fall-apart decay of q +
DESCRIPTION
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 +. Outline. Fall apart Quark model calculation Comments Possibility of spin 3/2 - Conclusion. - PowerPoint PPT PresentationTRANSCRIPT
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