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1. “Exotic” S-wave Interaction
Why interested ? How “exotic” ? Similarity between and N s-wave scattering
What’s the nature of the broad ? Why it appears narrower in production processes ? Why f0(980)’s peak width is so narrow ?
2.S0pp & I=1 S0pp near threshold enhancement
3. KS-wave near threshold enhancement in J/p K-vs p p p
1. “Exotic” S-wave Interaction Why interested ?
1) a fundamental strong interaction process and a necessary input for many reactions involving multi-pions
2) I=0 S-wave has the same quantum number of f0 resonances which include : /f0(600) (-model, exchange for NN interaction)
and the lightest glueball candidate f0(1500)/f0(1710)
f0
Exotic I=0 S-wave
I=0 D-wave
I=1 P-wave
I=1 F-wave
(770)
(1690)f2(1270)
D.V.Bugg, A.Sarantsev,B.S.Zou, Nucl. Phys. B471 (1996) 59
What’s the nature of the broad ?
Important role by t-channel exchange for all these processes
=0 = - 2 K
I=2 =1/2 = - 2 K
I=3/2
D. Lohse, J.W. Durso, K. Holinde, J. Speth, Nucl.Phys.A516, 513 (1990) B.S.Zou, D.V.Bugg, Phys. Rev. D50, 591 (1994)
Basic features of I=2 Interaction F.Q.Wu, B.S.Zou et al., Nucl. Phys.A735 (2004) 111
repulsive force by t-channel
attractive force by t-channel f2
Inelasticity by
S-wave
An important cause for hadron-hadron S-wave interactions appearing “exotic” is
t-channel meson-exchange amplitude has a comparable strength as s-channel resonance contribution for S-waves.
For higher partial waves, s-channel resonance contributiondominates.
Why broad appears narrower in production processes than in elastic scattering?
Tel= K / ( 1 - i K ) = K + K i K + K i K i K + …
Tprod= P / ( 1 - i K ) = P + P i K + P i K i K + …
el
prod
Tel from Bugg,Sarantsev,Zou Nucl. Phys. B471 (1996) 59
with pole at ( 0.571 – i 0.420 ) GeV
Tprod = Tel * P / K , K = tan
assuming P=1
How about production vertex P ?
P(V’V)
T. Mannel, R. Urech, Z. Phys.C73, 541 (1997); Ulf-G. Meißner, J.Oller, Nucl.Phys. A679 (2001) 671; L. Roca, J. Palomar, E. Oset, H.C.Chiang, Nucl. Phys. A744 (2004) 127F.K.Guo,P.N.Shen, H.C.Chiang, R.G.Ping, Nucl.Phys.A761 (2005) 269
For ’J/ , E small, 1st term dominates higher peak
For , E large, 2nd term dominates lower peak
peak position is process dependent !
P ~ c1 + c2 s
Why f0(980)’s peak width is so narrow ?
BES, hep-ex/0411001M = 965 MeVg1 = 165 MeV2
r = g2/g1 = 4.21
r = 0
r = 4.21
Strong coupling toKKstrongly reduce the peak width of f0(980)
B.S.Zou, hep-ph/9611235, “ S-wave interaction and 0++ particles”
0++ particles with substantial couplings to : /f0(600), f0(980), f0(1500), f0(1780-1800)
S0pp & I=1 S0pp near threshold enhancement
pmppM 2)(
|M|2BES
elasticelasticM ~|| 2
Both arbitrary normalization
BES, Phys. Rev. Lett. 91, 022001 (2003)
J/ → pp p p p p
COSY-TOF, Eur.Phys.J.A16, 127 (2003)
One-Pion-Exchange and BES pp (1S0) near threshold enhancement Zou B.S., Chiang H.C. Phys.Rev.D69 (2004) 034004
NN interaction :
9 (S , I ) = (0,0) 1 (S , I ) = (1,1)-3 (S , I ) = (1,0) or (0,1) {
NN interaction :
I=0, pp (1S0) gets the biggest attractive force !
deuteron
A.Sibirtsev, J. Haidenbauer, S. Krewald, Ulf-G. Meißner, A.W. Thomas, hep-ph/0411386
P-waveI=0 s-wave
I=1 s-wave
Pure I = 1
(I=0) + (I=1)
Near threshold enhancement for I=0NN annihilation
E. Klempt, F. Bradamante, A. Martin, J. Richard, Phys. Rept. 368 (2002) 119
BES, Phys. Lett. B472 (2000) 207
PWA Results on J/ to 4
0- +
BES, Phys. Lett. B446 (1999) 356
J/
0-+ resonances decaying to meson channels
0- +
In summary,pp near threshold enhancement is very likely due to some broad sub-threshold 0-+ resonance(s) plus FSI.
3. Ks-wave near threshold enhancement
complimentary BES and COSY experiments
J/P K-vs P P P
P&P the samet-channel interaction
K-& the same interaction
P K- for * P K+ for pentaquarks
)(GeV/c2KΛM
Eve
nts
/10
MeV
Nx
Nx
Nx
)(GeV/c2 MMM KKΛ
PS, eff. corrected
(Arbitrary normalization)
Near-threshold enhancement in MK
B.C.Liu and B.S.Zou, Phys. Rev. Lett. 96 (2006) 042002
From relative branching ratios of
J/pN* p (K-p (p
gN*K/gN*p/gN*p~ 1.3 : 1 : 0.6
Smaller N*(1535) BW mass
previous results 0 ~ 2.6 from N and N data
P P P withgN*K/gN*p= 1.3
without N*(1535)K.Tsushima, A.Sibirtsev, A.Thomas, Phys.Rev.C59 (1999) 369
with N*(1535)
A.Zhang, Y. Liu, P. Huang, W. Deng, X.Chen, S.L. Zhu, hep-ph/0403210 :
1/2- and 1/2+ octet N* pentaquarks have similar masses in Jaffe-Wilczek diquark model
N*(1535) ~ uud (L=1) + [ud][us]s + …
N*(1440) ~ uud (n=1) + [ud][ud]d + …
*(1405) ~ uds (L=1) + [ud][su]u + …
Larger [ud][us]s component in N*(1535) makes it coupling stronger to N & K, weaker to N & K and heavier ! B.C.Liu, B.S.Zou, PRL 96(2006)042002
ud
du
q
u
du
qSq ½+
[ud][ud]
}L=1
q ½ -[ud][us]
}L=0
Summary for our study on J/P K-and P P P
1) near-threshold enhancement due to N*(1535) with gN*K/gN*p= 1.0 ~ 1.6 compatible with all data
2) Larger [ud][us]s component in N*(1535) makes it coupling stronger to strangeness and heavier !