Photoproduction of K* for the study of Λ(1405)�

Tetsuo Hyodoa �

a RCNP, Osaka b IFIC, Valencia

2004, January 30th

A. Hosakaa, M. J. Vicente Vacasb and E. Osetb

Special thanks to Prof. Morimatsu

Contents

1.  Chiral unitary model�1. Motivation : Two poles? �2. Framework of the chiral unitary model"3. Example : K-p scatterings"4. Pole structure of Λ(1405)�

2.  K*Λ(1405) production�1. Advantage of the reaction"2. Effective interactions"3. Numerical results"4. Summary and conclusions �

Motivation : 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 amplitude"around nominal Λ(1405) energy region."

Λ(1405) : JP=1/2-, I=0"

ChU model, T. Hyodo

Chiral unitary model

Unitarity of S-matrix"Chiral symmetry"Flavor SU(3) meson-baryon scatterings (s-wave)"

Resonances"

Low energy "behavior"

Non-perturbative"resummation"

Λ(1405), Λ(1670), N(1535), Σ(1620), Ξ(1620)

Dynamical"generation"

Chiral perturbation theory"

Unitarization

Framework of the chiral unitary model

Resonances"

Generated resonances are"expressed as poles of the "scattering amplitude."

Total cross sections of K-p scatterings

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

200

150

100

50

0

σ T [m

b]

300200100

K-p70

60

50

40

30

20

10

0300200100

π0Λ

200

150

100

50

0300200100

π+Σ−

60

50

40

30

20

10

0

σ T [m

b]

300200100Plab [MeV/c]

K0n60

50

40

30

20

10

0300200100

Plab [MeV/c]

π0Σ080

60

40

20

0300200100

Plab [MeV/c]

π−Σ+

Poles of amplitude in S=-1 channel

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

8×8 ~ 1,8,8,10,10,27"attractive" repulsive"

Λ(1405) in the chiral unitary model

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

πΣ mass distribution"

1390 + 66i (πΣ)

1426 + 16i (KN)

Photoproduction of K* Λ(1405)

Only K-p channel appears at the initial stage"

Higher pole ??"

Advantage of this reaction

With polarized photon beam, the exchanged"particle can be identified."

Clear mechanism"

Effective interactions for vector meson

1.  γVP coupling"

2.  VPP coupling"

3.  Σ(1385)MB coupling"

4.  Form factor"

Effective interaction for baryon resonance

ChU amplitude"

Σ(1385) pole term"

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

σ [µ

b]

300028002600240022002000s [MeV]

π0Σ0 (I=0) π+Σ-

π-Σ+

π0Λ (I=1)

Λ(1405)K*KππΣ

Total cross section

4

3

2

1

0

d σ/d

MI[n

b/M

eV]

15001450140013501300MI [MeV]

π0Σ0 (I=0) π+Σ-

π-Σ+

π0Λ (I=1)

Ιnvariant mass distribution

Plab = 2.5 GeV/c sqrt s ~ 2.35 GeV

Isospin decomposition of πΣ states

•  Difference among charged states" -> when summed up, this term vanishes""•  No p-wave contribution" -> I=1 s-wave amplitude"

4

3

2

1

0

dσ/d

MI[n

b/M

eV]

15001450140013501300MI [MeV]

π0Σ0 (I=0) π+Σ-

π-Σ+

π0Λ (I=1)

( π+Σ- + π-Σ+ ) / 2

Ιnvariant mass distribution 2

Plab = 2.5 GeV/c sqrt s ~ 2.35 GeV

I=1, s-wave amplitdue

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5dσ

/dM

I[nb/

MeV

]

15001450140013501300MI [MeV]

π+Σ- − π-Σ+

πΣ (I=1)

Summary and conclusions 1

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

�  There are two poles of the scattering " amplitude around nominal Λ(1405)."Pole 1 (1426+16i) : strongly couples to KN state"Pole 2 (1390+66i) : strongly couples to πΣ state""�  By observing the charged πΣ states in " the γp -> K*Λ(1405) reaction, it is " possible to isolate higher energy pole."

Summary and conclusions 2 "�  If we observe neutral πΣ state, clear I=0" distribution is obtained.""�  Combining three πΣ states, we can also " study the s-wave I=1 amplitude, where" the existence of another pole is argued."

T. Hyodo, et al, nucl-th/0401051�

http://www.rcnp.osaka-u.ac.jp/~hyodo/ �

Appendix : other processes

γp -> K-πΣ

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

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