Ghil-Seok Yang, Hyun-Chul Kim NTG (Nuclear Theory Group), Inha University, Inha University, Incheon, Korea G. S. Yang, H.-Ch. Kim, [arXiv:hep-ph/ , hep-ph/ ] 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 (2010) 4. G. S. Yang ph.D Thesis 4. G. S. Yang, ph.D Thesis, 2010 (unpublished), Ruhr-Universität, Bochum, Germany

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

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

Θ , Diakonov, Petrov, and Polyakov : Narrow 5-quark resonance (q 4 q : Θ + ) ( M = 1530, Γ ~ 15 MeV from Chiral Soliton Model ) ( uddss ) T3T3 1 Θ + Θ + ( uudds ) ½-½ 2 Ξ+Ξ+Ξ+Ξ+3/2 Ξ0Ξ0Ξ0Ξ03/2 Ξ-Ξ-Ξ-Ξ-3/2 Ξ --3/2 Σ-Σ-Σ-Σ-10 Σ0Σ0Σ0Σ010 Σ+Σ+Σ+Σ+10 ( uudss ) p * p * ( uud ) n * ( udd ) n * Y S = 1 S = 0 Anti-decuplet Anti-decuplet (10) S = -1 S = -2

Successful searches for Θ + (2003~2005) : 2007 PDG Successful searches for Θ + (2003~2005) : 2007 PDG

Unsuccessful searches for Θ + (2006~2008) : 2010 PDG Unsuccessful searches for Θ + (2006~2008) : 2010 PDG ??? ? New positive experiments ( ) ■ DIANA 2010 ( Θ + ) : M = 1538±2, Γ= 0.39±0.10 MeV (K + n → K 0 p, higher statistical significance : 6σ - 8σ) LEPS, SVD, KEK [confirmed by LEPS, SVD, KEK, …] ■ GRAAL (N* ) : M = 1685±0.012 MeV, CBELSA/TAPS, LNS-Sendai ( CBELSA/TAPS, LNS-Sendai, …) (uddss) T3T3 1 Θ + Θ + ( uudds ) ½-½ 2 Ξ+Ξ+Ξ+Ξ+ 3/2 Ξ0Ξ0Ξ0Ξ0 3/2 Ξ-Ξ-Ξ-Ξ- 3/2 Ξ -- 3/2 Σ-Σ-Σ-Σ- 10 Σ0Σ0Σ0Σ0 10 Σ+Σ+Σ+Σ+ 10 (uudss) p * p * ( uud ) n * ( udd ) n * Y S = 1 S = 0 Anti-decuplet Anti-decuplet (10)

Mass splittings of baryons : crucial ! → model parameters : vector and axial-vector properties → model parameters : vector and axial-vector properties in particular, the effect of SU(3) symmetry breaking in particular, the effect of SU(3) symmetry breaking Problems in the previous solitonic approaches D.P.PE.K.PχQSM Considered Effects H SU(3) H. Input Masses [MeV] N * N * (1710) Θ + Θ + (1539±2) Ξ -- Ξ -- (1862±2) Σ πN [MeV] 4573Predicted → 41 Results I 2 [ fm ] m s α [MeV] m s β [MeV] m s γ [MeV] c Γ Θ+ [MeV] 15 for sym11.1 for sym0.71 for sym D.P.P : Diakonov, Petrov, Polyakov, Z. Physics. A. 359, (1997) E.K.P : Ellis, Karliner, Praszalowicz, JHEP. 0405, 002 (2004) χQSM : Tim Ledwig, H.-Ch. Kim, K. Goeke, Phys. Rev. D. 78, & Nucl. Phys. A

: Effective and relativistic low energy theory : Large N c limit : meson field → soliton : Quantizing SU(3) rotated-meson fields → Collective Hamiltonian, model baryon states Chiral Soliton Model Hedgehog Ansatz : Collective quantization SU(2) Witten imbedding into SU(3): SU(2) X U(1)

Octet (8) Octet (8) : J p = 1/2 + Decuplet Decuplet (10) : J p = 3/2 + Y T3T3 Y Y T3T3 1 N NN N Ξ ΞΞ Ξ Λ Σ0Σ0Σ0Σ Δ ΔΔ Δ Σ*Σ*Σ*Σ* Ξ*Ξ*Ξ*Ξ* Ω-Ω-Ω-Ω- n ( udd ) n p p ( uud ) Ξ - ( dss)Ξ - Ξ 0 Ξ 0 ( uss ) Σ-Σ-Σ-Σ- Σ+Σ+Σ+Σ+ Λ Σ0Σ0Σ0Σ0 -½ ½ Mass Δ - ( ddd )Δ - Δ ++ Δ ++ ( uuu ) Δ0Δ0Δ0Δ0 Δ+Δ+Δ+Δ+ Ω - Ω - ( sss ) Ξ*-Ξ*-Ξ*-Ξ*- Ξ*0Ξ*0Ξ*0Ξ*0 Σ*-Σ*-Σ*-Σ*- Σ*0Σ*0Σ*0Σ*0 Σ*+Σ*+Σ*+Σ*+ -½½ -3/ Mass SU(3) flavor symmetry breaking + Isospin symmetry breaking + Collective Hamiltonian for flavor symmetry breakings

★ 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. ★ Two sources for the isospin symmetry breaking 1. mass differences of up and down quarks (hadronic part) 2.Electromagnetic interactions (EM part)

Δ M B = M B 1 – M B 2 = ( Δ M B ) H + ( Δ M B ) EM B(p) k p p p - k EM mass corrections Electromagnetic (EM ) self-energy EM [MeV]Exp. (p – n) EM 0.76±0.30 ΣΣ (Σ + – Σ - ) EM -0.17±0.30 ΞΞ (Ξ 0 –Ξ - ) EM -0.86±0.30 ( p – n ) exp ~ – MeV ( p – n ) EM ~0.76 MeV n ( udd ) n p p ( uud ) T3T3 Ξ - ( dss)Ξ - Ξ 0 Ξ 0 ( uss ) Σ-Σ-Σ-Σ- Σ+Σ+Σ+Σ+ Λ Σ0Σ0Σ0Σ0 -½ 1 ½ 1 Y Gasser, Leutwyler, Phys.Rep 87, 77 “Quark Masses”

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)

Weinberg-Treiman formula M EM (T 3 ) = αT βT 3 + γ Dashen ansatz ΔM EM ~ κT 3 2 ~ κ’Q 2

Coleman-Glashow Coleman-Glashow relation EM [MeV] Exp. Exp. [input] (M p – M n ) EM0.76±0.30 (M Σ+ – M Σ - ) EM-0.17±0.30 (M Ξ 0 –M Ξ - ) EM-0.86±0.30

EM [MeV] Exp. Exp. [input]reproduced (M p – M n ) EM0.76± ±0.22 (M Σ+ – M Σ - ) EM-0.17± ±0.23 (M Ξ 0 –M Ξ - ) EM-0.86± ±0.28 Coleman-Glashow Coleman-Glashow relation Χ 2 fit

[ D.W.Thomas et al.] [ PDG, 2010 ] [ GW, 2006 ] [ Gatchina, 1981 ] Physical mass differences of baryon decuplet ■ Physical mass differences of baryon decuplet

Two advantages offered by the model-independent approach in the χSM by the model-independent approach in the χSM. model-parameters 1. the very same set of dynamical model-parameters allows 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. model-parameters 2. these dynamical model-parameters can be adjusted to the experimental data of the baryon octet which are well established with high precisions. Mass : α, β, γ (for ) Mass : α, β, γ (for octet, decuplet, antidecuplet,…) Vector transitions : w i (i=1,2,…,6) Axial transitions : a i (i=1,2,…,6) [10], [10] Baryons l = l 0 (1 + c ΔT) : linear expansion coefficient of a wire, c [8] model-parameters

Mass splittings within a Chiral Soliton Model Mass splittings within a Chiral Soliton Model Formulae for Baryon Octet Masses (ΔM) EM (ΔM) H hadronic mass part in terms of δ 1 and δ 2

Formulae for Baryon Decuplet Masses hadronic mass part in terms of δ 1 and δ 2

Formulae for Baryon Anti-Decuplet Masses hadronic mass part in terms of δ 3

Generalized Gell-Mann-Okubo ■ Generalized Gell-Mann-Okubo relation When the effect of the isospin sym. br is turned off, Coleman-Glashow ■ Coleman-Glashow relation is still satisfied Present analysis reproduces all kind of well-known mass relations ★ Generalized Guadagnini formulae

Baryon octet masses

Employing the value of the ratio 74±12 [Using Θ + & Ξ -- masses, based on χQSM: Σ πN =(74±12) MeV, P. Schweitzer, Eur. Phys. J. A 22, 89 (2004)] 64±8 [GWU analysis of πN scattering data : Σ πN =(64±8) MeV, Pavan et al, PiN Newslett.16: ,2002 ] 79±7 [Updated analysis in the pχQM : Σ πN =(79±7) MeV, Inoue, et al, Phys. Rev. D (2004) ]

Baryon decuplet masses

Baryon antidecuplet masses

magnetic transitions The full expression for the magnetic transitions μ BB’ = μ BB’ (0) + μ BB’ (op) + μ BB’ (wf) Vector transitions with

2. Magnetic transitions

Magnetic moments for baryon decuplet (in units of μ N ) 2. Magnetic transitions mass splitting analysis

Magnetic moments for baryon antidecuplet (in units of μ N ) 2. Magnetic transitions

|μ NΔ |~3.1 Exp. 1.61±0.08 <0.82 Transition magnetic moments (in units of μ N ) isospin asymmetry mass splitting analysis

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” - Good agreement with estimates for non-strange members of antidecuplet N* from Chiral Soliton Model - Being a candidate for the non-strange member Θ + of the anti-decuplet supports the existence of the Θ + T3T3 1 +Θ++Θ+ ½-½-½ 2 Ξ+Ξ+Ξ+Ξ+ 3/2 Ξ0Ξ0Ξ0Ξ0 3/2 Ξ-Ξ-Ξ-Ξ- 3/2 Ξ -- 3/2 Σ-Σ-Σ-Σ- 10 Σ0Σ0Σ0Σ0 10 Σ+Σ+Σ+Σ+ 10 Y n* n* n* n* p* p* p* 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) ]

Axial-vector transitions with The full expression for the axial-vector transitions g 1 BB’ = g 1 BB’ (0) + g 1 BB’ (op) + g 1 BB’ (wf)

Axial-vector transitions a 1 = ± 0.01 a 2 = 3.12 ± 0.03 a 3 = 0.62 ± 0.13 a 4 = 2.91 ± 0.07 a 5 = ± 0.03 a 6 = ± 0.04

Axial-vector transitions 84.7± ±0.29 Γ Θ + n = 0.80±0.12 MeV Γ Θ + N = 2 Γ Θ + n = 1.61±0.25 MeV DIANA 2010 ( Θ + ) : Γ= 0.38±0.11 MeV PDG 2007 ( Θ + ) : Γ= 0.9±0.3 MeV Γ Θ + N (0) = 0.52±0.13 MeV Γ Θ + N (op) = 1.31±0.07 MeV Γ Θ + N (wf) = 0.36±0.01 MeV

D.P.PE.K.PχQSMThis Work Analyzed Effects H SU(3) H. EMHH EM + iso H. + SU(3) H. Input Masses [MeV] N * N * (1710) Θ + Θ + (1539±2) Ξ -- Ξ -- (1862±2) Θ + Θ + (1524±0.005 LEPS) N * N * (1685±0.012 GRAAL) Σ πN [MeV] 4573Predicted (41)Predicted (72.0±13.6) Results I 2 [ fm ] m s α [MeV] m s β [MeV] m s γ [MeV] c g K*n Θ : sym 1.95 : sym Γ Θ+ [MeV] 15 : sym 11.1 : sym ±0.25 D.P.P : Diakonov, Petrov, Polyakov, Z. Physics. A. 359, (1997) E.K.P : Ellis, Karliner, Praszalowicz, JHEP. 0405, 002 (2004) χQSM : Tim Ledwig, H.-Ch. Kim, K. Goeke, Phys. Rev. D. 78, & Nucl. Phys. A Γ Θ+ : 0.38±0.11 MeV (DIANA), 0.9±0.3 MeV (2007 PDG)

T3T3 1 +Θ++Θ+ ½-½-½ 2 Ξ+Ξ+Ξ+Ξ+ 3/2 Ξ0Ξ0Ξ0Ξ0 3/2 Ξ-Ξ-Ξ-Ξ- 3/2 Ξ -- 3/2 Σ-Σ-Σ-Σ- 10 Σ0Σ0Σ0Σ0 10 Σ+Σ+Σ+Σ+ 10 Y Chiral Soliton Model Chiral Soliton Model : “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 ● M Θ+ = 1524 MeV [LEPS, DIANA], M N* = 1685 MeV [GRAAL] used as input, : reliable value within a chiral soliton model ● Γ Θ+ = 1.61±0.25 MeV [DIANA 2010 : 0.38±0.11]. small decay width is reproduced ● The study for the mass splittings to the 2 nd order : done [ hep-ph , Yang & Kim] Consequent results will appear elsewhere n* n* n* n* p* p* p* p*

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

Mixing coefficients Mixings of baryon states

1. Electric transitions Gell-Mann-Nishijima relation

Octet, Decuplet Anti-decuplet ( Θ +, N *) Parameters to be fixed: 1. Experimental data for the all masses of the baryon octet 2. Experimental values for the Σ* → I 1 3. Experimental values for the Θ + & N* Input for fixing the parameters ( χ 2 fitting)

Moment of inertia The ratio of current quark masses χ 2 fitting 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

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

1. Electric transitions

Vector transitions with Sachs’ form factor f E (q 2 ) = f 1 (q 2 ) + f 2 (q 2 ) [q 2 /(2M N ) 2 ] f M (q 2 ) = f 1 (q 2 ) + f 2 (q 2 ) n p pp p T3T3 Ξ-Ξ-Ξ-Ξ- Ξ0 Ξ0Ξ0 Ξ0 Σ-Σ-Σ-Σ- Σ+Σ+Σ+Σ+ Λ Σ0Σ0Σ0Σ0 -½ 1 ½ 1 Y

Model baryon state Constraint for the collective quantization : Mixings of baryon states

Mixing coefficients

δN *δN *δN *δN *

η, π, K Pseudoscalar meson ( η, π, K ) photoproduction γ n → K - Θ + : “missing resonances” ( γ n → K - Θ + ) γ n → η n Narrow resonant structure W ~ 1.67 – 1.68 GeV on γ n → η n GRAAL, LNS-Tohoku (2007) γ p → η p Beam asymmetry ( Σ on γ p → η p ) → amplify weak signal of a resonance Analysis of mass spectrum on n target is rather complicated (bound in deuteron) ● : Kuznetsov (GRAAL, 2008) ○ : Bartalini (GRAAL, 2007)

Breit-Wigner formula for electro- & magnetic multipoles where Reparametrized Breit-Wigner formula

● : ηn spectrum (CBELSA/TAPS) : ηn spectrum estimated with resonance : ηn spectrum estimated without resonance ▲ : ηp spectrum ( GRAAL, CBELSA/TAPS, CLAS ) P 11 additional to non-resonant contribution ( inputs : M R = 1685, Γ R = 20 MeV, θ = 130 o ) Fit the “Breit-Wigner form” with SAID data to the exp. data (GRAAL : Σ on p) – Photocoupling ratio (n / p) ~ 10 – 20 CSM Good agreement with estimates for non-strange members of antidecuplet N* from CSM Best Fit : P 11 ( M R ~ 1685, Γ R ~ 20 MeV )