Feb. 16 (2005) Chiral05, RIKEN 1

Atsushi Hosaka (RCNP, Osaka Univ)Feb. 16 (2005) Chiral05 RIKEN

Fall-apart decay of +

Based on hep-ph/0409102A. H., M. Oka and T. Shinozaki

Widths & a possible quark model state for +

Feb. 16 (2005) Chiral05, RIKEN 2

Outline Fall apart Quark model calculation Comments

Possibility of spin 3/2-

Conclusion

Feb. 16 (2005) Chiral05, RIKEN 3

Facts ・ 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

Feb. 16 (2005) Chiral05, RIKEN 4

Fall apart

Rearranged+

K

N

+

N NN*q-qbar annihilation

S-factorIntereaction

Expected to be a dominant decay mechanism of +

N-like

K-like

V

Feb. 16 (2005) Chiral05, RIKEN 5

€

M

€

E

€

M *

€

q

1/2+ P-wave coupling

M* = 1540 MeV, gKN ~ 10

€

L = gKNΘ N γ 5ΘK → Γ + =gKNΘ

2

2π

Mq3

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

Feb. 16 (2005) Chiral05, RIKEN 6

Mqq interaction

Quark model calculation

€

N

€

for

€

g ~ 2.6

Feb. 16 (2005) Chiral05, RIKEN 7

Negative parity

SU(6) WF for (l=0)5 ~ ground state

gKN ~ 3 ~ 500 MeV

Spectroscopic factor

Unique for the antidecuplet

€

+

Fall apart: form qq(K)+qqq(N) conf. => KN

p

s

(0s)5

Feb. 16 (2005) Chiral05, RIKEN 8

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

Feb. 16 (2005) Chiral05, RIKEN 9

(1) Most attractive channel for sf interaction

€

+ =5

192(udd)n (us )K +

+5

192(udd) p(us )K 0

+L

qqqq

€

S(1) =5

192~

1

6S(2) =

5

384~

1

9S(3) =

5

1152~

1

15

Other cases

SF SC JW> >

Feb. 16 (2005) Chiral05, RIKEN 10

Results

(0s)5 1/2 ー is dominated by the KN scattering states

Feb. 16 (2005) Chiral05, RIKEN 11

What we have learned:

・ Natural width of Pentaquarks　　 1/2− ~ GeV <= (0s)5 is expanded by KN　　 1/2 ＋ < 100 MeV <= Centrifugal force

・ Quark model values are consistent with them　　 Most likely (0s)5 1/2– can not be a narrow resonance　　 1/2 ＋ JW-diquark correlation -> 10 MeV　　 For 1 MeV width, we need more (spatial corr.)

Feb. 16 (2005) Chiral05, RIKEN 12

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==> Improper use of chiral symmetry

€

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

Assumption

Feb. 16 (2005) Chiral05, RIKEN 13

(2) QCD sum rule

Kondo-Morimatsu-Nishikawa (KEK)Ambiguities in the Fierz rearrangement€

0 JΘ JΘ 0 ~ 0 JΘ n n JΘ 0n

∑

= 0 JΘ KN KN JΘ 0 + 0 JΘ ′ n ′ n JΘ 0′ n

∑

Rearranged (Fierz) as

Should be subtracted in the sum rule

Five quark operator

€

∑ M(q q) ⋅B(qqq)

Feb. 16 (2005) Chiral05, RIKEN 14

Application of the soft kaon method

€

KN JΘ 0 ~ N [Q5K ,JΘ ] 0

~ N [Q5K ,uudds ] 0

~ N udd(u u + s s) 0 ~ u u + s s N udd 0

€

N

€

Proportional to fK

Feb. 16 (2005) Chiral05, RIKEN 15

(3) 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

(0s)5 1/2– (0s)40p 1/2+ could no longer survive neither

Fall apart when R→∞

Feb. 16 (2005) Chiral05, RIKEN 16

Other possibility

Could it be (0s)5 3/2 ー

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

Feb. 16 (2005) Chiral05, RIKEN 17

Phenomenology of 3/2- baryons

8-10 mixing

N

€

H =M10 − aY δ

δ M8 − bY + c[I(I +1) −Y 2 / 4]

⎛

⎝ ⎜

⎞

⎠ ⎟

Hyodo-Hosaka, hep-ph/0502093

€

+

(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

Feb. 16 (2005) Chiral05, RIKEN 18

• Pick up known resonances of JP = 1/2+ -, 3/2+ -

together with +

• Fitting into 8-10 mixing 1/2+

3/2-

Feb. 16 (2005) Chiral05, RIKEN 19

Coupling constants

€

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)

Feb. 16 (2005) Chiral05, RIKEN 20

Summary We have studied the fall-apart decay of +

• Naive quark model values (consistent with natural widths) 1/2+ Several tens MeV 1/2– ~ order of GeV 3/2– ~ zero or strongly suppressed

• CSF config. far from KN may provide a narrow width 1 MeV width needs more explanation of spatial corr.

• Full 5-body calculation could change the naïve results

• In the quark model, 3/2– is a natural candidate