On description of On description of resonance region in the resonance region in the

FKR modelFKR model

Krzysztof M. GraczykKrzysztof M. Graczyk, Jan T. Sobczyk, Jan T. SobczykInstitute of Theoretical PhysicInstitute of Theoretical Physicss

University of WrocławUniversity of WrocławPolandPoland

MotivationsMotivations Modification of the Modification of the FKRFKR model model Rein-Sehgal Rein-Sehgal

modelmodel MC MC generators generators Model which will better fit to experimental data in Model which will better fit to experimental data in

(1232) region(1232) region

I.I. Another idea of introducing form factorsAnother idea of introducing form factors (effective) (effective) We still keep only We still keep only two two form factors (form factors (vector and axialvector and axial))

II.II. Lepton mass in Charged Current Lepton mass in Charged Current N scatteringN scattering

III.III. 7 new resonances7 new resonances

How modification How modification II affect affectss cross section for cross section for Single Pion Production (Single Pion Production (SPPSPP) in Neutral Current () in Neutral Current (NCNC)) N N scattering?scattering?

FKR and RS modelsFKR and RS models

Feynman, Kislinger, and Ravndal 71Feynman, Kislinger, and Ravndal 71• Electroproduction: Ravndal 71Electroproduction: Ravndal 71• Neutrinoproduction: Ravndal 72Neutrinoproduction: Ravndal 72,, 73, Rein and Sehgal 81, 73, Rein and Sehgal 81,

Rein 87Rein 87• Baryon wave function Baryon wave function SymSym[SU([SU(33))xSU(2)xSU(2)xO(3)] xO(3)]

representationrepresentation

Elastic Limit of the description

ELASTIC SCATTERING

Form Factors of the FKR/RS model areexpressed by elastic nucleon form factors!!!

AA

had

VV

had

jWqGA

jWqGV

),(

),(2

2

Two Form Factors

FKR MODEL

This is not the only way of computing form factors

2/)1(

2

22

2

22

411),(

N

V W

q

M

qqWG

)2/1(

2

22

2,

22

, 411)(

N

AVAV M

q

M

qqG

Electroproduction NeutrinoproductionF. Ravndal, Phys. Rev. D 4, 1466 (1971) F. Ravndal, Nuovo Cimento, 18A 385 (1973)

M. Osipenko et al., The proton structure function F2 in the resonance regio, arXiv:hep-ex/0301033

Form Factor model for (1232) excitation O. Lalakulich, E. A. Paschos and G. Piranishvili, Phys. Rev. D 74 (2006) 014009

F2 underestimated in the FKR model Let’s introduce another Vector FF

FKR Form Factor EvaluationFKR Form Factor EvaluationForm Factor model for (1232) excitation

V

N

V CMW

q

WM

WMG 3

22

3

2

2

1432

1

New effective vector form factor

Significant correction for small Q2

Axial part

New effective axial form factor

2

2

22

2

2

5

311

2.1

AA

A

Mq

Mq

C

O. Lalakulich, E. A. Paschos, Phys.Rev.D71:074003,2005

interactioninteraction

SPP in NC SPP in NC N scatteringN scattering

We have different proportion of the vector and axial contribution!!!

almost 2 times more

D. Rein, L. Sehgal Annals Phys.133:79,1981.

SPP in NC SPP in NC N scatteringN scatteringW< 2 GeV

SPP in CC SPP in CC N scatteringN scatteringW< 2 GeV

The matrix elements of the Jt and Jz components of the hadronic current were computed separately

Lepton massLepton mass

Effect of the leptonmass

We introduced lepton mass into the model.It was done in a different way than V. Naumov et al..

Nucl.Phys.Proc.Suppl.139:158-161,2005

Some difficulties !!! to get a space part of the resonances wave functions for third and fourth level of the oscillator, Hey et al. Phys. Rept. 96 (1983) 71.

Does not contribute

F2(ep) structure functions

18

25

Only resonancecontribution

SummarySummary

We proposed three improvements:We proposed three improvements:

1.1. New form factors – the most New form factors – the most significant, in particular for the significant, in particular for the 11production in NC reactionsproduction in NC reactions

2.2. Lepton mass – relevant for small Q2Lepton mass – relevant for small Q2

3.3. Heavier resonances – not significant Heavier resonances – not significant