quark-hadron duality in lepton scattering off nucleons/nuclei from the nucleon to the nucleus
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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
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