exotic baryon resonances in the chiral dynamics

Exotic baryon resonances Exotic baryon resonances in the chiral dynamicsin the chiral dynamics

Exotic baryon resonances Exotic baryon resonances in the chiral dynamicsin the chiral dynamics

Tetsuo Hyodoa

a RCNP, Osaka b ECT* c IFIC, Valencia d Barcelona Univ. 2003, December 9th

A. Hosakaa, D. Jidob, S.I. Nama, E. Osetc, A. Ramosd and M. J. Vicente Vacasc

1. Structure of (1405)1. Motivation : Two poles?2. Chiral unitary model3. Pole structure of (1405)4. Photo-production of K*(1405)

2. Quantum numbers of

1. Present status of theoretical studies2. Chiral model for K+p -> +KN3. Results4. Polarization test

ContentsContents

Motivations : Two poles?Motivations : Two poles?

• Cloudy bag model (1990) J. Fink et al. PRC41, 2720

• Chiral unitary model (2001~) J. A. Oller et al. PLB500, 263 E. Oset et al. PLB527, 99 D. Jido et al. PRC66, 025203 T. Hyodo et al. PRC68, 018201

There are two poles of the scattering amplitudearound nominal (1405) energy region.

(1405) : JP=1/2, I=0

ChU model, T. Hyodo

Chiral unitary modelChiral unitary model

Unitarity of S-matrixChiral symmetry

Flavor SU(3) meson-baryon scatterings (s-wave)

Resonances

Low energy behavior

Non-perturbativeresummation

(1405), (1670), N(1535),(1620), (1620)

Dynamicalgeneration

Chiral perturbation theory

Unitarization

Framework of the chiral unitary modelFramework of the chiral unitary model

Resonances

Generated resonances areexpressed as poles of the scattering amplitude.

Total cross sections of Kp scatteringsTotal cross sections of Kp scatterings

T. Hyodo, et al., Phys. Rev. C 68, 018201 (2003)

200

150

100

50

0300200100

K-p

70

60

50

40

30

20

10

0300200100

0

200

150

100

50

0300200100

+−

60

50

40

30

20

10

0300200100

Plab [ / ]MeV c

K0n

60

50

40

30

20

10

0300200100

Plab [ / ]MeV c

0080

60

40

20

0300200100

Plab [ / ]MeV c

−+

(1405) in the chiral unitary model(1405) in the chiral unitary model

D. Jido, et al., Nucl. Phys. A 723, 205 (2003)

mass distribution

1390 + 66i (

1426 + 16i (KN)

Example : the p -> K0 reactionExample : the p -> K0 reaction

Chiralterm

N(1710)

Chiral unitary model

Results for p -> K0Results for p -> K0

T. Hyodo, et al., nucl-th/0307005, Phys. Rev. C, in press

Total cross sections [mb]Mass distribution

� There are two mechanisms in the initial stage interaction, which filter each one of the resonances.

Good agreement(1385) effect

Photoproduction of K* (1405)Photoproduction of K* (1405)

Only Kp channel appears at the initial stage

Higher pole ??

Effective interactions for meson partEffective interactions for meson part

1. VP coupling

2. VPP coupling

Effective interaction for (1385)Effective interaction for (1385)

3. (1385)MB coupling

4. KP -> (1385) -> MB amplitude

SU(6) symmetry

6

5

4

3

2

1

015001450140013501300

MI [ ]MeV

00 (~ =0)I average of charged 0 ( =1)I

invariant mass distribution invariant mass distribution

Plab = 2.5 GeV/csqrt s ~ 2.35 GeV

Preliminary

1.2

1.0

0.8

0.6

0.4

0.2

0.0300028002600240022002000

sqrt s

π0Σ0 (~I=0) average of charged πΣ

π0Λ (I=1)

ΛK*KππΣ

Result : Total cross sectionResult : Total cross section

Preliminary

Summary and conclusionsSummary and conclusions

We study the structure of (1405) using the chiral unitary model.

� There are two poles of the scattering amplitude around nominal (1405).

Pole 1 (1426+16i) : strongly couples to KN statePole 2 (1390+66i) : strongly couples to state

� By observing the mass distribution in the p -> K*(1405) reaction, it could be possible to isolate higher energy pole.

Appendix : other processesAppendix : other processes

p -> K

p -> J.C. Nacher, et al., PLB461, 299(1999)

J.C. Nacher, et al., PLB445, 55(1999)

SPring-8

J-PARC?

baryon : Introduction baryon : Introduction

+ : 5-quark (4 quark + 1 anti-quark)LEPS, T. Nakano et al., Phys. Rev. Lett. 91 (2003) 012002

Quantum numbers are not yet determinedTheory prediction D. Diakonov et al. (chiral quark soliton) Naive quark model S. Capstick et al. (isotensor formulation) A. Hosaka (chiral potential) R. L. Jaffe et al. (qq-qq-q : 10 + 8) J. Sugiyama et al. (QCD sum rule) F. Csikor et al. (Lattice QCD) S. Sasaki (Lattice QCD)

: 1/2+, I=0: 1/2

: 1/2, 3/2, 5/2, I=2: 1/2+ (strong ): 1/2+, I=0: 1/2, I=0: 1/2+ -> 1/2

: 1/2

S = +1, M ~ 1540 MeV, < 25 MeV

Photo-production processPhoto-production process

W. Liu et al. nucl-th/0308034S. I. Nam et al. hep-ph/0308313W. Liu et al. nucl-th/0309023Y. Oh et al. hep-ph/0310117

p -> K0, n -> K

Model (mechanism) dependence

Form factor dependence

Unknown parameters

Initial cm energy ~ 2 GeV (pcm ~ 750 MeV) not low energy -> linear or nonlinear?N* resonances, K* exchange, 1 exchange,…

Monopole, dipole… , value of , …

coupling, K*p coupling, …

Assuming the quantum numbers (spin, parity), we can calculate a reaction

Motivation and advantageMotivation and advantage

K+p -> ++ -> +K+n(K0p) Low energy model is sufficient (pcm ~ 350 MeV) take decay into account -> background estimation -> Width independent Hadronic process : clear mechanism

We propose

to extract a qualitative behavior which dependson the quantum numbers of .

Determination of quantum numbersNew : pp -> , A. W. Thomas, K. Hicks, and A. Hosaka, hep-ph/0312083

A model for p -> +K+n A model for p -> +K+n

E. Oset and M. J. Vicente Vacas, PLB386, 39(1996)

Vertices are derived from the chiral Lagrangian

Proportional to vanishes

Assume final + is almost at rest

Dominant

DiagramsDiagrams

Tree level(background)

One loop

Possibilities of spin & parityPossibilities of spin & parity

1/2 (KN s-wave resonance)1/2 , 3/2 (KN p-wave resonance)

MR = 1540 MeV = 20 MeV

Resonance termResonance term

Amplitude of resonance term for K+p -> +K+n :

Angular dependenceAngular dependence

total resonance background

10

8

6

4

2

01.00.50.0-0.5-1.0

cosθ

10

8

6

4

2

01.00.50.0-0.5-1.0

cosθ5

4

3

2

1

01.00.50.0-0.5-1.0

cosθ

,I JP=0,1/2- ,I JP=0,1/2+

,I JP=0,3/2+

Mass distributionsMass distributions

8

6

4

2

015801560154015201500

MI

,I JP=0,1/2-

,I JP=0,1/2+

,I JP=0,3/2+kin( ) = 850 /Lab MeV cθ = 90 deg

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.015801560154015201500

MI

Polarization testPolarization test

# Same result is obtained for final pK0

Angular dependence : polarization testAngular dependence : polarization test

total resonance background

5

4

3

2

1

01.00.50.0-0.5-1.0

cosθ

20

15

10

5

01.00.50.0-0.5-1.0

cosθ5

4

3

2

1

01.00.50.0-0.5-1.0

cosθ

,I JP=0,1/2- ,I JP=0,1/2+

,I JP=0,3/2+

Polarization test

Mass distributions : polarization testMass distributions : polarization test

14

12

10

8

6

4

2

015801560154015201500

MI

,I JP=0,1/2-

,I JP=0,1/2+

,I JP=0,3/2+kin( ) = 850 /Lab MeV cθ = 90 deg

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.015801560154015201500

MI

Polarization test

Incomplete polarizationIncomplete polarization

14

12

10

8

6

4

2

015801560154015201500

MI

,I JP=0,1/2-

,I JP=0,1/2+ kin( ) = 850 /Lab MeV cθ = 90 deg

Polarization

100 %80 % 0 %

ConclusionConclusion

We calculate the Kp -> 0KN reaction usinga chiral model, assuming the possible quantum numbers of + baryon. � If we find the resonance with polarization test, the quantum number of + can be determined as I=0, JP=1/2+

T. Hyodo, et al, nucl-th/0307105, Phys. Lett. B, in pressE. Oset, et al, nucl-th/0312014, Hyp03 proceedings

Future workFuture work

� Full calculation of the present reaction without approximation of kinematics -> information from + angular dependence� photo-production of K* and V. Kubarovsky et al., hep-ex/0307088