Ghil-Seok Yang, Yongseok Oh, Hyun-Chul Kim NTG (Nuclear Theory Group), (Nuclear Theory Group), Inha...

39
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 NTG (Nuclear Theory Group), Inha University HEP (Center for High Energy Physics), Kyungpook Nat‘l University New Frontiers in QCD”, 27 th – 28 th October 2011, Engineering Research Park, Yonsei University, Seoul, Republic of Korea

Transcript of Ghil-Seok Yang, Yongseok Oh, Hyun-Chul Kim NTG (Nuclear Theory Group), (Nuclear Theory Group), Inha...

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

NTG (Nuclear Theory Group)

Inha University

HEP (Center for High Energy

Physics) Kyungpook Natlsquol

University

ldquoNew Frontiers in QCDrdquo 27th ndash 28th October 2011 Engineering Research Park Yonsei University Seoul Republic of Korea

bull Prehistory of SU(3) Baryons

bull Motivation (Θ+ N )

bull Chiral Soliton Model

bull Masses and Decay Width

bull Summary

Outline

Naiumlve Quark Model (up down strange light quarks)

SU(3) scheme to classify particles with the same spin

and parity

Fundamental Particles

multiplets (proton neutron) isospin [ SU(2) ] rarr higher symmetry (Σ

K) SU(3)

SU(3) Baryons SU(3) Baryons

Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet

Why not 4 5 6 hellip quark states

representation 10 (10)

Nothing prevents such states to exist

Y s Oh and H c Kim Phys Rev D 70 094022 (2004)

1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)

(uddss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32

Ξ032Ξ-32Ξ--32

Σ-10

Σ010

Σ+10

(uudss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Motivation Motivation

S = -1

S = -2

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

Motivation Motivation

Unsuccessful searches for Θ+ (2006~2008) 2010 PDG

Motivation Motivation

Motivation Motivation

Experimental Status

New positive experiments (2005 - 2010)

DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010

MeV

(K+n rarr K0p higher statistical significance 6σ - 8σ)

[Signals are confirmed by LEPS SVD KEK hellip]

GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

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  • Slide 38
  • Slide 39

bull Prehistory of SU(3) Baryons

bull Motivation (Θ+ N )

bull Chiral Soliton Model

bull Masses and Decay Width

bull Summary

Outline

Naiumlve Quark Model (up down strange light quarks)

SU(3) scheme to classify particles with the same spin

and parity

Fundamental Particles

multiplets (proton neutron) isospin [ SU(2) ] rarr higher symmetry (Σ

K) SU(3)

SU(3) Baryons SU(3) Baryons

Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet

Why not 4 5 6 hellip quark states

representation 10 (10)

Nothing prevents such states to exist

Y s Oh and H c Kim Phys Rev D 70 094022 (2004)

1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)

(uddss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32

Ξ032Ξ-32Ξ--32

Σ-10

Σ010

Σ+10

(uudss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Motivation Motivation

S = -1

S = -2

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

Motivation Motivation

Unsuccessful searches for Θ+ (2006~2008) 2010 PDG

Motivation Motivation

Motivation Motivation

Experimental Status

New positive experiments (2005 - 2010)

DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010

MeV

(K+n rarr K0p higher statistical significance 6σ - 8σ)

[Signals are confirmed by LEPS SVD KEK hellip]

GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Naiumlve Quark Model (up down strange light quarks)

SU(3) scheme to classify particles with the same spin

and parity

Fundamental Particles

multiplets (proton neutron) isospin [ SU(2) ] rarr higher symmetry (Σ

K) SU(3)

SU(3) Baryons SU(3) Baryons

Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet

Why not 4 5 6 hellip quark states

representation 10 (10)

Nothing prevents such states to exist

Y s Oh and H c Kim Phys Rev D 70 094022 (2004)

1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)

(uddss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32

Ξ032Ξ-32Ξ--32

Σ-10

Σ010

Σ+10

(uudss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Motivation Motivation

S = -1

S = -2

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

Motivation Motivation

Unsuccessful searches for Θ+ (2006~2008) 2010 PDG

Motivation Motivation

Motivation Motivation

Experimental Status

New positive experiments (2005 - 2010)

DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010

MeV

(K+n rarr K0p higher statistical significance 6σ - 8σ)

[Signals are confirmed by LEPS SVD KEK hellip]

GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)

(uddss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32

Ξ032Ξ-32Ξ--32

Σ-10

Σ010

Σ+10

(uudss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Motivation Motivation

S = -1

S = -2

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

Motivation Motivation

Unsuccessful searches for Θ+ (2006~2008) 2010 PDG

Motivation Motivation

Motivation Motivation

Experimental Status

New positive experiments (2005 - 2010)

DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010

MeV

(K+n rarr K0p higher statistical significance 6σ - 8σ)

[Signals are confirmed by LEPS SVD KEK hellip]

GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

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

Motivation Motivation

Unsuccessful searches for Θ+ (2006~2008) 2010 PDG

Motivation Motivation

Motivation Motivation

Experimental Status

New positive experiments (2005 - 2010)

DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010

MeV

(K+n rarr K0p higher statistical significance 6σ - 8σ)

[Signals are confirmed by LEPS SVD KEK hellip]

GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Unsuccessful searches for Θ+ (2006~2008) 2010 PDG

Motivation Motivation

Motivation Motivation

Experimental Status

New positive experiments (2005 - 2010)

DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010

MeV

(K+n rarr K0p higher statistical significance 6σ - 8σ)

[Signals are confirmed by LEPS SVD KEK hellip]

GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Motivation Motivation

Experimental Status

New positive experiments (2005 - 2010)

DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010

MeV

(K+n rarr K0p higher statistical significance 6σ - 8σ)

[Signals are confirmed by LEPS SVD KEK hellip]

GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model Chiral Soliton Model

Effective and relativistic low energy theory

Large Nc limit meson field

rarr soliton

Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states

Chiral Soliton Model

Hedgehog Ansatz

Collective quantization

SU(2) Witten imbedding into SU(3) SU(2) X U(1)

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Model baryon state

Constraint for the collective quantization

Mixings of baryon states

Chiral Soliton Model Chiral Soliton Model

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Mixing coefficients

Chiral Soliton Model Chiral Soliton Model

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

-frac12 frac12

940

11161193

1318

Mass

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Collective Hamiltonian for flavor symmetry breakings

α β γ

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

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

Chiral Soliton Model Chiral Soliton Model

Mass α β γ (for octet decuplet antide-cuplethellip)

Vector transitions wi (i=12hellip6)

Axial transitions ai (i=12hellip6)

[10] [10]

Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c

[8]

model-parame-tersHowever

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Octet (8) J p = 12 + Decuplet (10) J p = 32 +

Y

T3

YY

T3

-1

1 N

Ξ

Λ

Σ0

1

-1

-2

Δ

Σ

Ξ

Ω-

( udd ) n p ( uud )

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12 frac12

940

11161193

1318

Mass

( ddd )Δ- Δ++ ( uuu )Δ0 Δ+

Ω-( sss )

Ξ- Ξ0

Σ- Σ0 Σ+

-frac12 frac12-32 -32

1232

1385

1533

1673

Mass

SU(3) flavor symmetry breaking+ Isospin symmetry breaking

Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Mass splittings within a Chiral Soliton Model

Formulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Motivation Motivation

DPP EKP χQSM

Considered Effects SU(3) H SU(3) H SU(3) H

Input Masses

[MeV]

N(1710 )Θ+(1539plusmn2)

Ξ--

(1862plusmn2 )

ΣπN [MeV] 45 73 Predicted rarr 41

Results

I2 [fm] 04 049 048

msα [MeV]

msβ [MeV]

msγ [MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches1

2

3

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (mass) 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

Two sources for the isospin symmetry breaking

1 mass differences of up and down quarks (hadronic part)

2Electromagnetic interactions (EM part)

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

ΔMB = MB1 ndash MB2

= (ΔMB )H + (ΔMB )EM

B(p) B(p)

k

p pp - k

EM mass corrections

Electromagnetic (EM ) self-energy

EM [MeV] Exp

(p ndash n)EM 076plusmn030

(Σ+ ndash Σ-)EM-017plusmn030

(Ξ0 ndashΞ-)EM-086plusmn030

( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV

9383 9396

1197 1189

1321 1315

( udd ) n p ( uud )

T3

( dss)Ξ- Ξ0 ( uss )

Σ- Σ+

Λ

Σ0

-frac12-1 1frac12

-1

1

Y

Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (mass) 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)

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

Coleman-Glashow relation

EM [MeV] Exp [input]

(Mp ndash Mn)EM076plusmn030

(MΣ+ ndash MΣ-)EM-017plusmn030

(MΞ0 ndashMΞ-)EM-086plusmn030

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

EM [MeV] Exp [input] reproduced

(Mp ndash Mn)EM076plusmn030 074plusmn022

(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023

(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028

Coleman-Glashow relation

Χ 2 fit

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (mass) Chiral Soliton Model (mass)

[ DWThomas et al]

[ PDG 2010 ]

[ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (mass) 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)

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Motivation Motivation

DPP EKP χQSM This Work

Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H

Input Masses

[MeV]

N(1710 )

Θ+(1539plusmn2)

Ξ--(1862plusmn2 )

Θ+ 1500-1580 MeV

ΣπN [MeV] 45 73 Predicted rarr 41

Re-sults

I2 [fm] 04 049 048

msα [MeV]

msβ

[MeV]

msγ

[MeV]

-218-156-107

-605-23152

-197-94-53

c10 0084 0088 0037

ΓΘ+ [MeV] 15 for sym

111 for sym

071 for sym

DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008

Problems in the previous solitonic approaches

1

2

3

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Slide 23
  • Slide 24
  • Slide 25
  • Slide 26
  • Slide 27
  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

with

The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo

(0) + g 1BBrsquo(op)

+ g 1BBrsquo(wf)

SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

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  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)

Axial-vector transitions

036plusmn008

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
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  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

ResultsResults

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
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  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Baryon octet masses

ResultsResults

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
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  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Baryon decuplet masses

ResultsResults

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
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  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Various experimental data for Θ+

and N

Mass of Θ+ 1525 ndash 1565 MeV

Mass of N 1665 ndash 1695 MeV

DIANALEPS

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
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  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

NA49 Mass of Ξ--32 = 1862 MeV

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
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  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

DIANALEPS

GRAALSAID

MAMI

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
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  • Slide 9
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  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

DIANA

LEPS DIANA

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Slide 8
  • Slide 9
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  • Slide 28
  • Slide 29
  • Slide 30
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Chiral Soliton Model ldquomodel-independent approachrdquo

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 rarr 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+ = 038plusmn011 MeV [DIANA]

reliable values within a chiral soliton model

Summary Summary

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
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  • Slide 34
  • Slide 35
  • Slide 36
  • Slide 37
  • Slide 38
  • Slide 39

Спасибо

Thank you

ありがとうございます 감사합니다

Danke schoumln

謝謝TERIMA KASIH

  • Slide 1
  • Slide 2
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
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