On description of resonance region in the FKR model

Krzysztof M. Graczyk, Jan T. Sobczyk Institute of Theoretical Physics University of Wrocław Poland



Motivations

 Modification of the FKR model  model MC generators  Rein-Sehgal Model which will better fit to experimental data in D (1232) region I.

II.

Another idea of introducing form factors (effective)  We still keep only

two

form factors (

vector and axial

) Lepton mass in Charged Current n N scattering III. 7 new resonances How modification

I

affects cross section for Single Pion Production (

SPP

) in Neutral Current (

NC

) n N scattering?

FKR and RS models

 Feynman, Kislinger, and Ravndal 71 • Electroproduction: Ravndal 71 • Neutrinoproduction: Ravndal 72, 73, Rein and Sehgal 81, Rein 87 • Baryon wave function  Sym[SU(3)xSU(2)xO(3)] representation

Two Form Factors

V A



had had

  

G G V A

( (

q q

2  2  , ,

W W

) )

j j V



A

 FKR MODEL Elastic Limit of the description ELASTIC SCATTERING Form Factors of the FKR/RS model are expressed by elastic nucleon form factors!!!

This is not the only way of computing form factors

G

(

W

,

q

2 )    1 

q

2

M V

2    2   1 

q

2 4

W

2   ( 1 

N

) / 2

G V

,

A

(

q

2 )   1 

q

2

M V

2 ,

A

 2   1 

q

2 4

M

2   ( 1 / 2 

N

) Electroproduction F. Ravndal, Phys. Rev. D 4, 1466 (1971) Neutrinoproduction F. Ravndal, Nuovo Cimento,

18A

385 (1973)

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

M. Osipenko et al., The proton structure function

F2 in the resonance regio, arXiv:hep-ex/0301033

Form Factor model for

D

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

FKR Form Factor Evaluation

Form Factor model for

D (1232)

excitation

G V

New effective vector form factor  2 1 3 

M



W

4

WM

   1  

W q

2 

M

 2   3 2 

N

2

C

3

V

Significant correction for small Q2

Axial part

nN

interaction

New effective axial form factor

C A

5    1  1 .

2

q

2

M

2

A

  2   1 

q

2 3

M

2

A

  2

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

SPP in NC

n

N scattering

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

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

almost 2 times more

SPP in NC

n

N scattering

W< 2 GeV

SPP in CC

n

N scattering

W< 2 GeV

Lepton mass

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

The matrix elements of the J t and J z components of the hadronic current were computed separately Effect of the lepton mass

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 Only resonance contribution 25 18

Summary

 1.

2.

3.

We proposed three improvements: New form factors – the most significant, in particular for the 1 p0 production in NC reactions Lepton mass – relevant for small Q2 Heavier resonances – not significant