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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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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 (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 G. S. Yang, ph.D Thesis, 2010 (unpublished), Ruhr-Universität, Bochum, Germany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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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

S = -1

S = -2

-1

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Motivation

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

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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

-1

Anti-decuplet (10)

???

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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

-3/2

-3/2

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

  • 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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

k

939.6

938.3

Y

B(p)

B(p)

( udd) n

p( uud)

1

p - k

1189

p

p

1197

Λ

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (mass)

Coleman-Glashow relation

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (mass)

Χ2 fit

Coleman-Glashow relation

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (mass)

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

[ 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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (mass)

Baryon octet masses

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (mass)

Baryon decuplet masses

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (mass)

Baryon antidecupletmasses

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (Vector)

2. Magnetic transitions

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Σ+

Σ0

Σ-

Y

Θ+

2

1

Ξ--

Ξ0

Ξ-

3/2

3/2

3/2

T3

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Σ+

Σ0

Σ-

Y

Θ+

2

1

Ξ--

Ξ0

Ξ-

3/2

3/2

3/2

T3

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Спасибо

Thank you

ありがとうございます 감사합니다

Danke

schön

TERIMA KASIH

謝謝


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Mixings of baryon states

Chiral Soliton Model (mass)

Mixing coefficients

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (Vector)

1. Electric transitions

Gell-Mann-Nishijima relation


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (Vector)

1. Electric transitions

Flavor SU(3) breaking: The Ademollo-Gatto Theorem

Mixing coefficients from mass splittings


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (Vector)

1. Electric transitions


Vector and axial vector properties of su 3 baryons within a chiral soliton model

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

-1

1

Σ0

Σ-

Σ+

-1

Ξ-

Ξ0


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Isobar Model


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Isobar Model


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Mixings of baryon states

Constraint for the collective quantization :

Chiral Soliton Model

Model baryon state

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model

Mixing coefficients

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Chiral Soliton Model (mass)

δN*

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Isobar Model

Pseudoscalar meson ( η, π, K) photoproduction

: “missing resonances” ( γ n → K-Θ+ )

Narrow resonant structure W ~ 1.67 – 1.68GeV on γ n → η n

GRAAL, [email protected], LNS-Tohoku (2007)

Analysis of mass spectrum on n target

is rather complicated (bound in deuteron)

Beam asymmetry ( Σon γ p → η p )

→ amplify weak signal of a resonance

● :Kuznetsov (GRAAL, 2008)

○ : Bartalini (GRAAL, 2007)

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Isobar Model

Breit-Wigner formula for electro- & magnetic multipoles

where

ReparametrizedBreit-Wigner formula

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


Vector and axial vector properties of su 3 baryons within a chiral soliton model

Photocoupling ratio (n / p) ~ 10 –20

Best Fit : P11 (MR ~ 1685, ΓR ~ 20 MeV)

Good agreement with estimates for non-strange members of antidecupletN*fromCSM

● : ηn spectrum (CBELSA/TAPS)

: ηn spectrum estimated with resonance

: ηn spectrum estimated without resonance

▲ : ηp spectrum (GRAAL, CBELSA/TAPS, CLAS)

Isobar Model

Fit the “Breit-Wigner form” with SAID data to the exp. data (GRAAL : Σon p)

P11 additional to non-resonant contribution

( inputs : MR = 1685, ΓR = 20 MeV, θ= 130o)

SU(3) baryons MotivationMass splitting Vector Axial-vector Summary


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