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### Fall-apart decay of Q+

Atsushi Hosaka (RCNP, Osaka Univ)

Feb. 16 (2005) Chiral05 RIKEN

Based on

hep-ph/0409102

A. H., M. Oka and T. Shinozaki

Widths & a possible quark model state for Q+

Chiral05, RIKEN

・In production experiments, G << 20 MeV

・In KN scattering 1 MeV or less

G = 1, 5, 10, 20 MeV

Sibirtsev et al,

PLB599 (2004) 230-235

T. Nakano et al.

PRL, 91, 012002 (2003)

Chiral05, RIKEN

N-like

N

N*

Q+

N

Fall apartExpected to be a dominant decay mechanism of Q+

K

Q+

Rearranged

V

N

S-factor

Intereaction

q-qbar annihilation

Chiral05, RIKEN

G = 5 GeV

Effect of entrifugal barrier ~ 50 !

Simple estimate1/2+ P-wave coupling

M* = 1540 MeV, gKNQ ~ 10

G = 100 MeV

Empirical fact: gmNN* < 10 (pNN or sNN)

Chiral05, RIKEN

p

s

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

Unique for the antidecuplet

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

Spectroscopic factor

gKNQ ~ 3

G ~ 500 MeV

Chiral05, RIKEN

p

s

Positive parityMore complicated than s-wave

due to p-wave excitation

MinimizeSpin-Flavor interaction

MinimizeSpin-Color

(3) Diquark correlation of JW

Chiral05, RIKEN

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)51/2– can not be a narrow resonance

1/2＋JW-diquark correlation -> 10 MeV

For 1 MeV width, we need more (spatial corr.)

Chiral05, RIKEN

Comments

A related work

Melokov, Simula and Stech, PLB 594 (2004) 265

Claimed that G ~ 150 MeV for the JW wf

Assumption

In the quark model, there is no pole (hA) term

==> Improper use of chiral symmetry

Chiral05, RIKEN

(2) QCD sum rule

Five quark operator

Rearranged (Fierz) as

Should be subtracted in the sum rule

Kondo-Morimatsu-Nishikawa (KEK)

Ambiguities in the Fierz rearrangement

Chiral05, RIKEN

(3) 5-body calculation

Recent calculation by Hiyama

Gaussian Expansion Method

+

+ . . .

KN Scattering state

Confined state

Fall apart when R→∞

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

Chiral05, RIKEN

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

Chiral05, RIKEN

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

together with Q+

• Fitting into 8-10 mixing

1/2+

3/2-

Chiral05, RIKEN

Coupling constants

• qN can be fixed by masses

• Two nucleon decay widths

determine g8 and g10

• The resulting g10 determines GQ

GQ (MeV)

Chiral05, RIKEN

SummaryWe have studied the fall-apart decay of Q+

• 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

Chiral05, RIKEN

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