Qiang Zhao

Theory Division Institute of High Energy Physics, CAS

Email: zhaoq@ihep.ac.cn

Topics on charmonium hadronic decays

Topics on charmonium hadronic decays

Univ. of Science and Technology of China

June 22, 2007

Outline

• Charm quark and charmonium spectrum• “ puzzle” and “12% rule” in J/, ’ V P ( V= , , , K*; P = , , , K)

• Isospin violations in V V P, e.g. , J/ 0

• Scalar glueball search in charmonium hadronic decays

• Summary

Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3;2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge.

Quarks as building blocks of hadrons: meson (qq), baryon (qqq)

• Quarks are not free due to QCD colour force (colour confinement).

• Chiral symmetry spontaneous breaking gives masses to quarks.

• Hadrons, with rich internal structures, are the smallest objects in Nature that cannot be separated to be further finer free particles.

• Quarks are not free due to QCD colour force (colour confinement).

• Chiral symmetry spontaneous breaking gives masses to quarks.

• Hadrons, with rich internal structures, are the smallest objects in Nature that cannot be separated to be further finer free particles.

• 原子 – 10–10 m

• 原子核 – 10–14 m

• 核子 ( 质子 , 中子 ) – 10–15

m

• 核子内部 ( 夸克 - 胶子 )自由度 (0.1~0.5)×10–15 m• 产生新强子 (, , K…)

电磁探针电磁探针

光子 E= 2×197.3 MeV·fm/

强子 ( 重子 + 介子 ) 是目前能从物质中分离出来、具有内部结构的

最小单元。

强子物理

探索物质的微观结构

• Charm quark and charmonium state

c

L

S=0

c

c

L

S=1

c

Parity:P=(1)L+1 Charge conjugate:C=(1)L+S

……….

J/

n=0c(2980) J/(3096)

'(3686)

0 (L=0,S=0) 1 (L=0,S=1) 0 (L=1,S=1)

Ma

ss (

MeV

)

c0(3414)

n=1

• Charm quark and charmonium states

1976 Nobel Prize: B. Richter and S. C.-C. Ting

"for their pioneering work in the discovery of a heavy

elementary particle of a new kind"

J/*e+

e-

Beijing Electron-Positron Collider

Vector meson production in electron-positron collision

c(2980)J/(3096)

0 (L=0,S=0) 1 (L=0,S=1)

Ma

ss (

MeV

) DD threshold

c(2980)

Light mesons, , K*K, …

J/ hadronic decay

glue

c

c Meson

J/

Glue rich intermediate states

f0

Lattice QCD prediction

Lattice QCD 0++: 1.5 ~ 1.7 GeV

Exp. Scalars: f0(1370)f0(1500)f0(1710)f0(1790) (?) f0(1810) (?)

Mesonq

q

q

q

• A probe of strong QCD dynamics

Close & Zhao, PRD71, 094022(2005); Zhao, PRD72, 074001 (2005)

Why study charmonium hadronic decays?

J/

c

c uudd(I=0)

J/

c

c

(I=0)

ss(I=0)

= (uu+dd)/2 = ss

• A flavour filter for Okubo-Zweig-Iizuka (OZI) disconnected transitions

V=

• Structure of the light hadrons: qq, glueball, multiquark, hybrid …• OZI rule violations• Isospin violations

(I=0)

qq (I=1)

• Exclusive decays of J/, ' Vector + Pseudoscalar OZI singly or doubly disconnected process “12% rule” for J/ and ‘ and “ puzzle”

• Isospin violated process: , J/, ' 0 , and its correlation with the OZI-rule violation

OZI doubly disconnected process Separate the EM and strong isospin violating processes

Focus Focus

“12% rule” and “” puzzle

• pQCD expectation of the ratio between J/ and ' annihilation:

• “ puzzle” R() =

c

J/, '

g c

c*

*

J/, '

c*

Large “12% rule” violation in !

JPC = 1

0.2 %

Theoretical explanations:

1. J/ is enhanced• J/-glueball mixing:

Freund and Nambu, Hou and Soni, Brodsky, Lepage and Tuan

• Final state interaction:

Li, Bugg and Zou

• Intrinsic charmonium component within light vectors:

Brodsky and Karliner, Feldman and Kroll

2. ' is suppressed• Karl and Roberts: sequential fragmentation model

• Pinsky: hindered M1 transition model

• Chaichian and Tornqvist: exponential form factor model

• Chen and Braaten: color octet Fock state dominance in J/• Rosner: ' and " mixing

3. Others …

Isospin violation process and its implication

c

c*

V

P

J/

g c

c*

V

P

J/

*

Comparable !?

Particle D

ata Gro

up

3g

3g

• “12% rule” will not hold if EM transitions are important.• Otherwise, interferences from the EM decays with the strong decays are unavoidable.

+/ EM + …

+/ EM + …

*c

c*

V

P

J/

* J/V

P

V

(, , …)

• Vector meson dominance model

V* coupling:

EM field in terms of vector meson fields:

*e+

e-

*e+

e-

=

• Vector meson dominance model

VP coupling:

V* coupling:

Transition amplitude:

I. Determine gVP in V P

V

P

II. Determine e/fV in V e+ e-

V*

e+

e-

III. Determine gP in P

All the relevant data are available !

IV. Form factors

Corrections to the V*P vertices:

P

Isospinviolatedprocess

Isospinviolatedprocess

For the isospin violated decays, the 12% rule has been violated.One cannot expect the 12% rule to hold in exclusive hadronic decays.

For those channels exhibiting large deviations from the empirical 12%, their EM contributions to 'VP are also relatively large.

with

Evidence for large EM transition interferences in :

Large branching ratio differences exist between the charged and neutral K*K-bar implies significant isospin violations.

A

Left = Right =

B

Left = Right =

C

Left = Right =

D

Left = Right =

Including EM and strong transitions (G. Li, Q. Z. and C.H. Chang, hep-ph/0701020)

• For the isospin violated decays, the 12% rule has been violated due to the contributions from the form factor corrections. One cannot expect the 12% rule to hold in exclusive hadronic decays.

• For those channels exhibiting large deviations from the empirical 12%, their EM contributions to ’ VP are also relatively large. Interferences from the EM transitions are important in the branching ratio fraction between J/psi and psi-prime. This could be one of the sources causing the large deviations from the empirical 12% rule (Zhao, Li and Chang, PLB645, 173 (2007)).

• One has to combine the strong interaction in the study of “ puzzle”, and this has been done in a QCD factorization scheme (Li, Zhao and Chang, hep-ph/0701020).

A brief summary A brief summary

Two sources:

I) Isospin violation via electromagnetic decays EM interaction does not conserve isospin

II) Isospin violation in strong decays

u and d quark have different masses Correlation with the OZI rule violation

Isospin violations in V V P Isospin violations in V V P

Isospin violation in 0

s

s

(I=0)

0 (I=1)

(I=0)

g

*

s

(I=0)

s (I=0)

0 (I=1)

I) EM process in VMD:

Isospin violation in 0

Decompose the EM field in terms of vector mesons in Process-I:

II) Isospin violation in strong decays:

Physical vacuum is not invariant under chiral symmetries

Chiral symmetry is spontaneously broken: Current quarks are no longer massless Chiral symmetry is explicitly broken: mu md

Manifestations: Light 0 octet mesons (Goldstone bosons), , K, Strong isospin violation: m(0) < m(); m(K0) >

m(K); m(p) < m(n) …

• Strong isospin violation via intermediate meson exchanges

If mu = md,

(a)+(b) = 0 and (c)+(d) = 0.

If mu md,

(a)+(b) 0 and (c)+(d) 0.

Li, Zhao and Zou, arXiv:0706.0384[hep-ph]

Three schemes for the intermediate meson exchange loops

1. On-shell approximation

2. Feynman integration with a monopole form factor

3. Feynman integration with a dipole form factor

1. On-shell approximation

0, No form factorn = 1, monopole 2, dipole

(GeV) : to be determined by experimental data.

Numerical results :

Experimental branching ratio:

On-shell approximation

underestimates the data.

Exclusive KK(K*) loop

EM and KK(K*) out of phase EM and KK(K*) in phase

• -dependence of the sum of EM and KK(K*) loop

Still underesitmate the experimental data.

2. Feynman integration with a monopole form factor

Similarly for the neutral meson loop …

• -dependence of the exclusive KK(K*) loop with a monopole form factor

• -dependence of the exclusive KK*(K) loop with a monopole form factor

3. Feynman integration with a dipole form factor

Exclusive KK(K*) loop contribution to BR

Exclusive KK*(K) loop contribution to BR

Inclusive contributions from the isospin violating transitions

Isospin violation = EM Strong decay loops

Exp.

Exp.

In phase Out of phase

V V P is a P-wave decay, favors a dipole form factor.

• The correlation between the OZI-rule violation and strong isospin violations makes the intermediate meson exchange process a possible dynamic solution for separating the EM and the strong isospin violation mechanisms.

• Application to the study of a0(980)-f0(980) mixing in J/ a0(980) 0 (J.J. Wu, Q.Z. and B.S. Zou, Phys. Rev. D in press).

• Experimental focuses of BES, CLEO-c, KLOE, B-factories…

Summary Summary

Thanks !Thanks !

• Conventional and unconventional meson

• Scalar mesons between 1~2 GeV

• Scalar glueball-qq mixing

• Scalar meson production in charmonium hadronic decays

Scalar meson structures probed in charmonium hadronic decays

Scalar meson structures probed in charmonium hadronic decays

Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3;2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge.

Meson spectroscopyMeson spectroscopy

I) QQ mesons Quarks as building blocks of hadrons: meson (qq), baryon (qqq)

Conventional QQ mesons:

1. Mesons are bound state of QQ with baryon number B=0; 2. The parity is given by P=(1)L+1 with orbital angular momentum L; 3. The meson spin J is given by |LS| < J < | L+S| , where S=0, 1 are the total spin of the quarks.4. Charge conjugate is defined as C=(1)L+S for mesons made of quarkand its own antiquark.

For light quarks: u, d, and s, the SU(3) flavor symmetry constrains the number of flavor QQ multiplet:

3 3 = 8 1

3 4 1 1

II) Non-QQ mesons

Type (a): JPC are not allowed by QQ configuration

+

L

S=1

For states in natural spin-parity series P=(1)L+1 =(1)J , the state must have S=1 and hence CP=(1)(L+S)+(L+1) =+1. Therefore, mesons with natural spin-parity but CP= 1 will be forbidden, e.g.

0+, 1+, 2+, 3+, …

Natural: 0++, 1, 2++, 3, …Unnatural: ( 0), 1++, 2,3++, …

+

L

S=0

Unnatural: 0+, 1+, 2+, 3+, …

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

Jaffe’s Multiquarks? Meson molecule ?

Glueball ?QQ-glue mixing ?

Ma

ss f0(1790)

f0(1810)

Experimental signals for scalar mesonsExperimental 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

MeV

MeVM

40265

501350

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)

MeV

MeVM

20125

301740

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 ?

glue

c

c M

J/

Glue rich intermediate states

f0

Lattice QCD prediction

Morningstar and Peardon, PRD60, 034509 (1999)

Interest in scalar glueball search: Mesons are made of colored gluons confined by strong interaction

Lattice 0++: 1.5 ~ 1.7 GeV

Exp. Scalars: f0(1370)f0(1500)f0(1710)f0(1790) (?) f0(1810) (?)

Mq

q

q

q

Glueball and QQ mixing in the scalar mesons 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 PPParameterization of f0 PP

g0 r2 g0r3 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:

ii) OZI rule on f0(1370): br(J/ f0(1370)KK)<< br(J/ f0(1370)) Exp: br(J/ f0(1370)) is dominant !

KK

gg ss nn

0.36 0.93 0.09

0.84 0.35 0.41

0.40 0.07 0.91

c

c

ss

f0(1710)i) 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 !

Scalar mesons production in J/ V f0 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.

gg

J/

V (, )

f0

P

P

Factorization of J/ V f0 V P PFactorization 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 PPartial 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 ?

OZI violation mechanism for J/ V f0OZI violation mechanism for J/ V f0

Large J/K*K coupling;Large K*K coupling;Large f0(1710)KKbar coupling

c

c*

J/

K*

K

K

Zhao, Zou & Ma, PLB631, 22(2005), hep-ph/0508088.

Intermediate K*K rescattering contributions to J/ f0, f0

Factorization for c0,2 VV, PP, & SS Factorization for c0,2 VV, PP, & SS

(a) (b)

g0: basic gqq* coupling

r: OZI-rule violation

R: SU(3)f breaking

t: 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. (PRD2005, 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

Factorization for c VV Factorization for c VV

BES Collaboration, PRD72, 072005(2005).

OZI violation mechanism for c

BES estimate:

Summary-1Summary-1

I. Charmonium hadronic decays are useful for providing additional information about the scalar meson structures.

II. The glueball contents are essentially important for interpreting the “puzzling” data from BES for the scalar meson production in J/ decays.

III. 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.

IV. A possible source for the OZI-rule violation is transitions via intermediate meson rescatterings for which a systematic investigation can be pursued.

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-2Summary-2