Qiang ZhaoInstitute of High Energy Physics, CAS, P.R. China
• “Scalar puzzles” from the recent exp. data• Scalar glueball and QQ* mixing • Mechanisms for scalar meson productions in (i) J/ V f0 V PP ( V= , ; P = , , , K), (ii) c0 PP, VV, f0 f0. • Summary
Mixing of scalar meson and glueball
Charm 2006, Beijing, June 6, 2006
In collaboration with Frank Close and Bing-song Zou
Exotic type 1: Mesons have the same JPC as a QQ*, but cannot be accommodated into the SU(3) nonet: 3 3* = 8 1
3 4 1 1
I=0
f0(980)(958)
(547)(782)
(1020)
/f0(600)
f0(1370)f0(1500)
f0(1710)
0 1 0
Multiquarks? Meson molecule ?
Glueball ?QQ*-glue mixing ?
Mas
s
f0(1790)f0(1810)M. Chanowitz
Experimental signals for scalar mesons
• Crystal Barrel, WA102, MARKIII, DM2 …
• Beijing Spectrometer (BES) J/ V f0; f0 PP, J/ f0; f0 PP, VV cj f0 f0, f0 f2 V=, , K*, ; PP=, , , KK^,
f0(1370) clearly seen in J/ , but not seen in J/ .
/J
/J
f0(1370)
NO f0(1370)
f0(1370) at BES
MeVMeVM
40265501350
S. Jin, Plenary talk at ICHEP04
f0(1370) is dominantover K K, , ; nonstrange nn*
• Clear f0(1710) peak in J/ KK.
• No f0(1710) observed in J/ !
f0(1710) at BES
KKJ /
/J
f0(1710)
NO f0(1710)
MeVMeVM
20125301740
CLKKfBR
fBR %[email protected]))1710(())1710((
0
0
S. Jin, Plenary talk at ICHEP04
f0(1710) KK^ is dominant. ss*
J/
c
c
uudd
J/
c
c
ss
= (uu+dd)/2 = ss
• A flavour filter for OZI singly disconnected transitions:
V=
f0(1370) f0(1710)
Could the exp. puzzle imply correlations between the structure of scalars and their prod. mechanism in J/ V f0 ?
gluec
c* M
J/
Glue rich intermediate statesf0
Lattice QCD prediction
Morningstar and Peardon, PRD60, 034509 (1999)
Glueball: Mesons are made of colored gluons confined by strong interaction
Lattice 0++: 1.5 ~ 1.7 GeVExp. Scalars: f0(1370)
f0(1500)f0(1710)f0(1790) (?) f0(1810) (?)
Mq
q*
q*
q
Glueball and QQ* mixing in the scalar mesons
In the basis of |G> = gg, |S> = ss*, and |N> = nn* = (uu*+dd*)/2, the glueball-quarkonia mixing can be expressed as:
S
N
G
Amsler & Close, PLB353, 385(1995); PRD53, 295(1996); Close & Kirk, PLB483, 345(2000).
where i=1,2,3, and f1,2,3 = f0(1710), f0(1500) and f0(1370), respectively.
Parameterization of f0 PP
g0 r2 g0 r3 g0
f0
P
P
Partial decay widths for f0 PP:
Close & Zhao, PRD71, 094022(2005)
S
N
G
Lattice QCD: MG ~ 1.5 – 1.7 GeV
f0 states
1710
1370
1500
WA102 WA102+BES
Strong QCD character.
Implications of the OZI-rule violation:
i) OZI rule on f0(1370): br(J/ f0(1370)KK^)<< br(J/ f0(1370)) Exp: br(J/ f0(1370)) is dominant !
ii) OZI rule on f0(1710): br(J/ f0(1710)KK^) > br(J/ f0(1710)KK^) Exp: br(J/ f0(1710)KK^) / br(J/ f0(1710)KK^) ~ 0.3 !
KK^
gg ss* nn*
0.36 0.93 0.09
0.84 0.35 0.41
0.40 0.07 0.91
c
c
ssf0(1710)
Scalar mesons production in J/ V f0
c
c*
(ss*)
f0 (ss*)
c
c*
J/ J/
(ss*)
f0 (nn*)
I) Singly disconnected diagram II) Doubly disconnected diagram
III) Glue configuration
c
c*
J/
(ss*)
f0 (gg)
pQCD Okubo-Zweig-Iizuka (OZI) rule: I) ~III) ~ II) =g2/4 ~ 0.3
However, a glueball component implies significant OZI-rule violations.
g g
J/
V (, )
f0
P
P
Factorization of J/ V f0 V P P
Transition amplitudes via potential V
III)I)II) Doubly OZI disconnected
Project to the final physical states:
Gluon-counting rule: I) ~ III)
Partial decay width for J/ V f0 V P P
c
c*
J/
(ss*)
G(gg)
c
c*
J/
(nn*)
G(gg)
Flavor-blindness of quark-gluon interaction:
Step 1: Direct test of the OZI rule
a) OZI rule applies: r 0
b) OZI rule violated: r ~ 1
r = 2.2
where
PDG estimate: Rexp = 0.75
BES Experiment: br(J/ f0(1710)KK*) = (2.0 0.7) 104
br(J/ f0(1710)KK*) = (13.2 2.6) 104
Step 2: Normalize the G production
Normalized glueball production b.r. ratios
Scalar decay br. ratios
Step 3: Theoretical predictions for J/V f0 V KK*, V
The “puzzle” can be explained in the glueball-QQ* mixing scheme, which implies large OZI violation effects in the scalar production.
Puzzle Evidence for the presence of scalar glueball ?
Further test of the gluon-QQ*mixings
i) f0 probe the quark components of
the scalars: f0(1370) : f0(1500) : f0(1710) ~
12 : 2 : 1
ii) f0 V, (V= , 0) f0(1710) ( ) > ( 0) f0(1370) ( ) < ( 0) f0(1500) ( ) < ( 0)
iii) J/ f0 f0(1710) > f0(1500) > f0(1370)
iv) c0f0f0, f0f2
0.36 0.93 0.09
0.84 0.35 0.41
0.40 0.07 0.91
gg ss* nn*
f0(1710)
f0(1500)
f0(1370)
+ + + + +
gg ss* nn*
f0(1710)
f0(1500)
f0(1370)
1 billion J/ events from BESIII
2. c0,2 hadronic decays VV, PP, & SS
(a) (b)
g0: basic gqq* coupling
r: OZI-rule violationR: SU(3)f breakingt: glueball coupling strength
g0
r
(c) (d)
Zhao, PRD72, 074001 (2005)
For a typical state:
the transition amplitude is factorized to be:
A commonly used form factor:
i) c0,2 V V
c0
c2
BES data
Predictions
The OZI violation need to be constrained by data for channel.
ii) c0,2 P P
Improved data for channel are required.
Exp. Data from BES for c0 f0(1710) f0(1370) KK. (hep-ex/0508050)
normalized
Branching ratio fractions
a) If OZI-rule is respected, i.e. r0,
will be the smallest decay channel.
b) If OZI-rule is violated, i.e. r1, will be the largest
decay channel.
iii) c0,2 f0 f0
Summary-1
I. The glueball contents are essentially important for interpreting the “puzzling” data from BES for the scalar meson production in J/ decays.
II. The strong glueball-QQ* mixings within the scalar mesons imply large OZI violations in J/ V f0, and suggest the crucial role played by the doubly disconnected processes.
A possible source for the OZI-rule violation is transitions via intermediate meson exchanges.
Zhao, Zou & Ma, PLB631, 22(2005), hep-ph/0508088.
K*
K
K
III. A normalization of the glueball production rate is obtained, which possesses predictive power for the study of the glueball mixing effects in the J/ radiative decay channel and c0 f0f0.
Further experimental data will be useful for establishing these f0 states as glueball-QQ* mixing states:
BES, CLEO-c, GSI (?)…Glue-X at JLab?
Summary-2
Thanks !
