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)]
June 16-20, 2005 北京 4
1. Decay of +
June 16-20, 2005 北京 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
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~
5q2q
5q~
Other mechanisms?
Ni = Nf
Ni < Nf
June 16-20, 2005 北京 7
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
June 16-20, 2005 北京 9
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,
June 16-20, 2005 北京 10
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) =5
192~
1
6S(2) =
5
384~
1
9S(3) =
5
1152~
1
15
SF SC JW
> >
Carlson et al, PRD70, 037501 (2004), hep-ph/0312325,Jennings-Maltman, PRD 69, 094020 (2004), hep-ph/0308286
June 16-20, 2005 北京 12
Results
(1/2-) >> (1/2+)
June 16-20, 2005 北京 13
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
June 16-20, 2005 北京 15
2. Phenomenology of 3/2- baryons
Hyodo-Hosaka, hep-ph/0502093, PRD71:054017 (2005)
June 16-20, 2005 北京 16
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
June 16-20, 2005 北京 17
• 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
June 16-20, 2005 北京 20
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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
June 16-20, 2005 北京 21
Theoretical studyEffective Lagrangian method
hep-ph/0505134Nam-Hosaka-Kim
appears only for n-target
June 16-20, 2005 北京 22
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
June 16-20, 2005 北京 23
Total
Angular dist
Log
-sca
le
Log
-sca
le
Theta production, JP = 3/2-
June 16-20, 2005 北京 24
The role of the contact term is more important for JP = 3/2- than 1/2+
June 16-20, 2005 北京 25
Predictions
• We see a large asymmetry between pn targets • Cross section for proton ~ few nb is consistent with
the upper limit estimated by CLAS
June 16-20, 2005 北京 26
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
June 16-20, 2005 北京 27
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→∞
June 16-20, 2005 北京 29
1/2– 1/2+
KN-like JW-type
(0s)5 1/2– , (0s)40p 1/2+ can no longer survive