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Vector and axial-vector properties of SU(3) baryons within a chiral soliton model

Vector and axial-vector properties of SU(3) baryons within a chiral soliton model. Ghil-Seok Yang, Hyun-Chul Kim. NTG ( N uclear T heory G roup), Inha University , Incheon , Korea. 1. 2. G. S. Yang, H.-Ch. Kim , [ arXiv:hep-ph /1010.3792, hep-ph /1102.1786]

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Vector and axial-vector properties of SU(3) baryons within a chiral soliton model

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  1. Vector and axial-vector properties of SU(3) baryons within a chiral soliton model Ghil-Seok Yang, Hyun-Chul Kim NTG (Nuclear Theory Group), Inha University, Incheon,Korea 1. 2. G. S. Yang, H.-Ch. Kim, [arXiv:hep-ph/1010.3792,hep-ph/1102.1786] 2. G. S. Yang, H.-Ch. Kim, M. V. Polyakov, Phys. Lett. B 695, p214, Jan, (2011) 3. G. S. Yang, H.-Ch. Kim, Prog. Theor. Phys. Suppl. No. 186 pp. 222-227 (2010) 4. G. S. Yang, ph.D Thesis, 2010 (unpublished), Ruhr-Universität, Bochum, Germany Hadron Nuclear Physics 2011 “Quarks in hadrons, nuclei, and hadronicmatter” Pohang, Feb. 21, 2011

  2. Outline • SU(3) baryons ( exotic states ) • Motivation ( Θ+, N* ) • Chiral Soliton Model [Mass splittings] [Vector Transitions] - Magnetic Moments - Transition Magnetic Moments - Radiative Decay Widths [Axial-Vector Transitions] - Axial-vector Coupling Constants - Decay Widths • Summary

  3. SU(3) Baryons Fundamental Particles ? multiplets (proton, neutron) : isospin [ SU(2)] → higher symmetry (Σ, K,···) : SU(3) Naïve Quark Model(up, down, strange light quarks): SU(3) scheme to classify particles with the same spin and parity Hadron [ baryon (qqq), meson (qq) ] : SU(3) color singlet representation 10*(10) Why not 4, 5, 6, … quark states ? Nothing prevents such states to exist Y. s. Oh and H. c. Kim, Phys. Rev. D 70, 094022 (2004) SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

  4. Σ+ Σ0 Σ- (uudss) (uddss) Ξ-- Ξ+ Ξ0 Ξ- 3/2 3/2 3/2 3/2 Anti-decuplet (10) 10 10 10 Motivation 1997, Diakonov, Petrov, andPolyakov : Narrow 5-quark resonance (q4q : Θ+) ( M =1530, Γ~15MeV from Chiral SolitonModel) Y Θ+(uudds) S = 1 2 p* ( uud ) ( udd) n* 1 S = 0 T3 -½ ½ S = -1 S = -2 -1 SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  5. Motivation Successful searches for Θ+ (2003~2005) : 2007 PDG SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  6. Σ+ Σ0 Σ- (uudss) (uddss) Ξ-- Ξ+ Ξ0 Ξ- 3/2 3/2 3/2 3/2 10 10 10 Motivation ? Unsuccessful searches for Θ+ (2006~2008) : 2010 PDG New positive experiments (2005 - 2010) ■DIANA2010 (Θ+) : M = 1538±2, Γ= 0.39±0.10 MeV (K+n → K0p, higher statistical significance : 6σ - 8σ) [confirmed by LEPS, SVD, KEK, …] ■GRAAL (N* ) : M = 1685±0.012 MeV, (CBELSA/TAPS, LNS-Sendai, …) Y Θ+(uudds) S = 1 2 p* ( uud) ( udd) n* 1 S = 0 T3 -½ ½ -1 Anti-decuplet (10) ??? SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  7. Motivation Problems in the previous solitonic approaches D.P.P : Diakonov, Petrov, Polyakov, Z. Physics. A. 359, 305-314 (1997) E.K.P : Ellis, Karliner, Praszalowicz, JHEP. 0405, 002 (2004) χQSM : Tim Ledwig, H.-Ch. Kim, K. Goeke, Phys. Rev. D. 78, 054005 & Nucl. Phys. A 811 353 2008 Masssplittings of baryons : crucial ! → model parameters : vectorand axial-vector properties in particular, the effect of SU(3) symmetry breaking SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  8. Chiral Soliton Model Chiral Soliton Model : Effective and relativistic low energy theory : Large Nclimit : meson field → soliton : Quantizing SU(3) rotated-meson fields → Collective Hamiltonian, model baryon states HedgehogAnsatz: Collective quantization SU(2) Witten imbedding into SU(3): SU(2) X U(1) SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  9. Chiral Soliton Model (mass) Collective Hamiltonian for flavor symmetry breakings + Y Y Y Mass Mass Δ+ Δ0 ( ddd)Δ- Δ++( uuu) ( udd) n p( uud) Δ N 1 1 940 1232 Λ Λ -½ ½ -3/2 -3/2 -½ ½ 1116 T3 T3 1385 1193 Σ* Σ*- Σ0 Σ0 Σ- Σ+ Σ*0 Σ*+ 1533 1318 Ξ* -1 -1 Ξ*- Ξ*0 Ξ ( dss)Ξ- Ξ0( uss) Ω- -2 1673 Ω-( sss) Decuplet (10): J p = 3/2+ Octet (8): J p = 1/2 + SU(3) flavor symmetry breaking + Isospin symmetry breaking SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  10. Two sources for the isospin symmetry breaking • mass differences of up and down quarks (hadronic part) • Electromagnetic interactions (EM part) Chiral Soliton Model (mass) • In order to take fully into account the masses of • the baryon octet as input, it is inevitable to consider • the breakdown of isospin symmetry. SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  11. k 939.6 938.3 Y B(p) B(p) ( udd) n p( uud) 1 p - k 1189 p p 1197 Λ -½ ½ -1 1 T3 1315 1321 Σ0 Σ- Σ+ -1 ( dss)Ξ- Ξ0( uss ) Chiral Soliton Model (mass) EM mass corrections Electromagnetic (EM) self-energy Gasser, Leutwyler, Phys.Rep 87, 77“Quark Masses” ΔMB = MB1 – MB2 = (ΔMB )H + (ΔMB )EM ( p – n )exp~ –1.293 MeV ( p – n ) EM~0.76MeV SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  12. Chiral Soliton Model (mass) In the ChSM, It can be further reduced to Because of Bose symmetry G. S. Yang, H.-Ch. Kim and M. V. Polyakov, Phys. Lett. B 695, 214 (2011) SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  13. Chiral Soliton Model (mass) Weinberg-Treiman formula MEM(T3) = αT32 + βT3+ γ Dashenansatz ΔMEM ~ κT32~ κ’Q2 SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  14. Chiral Soliton Model (mass) Coleman-Glashow relation SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  15. Chiral Soliton Model (mass) Χ2 fit Coleman-Glashow relation SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  16. Chiral Soliton Model (mass) SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  17. [ D.W.Thomas et al.] [ PDG, 2010 ] [ GW, 2006 ] [ Gatchina, 1981 ] Chiral Soliton Model (mass) ■Physical mass differences of baryon decuplet SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  18. Chiral Soliton Model Two advantages offered by the model-independent approach in the χSM. 1. the very same set of dynamical model-parametersallows us to calculate the physical observables of all SU(3) baryons regardless of different SU(3) flavor representations of baryons, namely octet, decuplet, antidecuplet, and so on. 2. these dynamical model-parameters can be adjusted to the experimental data of the baryon octet which are well established with high precisions. [8] Mass : α, β, γ(for octet, decuplet, antidecuplet,…) Vector transitions : wi (i=1,2,…,6) Axial transitions : ai (i=1,2,…,6) model-parameters [10], [10] Baryons l = l0(1 + cΔT): linear expansion coefficient of a wire, c SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  19. Chiral Soliton Model (mass) Mass splittings within a Chiral Soliton Model Formulae for Baryon Octet Masses (ΔM)EM (ΔM)H hadronic mass part in terms of δ1 and δ2 SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  20. Chiral Soliton Model (mass) Formulae for Baryon Decuplet Masses hadronic mass part in terms of δ1 and δ2 SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  21. Chiral Soliton Model (mass) Formulae for Baryon Anti-Decuplet Masses hadronic mass part in terms of δ3 SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  22. Chiral Soliton Model (mass) Present analysis reproduces all kind of well-known mass relations ■Coleman-Glashow relation is still satisfied ■Generalized Gell-Mann-Okubo relation When the effect of the isospin sym. br is turned off, • Generalized Guadagniniformulae SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  23. Chiral Soliton Model (mass) Baryon octet masses SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  24. Chiral Soliton Model (mass) Employing the value of the ratio [Using Θ+ & Ξ-- masses, based on χQSM: ΣπN=(74±12) MeV, P. Schweitzer, Eur. Phys. J. A 22, 89 (2004)] [GWU analysis of πN scattering data : ΣπN=(64±8) MeV, Pavan et al, PiN Newslett.16:110-115,2002] [Updated analysis in the pχQM: ΣπN=(79±7) MeV, Inoue, et al, Phys. Rev. D 69 035207(2004)] SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  25. Chiral Soliton Model (mass) Baryon decuplet masses SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  26. Chiral Soliton Model (mass) Baryon antidecupletmasses SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  27. Chiral Soliton Model (Vector) Vector transitions with The full expression for the magnetic transitions μBB’ = μBB’(0) + μBB’(op)+ μBB’(wf) SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  28. Chiral Soliton Model (Vector) 2. Magnetic transitions SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  29. Chiral Soliton Model (Vector) 2. Magnetic transitions Magnetic moments for baryon decuplet(in units of μN) mass splitting analysis SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  30. Chiral Soliton Model (Vector) 2. Magnetic transitions Magnetic moments for baryon antidecuplet (in units of μN) SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  31. Chiral Soliton Model (Vector) 2. Magnetic transitions Transition magnetic moments (in units of μN) Exp. |μNΔ|~3.1 1.61±0.08 <0.82 isospin asymmetry mass splitting analysis SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  32. Σ+ Σ0 Σ- Y Θ+ 2 1 Ξ-- Ξ0 Ξ- 3/2 3/2 3/2 T3 -½ ½ 10 10 10 -1 Ξ+ 3/2 Chiral Soliton Model (Vector) 2. Magnetic transitions Partial decay widths of the radiative decays (in units of keV) Consistent with GRAAL data - “Narrow nucleon resonance N* (1685) has much stronger photocoupling to the n than to the p” • [ Kuznetsov, Polyakov, T. Boiko, J.Jang, A. Kim, W. Kim, • H.S. Lee, A. Ni,G. S. Yang, Acta. Phys. Polon. B 39, 1949 (2008) ] n* p* - Good agreement with estimates for non-strange members of antidecupletN* from Chiral SolitonModel - Being a candidate for the non-strange member of the anti-decuplet supports the existence of theΘ+ SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  33. Chiral Soliton Model (axial-vector) Axial-vector transitions with The full expression for the axial-vector transitions g1BB’ = g1BB’(0) + g1BB’(op)+ g1BB’(wf) SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  34. Chiral Soliton Model (axial-vector) Axial-vector transitions a1 = -3.98 ± 0.01 a2 = 3.12 ± 0.03 a3 = 0.62± 0.13 a4 = 2.91± 0.07 a5 = -0.22± 0.03 a6 = -0.80± 0.04 SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  35. Chiral Soliton Model (axial-vector) Axial-vector transitions 84.7±0.02 30.4±0.29 ΓΘ+n = 0.80±0.12 MeV PDG 2007(Θ+) : Γ= 0.9±0.3 MeV ΓΘ+N = 2ΓΘ+n = 1.61±0.25 MeV DIANA 2010 (Θ+) : Γ= 0.38±0.11 MeV ΓΘ+N(0) = 0.52±0.13 MeV ΓΘ+N(op)=1.31±0.07 MeV ΓΘ+N(wf)=0.36±0.01 MeV SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  36. Chiral Soliton Model (Results) ΓΘ+ : 0.38±0.11MeV (DIANA), 0.9±0.3MeV (2007 PDG) D.P.P : Diakonov, Petrov, Polyakov, Z. Physics. A. 359, 305-314 (1997) E.K.P : Ellis, Karliner, Praszalowicz, JHEP. 0405, 002 (2004) χQSM : Tim Ledwig, H.-Ch. Kim, K. Goeke, Phys. Rev. D. 78, 054005 & Nucl. Phys. A 811 353 2008 SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

  37. Σ+ Σ0 Σ- Y Θ+ 2 1 Ξ-- Ξ0 Ξ- 3/2 3/2 3/2 T3 -½ ½ 10 10 10 -1 Ξ+ 3/2 Summary Chiral SolitonModel : “model-independent approach” ●Mass splittings : SU(3) and isospin symmetry breakings with EM → No Free Parameter ! ●Masses, magnetic moments (8, 10) Magnetic transitions and decay widths (8, 10) → very good agreement with experimental data ● MΘ+= 1524 MeV [LEPS, DIANA], MN*= 1685 MeV [GRAAL] used as input, : reliable value within a chiral soliton model ● ΓΘ+= 1.61±0.25MeV [DIANA 2010 : 0.38±0.11]. small decay width is reproduced ● The study for the mass splittings to the 2nd order : done [hep-ph 1102.1786, Yang & Kim] Consequent results will appear elsewhere n* p* SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  38. Спасибо Thank you ありがとうございます 감사합니다 Danke schön TERIMA KASIH 謝謝

  39. Mixings of baryon states Chiral Soliton Model (mass) Mixing coefficients SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  40. Chiral Soliton Model (Vector) 1. Electric transitions Gell-Mann-Nishijima relation

  41. Chiral Soliton Model (mass) Octet, Decuplet ( Θ+, N*) Anti-decuplet Parameters to be fixed: Input for fixing the parameters ( χ2fitting) • Experimental data for the all masses of the baryon octet • Experimental values for the Σ* → I1 • Experimental values for the Θ+ & N* SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  42. Chiral Soliton Model (mass) Moment of inertia The ratio of current quark masses χ2fitting from the octet mass formulae ( Gasser, Leutwyler: R = 43.5±2.2) J. Gasser & H. Leutwyler, Phys. Rept. 87, 77 (1982) & PDG 2008 More complete analysis gives us more information SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  43. Chiral Soliton Model (Vector) 1. Electric transitions Flavor SU(3) breaking: The Ademollo-Gatto Theorem Mixing coefficients from mass splittings

  44. Chiral Soliton Model (Vector) 1. Electric transitions

  45. Chiral Soliton Model (Vector) Vector transitions with Sachs’ form factor f E(q2) = f1(q2) + f2(q2) [q2/(2MN)2] fM(q2) = f1(q2) + f2(q2) Y 1 p n Λ T3 -½ ½ -1 1 Σ0 Σ- Σ+ -1 Ξ- Ξ0

  46. Isobar Model

  47. Isobar Model

  48. Mixings of baryon states Constraint for the collective quantization : Chiral Soliton Model Model baryon state SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  49. Chiral Soliton Model Mixing coefficients SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

  50. Chiral Soliton Model (mass) δN* SU(3) baryons MotivationMass splitting Vector Axial-vector Summary

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