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 %95@13.0))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 !