[PPT] - Covariant Electroweak Structure of Light and Strange Baryons PowerPoint Presentation

SLIDE 1

Karl-Franzens-Universität Graz, Austria Summary RCQMs Electromagnetic Weak

Covariant Electroweak Structure

f Light and Strange Baryons

Ki-Seok Choi and W. Plessas

SLIDE 2

Summary RCQMs Electromagnetic Weak

Proton Baryons are considered as colorless bound states

f three constituent quarks.

The constituent quarks are confined and interact by mutual hyperfine interactions

SLIDE 3

Summary RCQMs Electromagnetic Weak

Theoretical Framework

Relativistic quantum mechanics (RQM)

i.e. quantum theory respecting Poincar´ e invariance (theory on H corresponding to a finite number of particles, not a field theory)

Invariant mass operator

ˆ M|P, J, Σ = m|P, J, Σ

Eigenvalue equation : Confinement : ˆ

V conf

ij

= V0 + Crij

Relativistic kinetic energy : Hfree =

3

i=1
p2

i + m2 i

ˆ M = ˆ Mfree + ˆ Mint =

ˆ

H2

free − ˆ

P 2

free +

i<j
ˆ

V conf

ij

+ ˆ V hf

ij

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Hyperfine Interaction ( )

Summary RCQMs Electromagnetic Weak

L. Theussl, R. F. Wagenbrunn, B. Desplanques and W. Plessas : Eur. Phys. J. A 12, 91 (2001)

One-gluon-exchange potential (OGE) Extended-Goldstone-boson-exchange potential (EGBE)

K.Glantschnig, R. Kainhofer, W. Plessas, B. Sengl and R. F. Wagenbrunn : Eur. Phys. J. A 23, 507 (2005)

Pseudo-scalar-Goldstone-boson-exchange potential (psGBE)

L.Y. Glozman, W. Plessas, K. Varga and R. F. Wagenbrunn : Phys. Rev. D 58, 094030 (1998)

ˆ V hf

ij

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Summary RCQMs Electromagnetic Weak

Transition Matrix Elements

Incoming / Outgoing baryon states :

where and

|V, M, J, Σ = |P, J, Σ

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Summary RCQMs Electromagnetic Weak

Transition Matrix Elements

Incoming / Outgoing baryon states :

where and

|V, M, J, Σ = |P, J, Σ

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Summary RCQMs Electromagnetic Weak

Point Form Spectator Model

Point form spectator model Electromagnetic current Axial current

p′

1, σ′ 1| ˆ

Jµ

spec|p1, σ1 = e1¯

u(p′

1, σ′ 1)

F1( ˜

Q2)γµ + i 2mi F2( ˜ Q2)σµν ˜ qν

u(p1, σ1)

p′

1, σ′ 1| ˆ

Aµ

a,spec|p1, σ1 = ¯

u(p′

1, σ′ 1)

gq

Aγµ +

2fπ ˜ Q2 + m2

π

gqqπ˜ qµ

γ5

τa 2 u(p1, σ1)

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Electromagnetic Structure

RCQM Electromagnetic Weak Summary

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RCQM Electromagnetic Weak Summary

E-M Nucleon Form Factors (I) in psGBE

R. F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas and M. Radici : Phys. Lett. B 511, 33 (2001)

Solid line : PFSM dashed line : NRIA dash-dotted line : Confinement only

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RCQM Electromagnetic Weak Summary

E-M Sigma Form Factors

K. S. Choi : PhD Thesis (2011)
H. W. Lin and K. Orginos : Phys. Rev. D 79, 074507 (2009)
T. V. Cauteren et al. : Eur. Phys. J. A 20, 283 (2004)

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RCQM Electromagnetic Weak Summary

E-M Xi Form Factors

K. S. Choi : PhD Thesis (2011)
H. W. Lin and K. Orginos : Phys. Rev. D 79, 074507 (2009)
T. V. Cauteren et al. : Eur. Phys. J. A 20, 283 (2004)

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RCQM Electromagnetic Weak Summary

E-M Delta Form Factors

K. S. Choi : PhD Thesis (2011)
C. Alexandrou et al. : Phys. Rev. D 79, 014507 (2009)

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RCQM Electromagnetic Weak Summary

E-M Omega Form Factors

K. S. Choi : PhD Thesis (2011)
C. Alexandrou et al. : Phys. Rev. D 79, 014507 (2009)

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RCQM Electromagnetic Weak Summary

Charge Radii

1. K. Berger, R. F. Wagenbrunn and W. Plessas :
Phys. Rev. D 70, 094027 (2004)
2. K. S. Choi : PhD Thesis (2011)
3. D. Merten et al. : Eur. Phys. J. A 14, 477(2002)
T. V. Cauteren et al. : Eur. Phys. J. A 20, 283 (2004)
4. H. W. Lin and K. Orginos :
Phys. Rev. D 79, 074507 (2009)
D. B. Leinweber et al. :
Phys. Rev. D 46, 3067(1992)
5. PDG (2010)
6. R. Pohl et al. : Nature 466, 213(2010)

4 1 2 5 6 3

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RCQM Electromagnetic Weak Summary

Magnetic Moments

1 2 4 5 3

1. K. Berger, R. F. Wagenbrunn and W. Plessas :
Phys. Rev. D 70, 094027 (2004)
2. K. S. Choi : PhD Thesis (2011)
3. D. Merten et al. :
Eur. Phys. J. A 14, 477(2002)
T. V. Cauteren et al. :
Eur. Phys. J. A 20, 283 (2004)
4. H. W. Lin and K. Orginos :
Phys. Rev. D 79, 074507 (2009)
D. B. Leinweber et al. :
Phys. Rev. D 46, 3067(1992)
5. PDG (2010)

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RCQM Electromagnetic Weak Summary

Weak Structure

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RCQM Electromagnetic Weak Summary

Chiral Restoration?

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RCQM Electromagnetic Weak Summary

Chiral Restoration?

Chiral doublets

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RCQM Electromagnetic Weak Summary

Chiral Restoration?

Chiral doublets

gπNN = gAMN fπ

Pion Nucleon coupling Pion decay constant Nucleon mass Axial charge

Goldberger-Treiman Relation

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RCQM Electromagnetic Weak Summary

Chiral Restoration?

Chiral doublets Restoration of the chiral symmetry :

gπNN ≃ 0

L. Y. Glozman : Phys. Rev. Lett. 99, 191602 (2007)

gπNN = gAMN fπ

Pion Nucleon coupling Pion decay constant Nucleon mass Axial charge

Goldberger-Treiman Relation

SLIDE 21

RCQM Electromagnetic Weak Summary

Chiral Restoration?

Chiral doublets Restoration of the chiral symmetry :

gπNN ≃ 0

L. Y. Glozman : Phys. Rev. Lett. 99, 191602 (2007)

gA ≃ 0

Requirement for restoration :

gπNN = gAMN fπ

Pion Nucleon coupling Pion decay constant Nucleon mass Axial charge

Goldberger-Treiman Relation

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RCQM Electromagnetic Weak Summary

Comparison of Nucleon Axial Charges

1. K. S. Choi, W. Plessas and R. F. Wagenbrunn : Phys. Rev. C 81, 028201 (2010)
2. T. T. Takahashi and T. Kunihiro : Phys. Rev. D 78, 011503 (2008) and further lattice QCD calculations
3. L. Y. Glozman, A. V. Nefediev : Eur. Phys. J. A 12, 91 (2001)

1 2 3

gA(N ∗(1675)) = 0.84 gA(N ∗(1680)) = 0.89

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RCQM Electromagnetic Weak Summary

1. K. S. Choi, W. Plessas and R. F. Wagenbrunn : Phys. Rev. C 81, 028201 (2010)
K. S. Choi, W. Plessas and R. F. Wagenbrunn : Phys. Rev. D 82, 014007 (2010)
2. H. W. Lin and K. Orginos : Phys. Rev. D 79, 034507 (2009)
3. G. Erkol, M. Oka and T. T. Takahashi : Phys. Lett. B 686, 36 (2010)
4. F. J. Jiang and B. C. Tiburzi : Phys. Rev. D 80, 077501 (2009)
F. J. Jiang and B. C. Tiburzi : Phys. Rev. D 78, 017504 (2008)

Axial Charges of Ground States

1 2 3 4

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RCQM Electromagnetic Weak Summary

Classification

T. Melde, W. Plessas and B. Sengl : Phys. Rev. D 77, 114002 (2008)

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RCQM Electromagnetic Weak Summary

Classification

T. Melde, W. Plessas and B. Sengl : Phys. Rev. D 77, 114002 (2008)

0.02

0.15
0.08
0.76

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RCQM Electromagnetic Weak Summary

Axial and Pseudo-scalar Form Factors of nucleon in psGBE

L. Y. Glozman, M.Radici, R.F. Wagenbrunn, S. Boffi, W. Klink and W. Plessas : Phys. Lett. B 516, 183 (2001)

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RCQM Electromagnetic Weak Summary

Axial Form Factors of Delta

C. Alexandrou et al. : PoS Lattice 2010, 141 (2010)
K. S. Choi : PhD Thesis (2011)

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RCQM Electromagnetic Weak Summary

Summary

Covariant predictions of RCQMs show generally considerable relativistic effects and describe experimental data well. In cases, where no experiments exist, there is reasonable agreement with lattice QCD results. Performed a consistent study of electromagnetic and weak structure for octet and decuplet baryons within RCQMs. The issue regarding chiral symmetry restoration remains

pen; the sizes of the for baryon resonances are

consistent with a recent classification into flavor multiplets. It will be interesting to extend these relativistic studies to electromagnetic and weak transition form factors.