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Dependence of the decay width for exotic pentaquark Θ + (1540) on its mass

Dependence of the decay width for exotic pentaquark Θ + (1540) on its mass and the mass of N*(1685) in a chiral soliton model. Ghil-Seok Yang, Yongseok Oh, Hyun-Chul Kim. HEP (Center for H igh E nergy P hysics), Kyungpook Nat‘l University. NTG

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Dependence of the decay width for exotic pentaquark Θ + (1540) on its mass

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  1. Dependence of the decay width for exotic pentaquarkΘ+(1540) on its mass and the mass of N*(1685) in a chiral solitonmodel Ghil-Seok Yang, Yongseok Oh, Hyun-Chul Kim HEP (Center for High Energy Physics), Kyungpook Nat‘l University NTG (Nuclear Theory Group), Inha University “New Frontiers in QCD”, 27th – 28th October 2011, Engineering Research Park, Yonsei University, Seoul, Republic of Korea

  2. Outline • Prehistory of SU(3) Baryons • Motivation (Θ+, N*) • Chiral Soliton Model • Masses and Decay Width • 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)

  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

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

  6. Motivation ? Unsuccessful searches for Θ+ (2006~2008) : 2010 PDG ???

  7. Σ+ Σ0 Σ- (uudss) (uddss) Ξ-- Ξ+ Ξ0 Ξ- 3/2 3/2 3/2 3/2 10 10 10 Motivation Experimental Status New positive experiments (2005 - 2010) ■DIANA2010 (Θ+) : M = 1538±2, Γ= 0.39±0.10 MeV (K+n → K0p, higher statistical significance : 6σ - 8σ) [Signals are 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 Various experimental data for Θ+and N* ■Mass of Θ+ : 1525 – 1565 MeV ■ Mass of N* : 1665 – 1695 MeV Anti-decuplet (10)

  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)

  9. Mixings of baryon states Constraint for the collective quantization : Chiral Soliton Model Model baryon state

  10. Chiral Soliton Model Mixing coefficients

  11. Chiral Soliton Model (mass) Collective Hamiltonian for flavor symmetry breakings α γ β Y Y Y Mass Mass Δ N 1 1 940 1232 Λ -½ ½ -3/2 -3/2 -½ ½ 1116 T3 T3 1385 1193 Σ* Σ0 1533 1318 Ξ* -1 -1 Ξ Ω- -2 1673 Decuplet (10): J p = 3/2+ Octet (8): J p = 1/2 + SU(3) flavor symmetry breaking

  12. Chiral Soliton Model Two advantages offered by the model-independent approach in the χSM. 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. 2. these dynamical model-parameters can be adjusted to the experimental data of the baryon octet which are well established with high precisions. However ! [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

  13. Motivation Problems in the previous solitonic approaches 1 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

  14. Chiral Soliton Model (mass) Collective Hamiltonian for flavor symmetry breakings α γ β α + γ β 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

  15. Motivation Problems in the previous solitonic approaches 1 2 3 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 In order to determine the values of model parameters, “Model-independent approach” needs more information (at least, 2 inputs for antidecuplet baryons).

  16. Chiral Soliton Model (mass) Mass splittings within a Chiral Soliton Model Formulae for Baryon Octet Masses hadronic mass part in terms of δ1 and δ2

  17. Chiral Soliton Model (mass) Formulae for Baryon Decuplet Masses hadronic mass part in terms of δ1 and δ2

  18. Chiral Soliton Model (mass) Formulae for Baryon Anti-Decuplet Masses hadronic mass part in terms of δ3

  19. Motivation Problems in the previous solitonic approaches 1 2 3 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

  20. 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.

  21. 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

  22. 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)

  23. Chiral Soliton Model (mass) Weinberg-Treiman formula MEM(T3) = αT32 + βT3+ γ Dashenansatz ΔMEM ~ κT32~ κ’Q2

  24. Chiral Soliton Model (mass) Coleman-Glashow relation

  25. Chiral Soliton Model (mass) Χ2 fit Coleman-Glashow relation

  26. [ D.W.Thomas et al.] [ PDG, 2010 ] [ GW, 2006 ] [ Gatchina, 1981 ] Chiral Soliton Model (mass) ■Physical mass differences of baryon decuplet

  27. 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 G. S. Yang, H.-Ch. Kim and M. V. Polyakov, Phys. Lett. B 695, 214 (2011)

  28. Σ+ Σ0 Σ- (uudss) (uddss) Ξ-- Ξ+ Ξ0 Ξ- 3/2 3/2 3/2 3/2 10 10 10 Motivation Problems in the previous solitonic approaches 1 3 2 Y Θ+(uudds) S = 1 2 p* ( uud) ( udd) n* 1 S = 0 T3 -½ ½ Various experimental data for Θ+and N* ■Mass of Θ+ : 1525 – 1565 MeV ■ Mass of N* : 1665 – 1695 MeV -1 Anti-decuplet (10) 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

  29. 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

  30. Chiral Soliton Model (axial-vector) Axial-vector transitions 0.36±0.08

  31. Results

  32. Results Baryon octet masses

  33. Results Baryon decuplet masses

  34. LEPS DIANA Various experimental data for Θ+and N* ■Mass of Θ+ : 1525 – 1565 MeV ■ Mass of N* : 1665 – 1695 MeV

  35. NA49 : Mass of Ξ--3/2 = 1862 MeV

  36. LEPS DIANA MAMI GRAAL, SAID

  37. LEPS DIANA DIANA ?

  38. Summary Chiral SolitonModel : “model-independent approach” ●Mass splittings : SU(3) and isospin symmetry breakings with EM in the range of MΘ+= 1500-1600MeV used as input ●Masses of octet and decuplet are not sensitive to the MΘ+ input. → very good agreement with experimental data ● Small value of pion-nucleon sigma term is estimated. (ΣπN = 35 - 40MeV) ● MΘ+= 1524 MeV [LEPS], MN*= 1685 MeV [GRAAL], ΓΘ+= 0.38±0.11 MeV [DIANA] : reliable values within a chiral soliton model.

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

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