Date post: | 15-Jan-2016 |
Category: |
Documents |
View: | 215 times |
Download: | 0 times |
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