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

RCQMs Electromagnetic Weak Summary Covariant Electroweak Structure of Light and Strange Baryons Ki-Seok Choi and W. Plessas Karl-Franzens-Universit ä t Graz, Austria

RCQMs Electromagnetic Weak Summary Baryons are considered as colorless bound states Proton of three constituent quarks. The constituent quarks are confined and interact by mutual hyperfine interactions

RCQMs Electromagnetic Weak Summary 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 � free − ˆ � � � V conf V hf � M = ˆ ˆ M free + ˆ ˆ ˆ + ˆ H 2 P 2 M int = free + ij ij i<j Eigenvalue equation : ˆ M | P, J, Σ � = m | P, J, Σ � 3 � Relativistic kinetic energy : H free = � p 2 i + m 2 � i i =1 V conf Confinement : ˆ = V 0 + Cr ij ij

RCQMs Electromagnetic Weak Summary V hf Hyperfine Interaction ( ) ˆ ij Pseudo-scalar-Goldstone-boson-exchange potential (psGBE) L.Y. Glozman, W. Plessas, K. Varga and R. F. Wagenbrunn : Phys. Rev. D 58, 094030 (1998) 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) One-gluon-exchange potential (OGE) L. Theussl, R. F. Wagenbrunn, B. Desplanques and W. Plessas : Eur. Phys. J. A 12, 91 (2001)

RCQMs Electromagnetic Weak Summary Transition Matrix Elements Incoming / Outgoing baryon states : | V, M, J, Σ � = | P, J, Σ � where and

RCQMs Electromagnetic Weak Summary Transition Matrix Elements Incoming / Outgoing baryon states : | V, M, J, Σ � = | P, J, Σ � where and

RCQMs Electromagnetic Weak Summary Point Form Spectator Model Point form spectator model Electromagnetic current � � i Q 2 ) γ µ + Q 2 ) σ µ ν ˜ 1 | ˆ F 1 ( ˜ F 2 ( ˜ J µ � p ′ 1 , σ ′ u ( p ′ 1 , σ ′ spec | p 1 , σ 1 � = e 1 ¯ 1 ) u ( p 1 , σ 1 ) q ν 2 m i Axial current � 2 f π � A γ µ + τ a 1 | ˆ g q A µ q µ � p ′ 1 , σ ′ u ( p ′ 1 , σ ′ a,spec | p 1 , σ 1 � = ¯ 1 ) g qq π ˜ 2 u ( p 1 , σ 1 ) γ 5 Q 2 + m 2 ˜ π

RCQM Electromagnetic Weak Summary Electromagnetic Structure

RCQM Electromagnetic Weak Summary E-M Nucleon Form Factors (I) in psGBE Solid line : PFSM dashed line : NRIA dash-dotted line : Confinement only R. F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas and M. Radici : Phys. Lett. B 511, 33 (2001)

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)

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)

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)

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)

RCQM Electromagnetic Weak Summary Charge Radii 1 2 3 4 5 6 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)

RCQM Electromagnetic Weak Summary Magnetic Moments 1 2 3 4 5 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)

RCQM Electromagnetic Weak Summary Weak Structure

RCQM Electromagnetic Weak Summary Chiral Restoration?

RCQM Electromagnetic Weak Summary Chiral Restoration? Chiral doublets

RCQM Electromagnetic Weak Summary Chiral Restoration? Goldberger-Treiman Relation Nucleon mass Axial charge g π NN = g A M N f π Chiral doublets Pion decay constant Pion Nucleon coupling

RCQM Electromagnetic Weak Summary Chiral Restoration? Goldberger-Treiman Relation Nucleon mass Axial charge g π NN = g A M N f π Chiral doublets Pion decay constant Pion Nucleon coupling Restoration of the chiral symmetry : g π NN ≃ 0 L. Y. Glozman : Phys. Rev. Lett. 99, 191602 (2007)

RCQM Electromagnetic Weak Summary Chiral Restoration? Goldberger-Treiman Relation Nucleon mass Axial charge g π NN = g A M N f π Chiral doublets Pion decay constant Pion Nucleon coupling Restoration of the chiral symmetry : g π NN ≃ 0 L. Y. Glozman : Phys. Rev. Lett. 99, 191602 (2007) Requirement for restoration : g A ≃ 0

RCQM Electromagnetic Weak Summary Comparison of Nucleon Axial Charges 1 2 3 g A ( N ∗ (1675)) = 0 . 84 g A ( N ∗ (1680)) = 0 . 89 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)

RCQM Electromagnetic Weak Summary Axial Charges of Ground States 1 2 3 4 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)

RCQM Electromagnetic Weak Summary Classification T. Melde, W. Plessas and B. Sengl : Phys. Rev. D 77, 114002 (2008)

RCQM Electromagnetic Weak Summary Classification 0.02 -0.15 -0.08 -0.76 T. Melde, W. Plessas and B. Sengl : Phys. Rev. D 77, 114002 (2008)

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)

RCQM Electromagnetic Weak Summary Axial Form Factors of Delta K. S. Choi : PhD Thesis (2011) C. Alexandrou et al. : PoS Lattice 2010, 141 (2010)

RCQM Electromagnetic Weak Summary Summary Performed a consistent study of electromagnetic and weak structure for octet and decuplet baryons within RCQMs. 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. The issue regarding chiral symmetry restoration remains open; the sizes of the for baryon resonances are g A consistent with a recent classification into flavor multiplets. It will be interesting to extend these relativistic studies to electromagnetic and weak transition form factors.