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

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

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+32Ξ0

32Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(uudss)

p ( uud )( udd ) n

Y

S = 1

S = 0

Anti-decuplet (10)

Motivation

S = -1

S = -2

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

Motivation

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

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+32Ξ032Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

YS = 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

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

Mixing coefficients

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)

Collective Hamiltonian for flavor symmetry breakings

α β γ

Two advantages offered by the model-independent approach in the χSM1 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

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

DPP EKP χQSMConsidered 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)Collective Hamiltonian for flavor symmetry breakings

α β γ

+ α β γ

Motivation

DPP EKP χQSMConsidered 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 approaches123

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 ModelFormulae for Baryon Octet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass)

Formulae for Baryon Decuplet Masses

hadronic mass part in terms of δ1 and δ2

Chiral Soliton Model (mass)

Formulae for Baryon Anti-Decuplet Masses

hadronic mass part in terms of δ3

Chiral Soliton Model (mass)

Motivation

DPP EKP χQSMConsidered 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 approaches123

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)

In the ChSM

It can be further reduced to

Because of Bose symmetryG S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)

Chiral Soliton Model (mass)

Weinberg-Treiman formulaM EM(T3) = αT3

2 + βT3 + γDashen ansatzΔM EM ~ κT3

2 ~ κrsquoQ 2

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)

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)

[ DWThomas et al][ PDG 2010 ][ GW 2006 ]

[ Gatchina 1981 ]

Physical mass differences of baryon decuplet

Chiral Soliton Model (mass)Mass splittings within a Chiral Soliton ModelFormulae 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

DPP EKP χQSM This WorkConsidered 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 approaches123

(ud-dss)

T3

1

Θ+(uudds)

frac12-frac12

-1

2

Ξ+32Ξ032Ξ-32Ξ--32

Σ-10 Σ010 Σ+

10

(u-udss)

p ( uud )( udd ) n

YS = 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