25, 2009 N 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

12

12

)/1(

)/1(

P

R

xF

xFsea

val

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 ComponentQuark-Hadron Duality

July 20-25, 2009 N u F a c t 0 9 IIT, Chicago

Valence like behavior of the resonance contribution!

data from I. Niculescu et al., Phys. Rev. Lett. 85, 1186

very naive constructionbut effective

valRES

RESRES

FF

parFF

22

22

4.0

or )(4.0

60.0)(/)modelquark ( dataresRresR

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 GeneratorGENI MC Generator

July 20-25, 2009

0 pn -N scattering

scalar

transverse (magnetic-like)

KMG, C.Juszczak, J.T.Sobczyk, Nucl. Phys. A781, 227

2

1

),(

),(

3))1232(,,(

))1232(,,(

33

33

DISneutronF

DISprotonF

PRESneutronF

PRESprotonF

CCi

CCi

CCi

CCi

BGduality?

Duality for the Isoscalar like (deuteron like) targetif appears then duality for neutrino-nucleon scattering

)(3

8)(

)(9

4)(

neutronRisoscalarR

protonRisoscalarR

6

)(

)(

neutronR

protonR simultaneous duality for bothproton and neutron targets is impossible to observe

For P33(1232) resonance!

July 20-25, 2009 N 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 P33(1232), P11(1440), D13(1520), S11(1535)

July 20-25, 2009 N u F a c t 0 9 IIT, Chicago

4

1

)(

)(

)(

)(

,3

,3

,3

,3 RESF

RESF

DISF

DISFNCC

NNC

NCC

NNC

nonres. backgroundDuality:

Charge Current=

Neutral Current1Based on: arXiv:0907.1886

July 20-25, 2009 N u F a c t 0 9 IIT, Chicago

higher moments

higher moments in 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?

0.8<Q2<3.3

Q2<5.0

Scaling curve EMC corrected!

elastic and quasielastic dataare removed

Taken from: J. Arrington et al..PRC73, 035205

July 20-25, 2009 N 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)

Xede

Spectral function+MAID07

Quasi-elastic peak

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 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

July 20-25, 2009 N 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

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 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 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 Q2=0.3 GeV• the experimental verification is required (waiting for Minera

measurements)• duality in neutrino scattering off nucleus waits for more

comprehensive studies