June 16-20, 2005 北京 1

Atsushi Hosaka (RCNP, Osaka Univ)

Decay and production of +

• hep-ph/0409102, PRD71: 074021 (2005) A. H., M. Oka and T. Shinozaki • hep-ph/0502093, PRD71: 054017 (2005)

T. Hyodo and A. H. • hep-ph/0505134, hep-ph/0503149 to appear PRD

S.I. Nam, A.H. and H.-Ch. Kim

Decay and production mechanism for + (JP)with renewed interest in (1520)

June 16-20, 2005 北京 2

Facts ~ very narrow width ・ In production experiments, << 20 MeV ・ In KN scattering 1 MeV or less

T. Nakano et al.PRL, 91, 012002 (2003)

A. Sibirtsev et al, PLB599 (2004) 230-235

= 1, 5, 10, 20 MeV

More data from Nakano in this conference

June 16-20, 2005 北京 3

Outline1. Decay of +

General remark Fall-apart in the quark model

2. Possibility of spin 3/2-

Phenomenological analysis3. Photoproduction reconsidered pn asymmetry

n -> K-+ vs. p -> K0+ [+ or (1520)]

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1. Decay of +

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€

M

€

E€

M *

€

q

1/2+ P-wave coupling

M* = 1540 MeV, gKN ~ 10

€

L = gKNΘ N γ 5ΘK → Γ + = gKNΘ2

2πMq3

E(E + M )M *

1/2– S-wave coupling

€

L = gKNΘ N ΘK → Γ − = Γ + (E + M )2

q2 = 5 GeV

Effect of entrifugal barrier ~ 50 !

Empirical fact: gmNN* < 10 (NN or NN) = 100 MeV

Simple estimate

June 16-20, 2005 北京 6

Fall apart decayExpected to be a dominant process in a constituent QM

Fall apart, or diossociate

5q4q

3q~

5q 2q

5q~

Other mechanisms?

Ni = Nf

Ni < Nf

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Amplitude

Rearranged+

K

NS-factor

Intereaction

N-like

K-like

V

T ~ <KN|+> • Vfi

We consider fall apart in the quark model

June 16-20, 2005 北京 8

Mqq of Yukawa type

Interaction ~ Vfi

€

N

€

for

€

g ~ 2.6

Useful as a referencefor further studies

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Negative parity ground state (0s)5

Unique ~ AS KN state

€

+

gKN ~ 3 => ~ 0.5 - 1 GeV

S-factor

S-factor ~ <KN|+> p

s

(0s)5

Carlson et al, PLB 573, 101 (2003)AH et al,

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Positive parity

More complicated than s-wave due to p-wave excitation

(1) Minimize Spin-Flavor interaction (2) Minimize Spin-Color(3) Diquark correlation of JW

p

s

(0s)40p

We consider

June 16-20, 2005 北京 11

Spectroscopic factors

€

S(1) = 5192

~ 16

S(2) = 5384

~ 19

S(3) = 51152

~ 115

SF SC JW

> >

Carlson et al, PRD70, 037501 (2004), hep-ph/0312325,Jennings-Maltman, PRD 69, 094020 (2004), hep-ph/0308286

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Results

(1/2-) >> (1/2+)

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We have seen:

・ Natural width of Pentaquarks　　 1/2− ~ GeV　　 1/2 ＋ < 100 MeV <= Centrifugal force

・ Quark model values are consistent with them (0s)5 1/2– : as dominated by KN => can not be a narrow resonance　　 1/2 ＋ with JW-diquark correlation -> 10 MeV (or could be less)　　 Spatial correlation can reduce ~ 1 MeV? dynamical question

June 16-20, 2005 北京 14

Other possibility

Could it be (0s)5 3/2 ー

• Decay into KN is suppressed due to d-wave • K*(1 ー )N dominant but no decay into this channel • No spin partner of 1/2– …. Too broad to see

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2. Phenomenology of 3/2- baryons

Hyodo-Hosaka, hep-ph/0502093, PRD71:054017 (2005)

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with 8-10 mixing

N

€

H =M10 − aY δ

δ M8 − bY + c[I(I +1) −Y 2 / 4] ⎛ ⎝ ⎜

⎞ ⎠ ⎟€

+

(p8, p10) (n8,n10)

(Σ8−,Σ10

− ) (Σ8−,Σ10

− ) (Σ8−,Σ10

− )

Ξ −− Ξ − Ξ 0 Ξ +

€

N1phys = N8 cosθN + N10 sinθN

N2phys = −N8 sinθN + N10 cosθN

€

1phys = Σ8 cosθΣ + Σ10 sinθΣ

Σ2phys = −Σ8 sinθΣ + Σ10 cosθΣ

SU(3) description+, N1, N2,

6 parameters

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• Choose suitable baryons of JP = 1/2+ -, 3/2+

-, adding + -> 6 baryons are enough • Fitting into the SU(3) scheme with 8-10 mixin

g 1/2+

3/2-

We can fix the mixing angle

June 16-20, 2005 北京 18

Coupling constants g8 and g10

€

gN 1 = gN 8 cosθN − g10

6sinθN

gN 2 = gN 8 sinθN + g10

6cosθN

• N can be fixed by masses • Two nucleon decay widths

determine g8 and g10

• The resulting g10 determines

(MeV)Decay widths

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3. Photoproductions

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This is serious, but showing absence of + ?

p -> n K+ K0

New data from J-Lab

pn

K+

K0

+

Teken from DeVita’s talk at spring APS meeting

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Theoretical studyEffective Lagrangian method

hep-ph/0505134Nam-Hosaka-Kim

appears only for n-target

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Prior to thisn -> K- (1520) and p -> K0 (1520)was studied and large pn asymmetry was found

Nam-Hosaka-Kim, hep-ph/0503149 to appear PRD

The role of the contact term (Kroll-Ruderman type) was emphasized

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Total

Angular dist

Log-

scal

e

Log-

scal

e

Theta production, JP = 3/2-

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The role of the contact term is more important for JP = 3/2- than 1/2+

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Predictions

• We see a large asymmetry between pn targets • Cross section for proton ~ few nb is consistent with

the upper limit estimated by CLAS

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Summary • Fall-apart decay in the quark model

1/2– ~ GeV 1/2+ Several tens MeV could be 10 MeV or less for JW 3/2– ~ zero or strongly suppressed • SU(3) analysis

3/2– is a natural candidate • Photoproduction, revised

There is a large pn asymmetry, especially for J = 3/2 No signal from the CLAS does not lead immediately to the absence of +

For (1520), consistent with recent observation of LEPS

New data from LEPS is interesting and important => Talk by Takashi Nakano

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Comments

(1) A related work

Melokov, Simula and Stech, PLB 594 (2004) 265 Claimed that ~ 150 MeV for the JW wf

In the quark model, there is no pole (hA) term==> Can not be applied to the quark model

€

N s γ μγ 5u Θ + ~ u N gA (q2)γ μγ 5 + hA (q2)qμγ 5( )uΘ

Assumption

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(2) 5-body calculation

Confined state KN Scattering state

+ + . . .

€

~ qqqqs =

Recent calculation by Hiyama Gaussian Expansion Method

Coupling to other channels including KN changes the nature of the confined state drastically

Fall apart when R→∞

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1/2– 1/2+

KN-like JW-type

(0s)5 1/2– , (0s)40p 1/2+ can no longer survive