Qiang Zhao

1
Univ. of Science and Technology of China June
22, 2007
Topics on charmonium hadronic decays

• Qiang Zhao
• Theory Division
• Institute of High Energy Physics, CAS
• Email zhaoq_at_ihep.ac.cn

2
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

3
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.

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.
4
?????????
?? (????) ?????????????????????????

• ?? 1010 m

• ??? 1014 m

????
?

• ??(??,??) 1015 m

????
?? E? 2?197.3 MeVfm/?

• ????(??-??)??? (0.10.5)1015 m
• ?????(?, ?, K)

5

• Charm quark and charmonium state

Parity P(?1)L1 Charge conjugate C(?1)LS
S0
c
?c
J/?
L
S1
c
?c
??
L
.
6

• 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"
Mass (MeV)
n1
?'(3686)
?c0(3414)
n0
J/?(3096)
?c(2980)
0?? (L0,S0)
1?? (L0,S1)
0?? (L1,S1)
7
Vector meson production in electron-positron
collision
e
?
J/?
e-
Beijing Electron-Positron Collider
8
J/? hadronic decay
D?D threshold
Mass (MeV)
?c(2980) ?
J/?(3096)
?c(2980)
Light mesons ??, ??, KK,
0?? (L0,S0)
1?? (L0,S1)
9
Why study charmonium hadronic decays?

• A probe of strong QCD dynamics

q
Meson
c
glue
?q
J/?
q
?c
Meson
?q
Glue rich intermediate states
Lattice QCD 0 1.5 1.7 GeV Exp.
Scalars f0(1370) f0(1500) f0(1710) f0(1790)
(?) f0(1810) (?)
f0
Lattice QCD prediction
Close Zhao, PRD71, 094022(2005) Zhao, PRD72,
074001 (2005)
10

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

? (uudd)/?2 ? ss
V
?(I0)
?(I0)
c
c
J/?
J/?
uu?dd (I0)
q?q (I1)
c
c
ss(I0)

• Structure of the light hadrons q?q, glueball,
  multiquark, hybrid
• OZI rule violations
• Isospin violations

11
Focus

• 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

12
12 rule and ?? puzzle

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

R(??)
? 0.2
Large 12 rule violation in ?? !
g
c
c
?
JPC 1??
J/?, ?'
J/?, ?'
c
c
13

• 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

14
Isospin violation process and its implication
Particle Data Group
Comparable !?
V
V
g
c
c
?
J/?
J/?
P
P
c
c
15
/? EM
3g
?
/? EM
3g

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

V
c
V
?
?
J/?
J/?
P
P
c
16

• Vector meson dominance model

??
e
e
?
?
V (?, ?, ? )

??
e-
e-
EM field in terms of vector meson fields
V? coupling
17

• Vector meson dominance model

V?P coupling
V? coupling
Transition amplitude
18
I. Determine gV?P in V ? ? P
?
V
P
19
II. Determine e/fV in V ? e e-
e
?
V
e-
20
III. Determine gP?? in P ? ??
?
P
?
IV. Form factors
Corrections to the V?P vertices
All the relevant data are available !
21
Isospin violated process
22
Isospin violated process
23
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.
24
Evidence for large EM transition interferences in
?? Large branching ratio differences exist
between the charged and neutral KK-bar implies
significant isospin violations.
A
Right
Left
with
25
B
Right
Left
C
Left
Right
D
Left
Right
26
Including EM and strong transitions (G. Li, Q.
Z. and C.H. Chang, hep-ph/0701020)
27
A brief summary

• 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).

28
Isospin violations in V ? V P

• 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

29
Isospin violation in ? ? ? ?0
? (I0)
g
s
? (I0)
?0 (I1)
?s
? (I0)
s
?
? (I0)
?0 (I1)
?s
30
Isospin violation in ? ? ? ?0
I) EM process in VMD
31
Decompose the EM field in terms of vector mesons
in Process-I
32
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) lt m(??) m(K0) gt
  m(K?) m(p) lt m(n)

33

• 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, arXiv0706.0384hep-ph
34
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
35
1. On-shell approximation
0, No form factor n 1, monopole
2, dipole
? (GeV) to be determined by experimental data.
36
Numerical results
Experimental branching ratio
On-shell approximation underestimates the data.
Exclusive KK(K) loop
37

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

EM and KK(K) out of phase
EM and KK(K) in phase
Still underesitmate the experimental data.
38
2. Feynman integration with a monopole form factor
?
Similarly for the neutral meson loop
39

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

40

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

41
3. Feynman integration with a dipole form factor
Exclusive KK(K) loop contribution to BR
42
Exclusive KK(K) loop contribution to BR
43
Inclusive contributions from the isospin
violating transitions
Isospin violation EM ? Strong decay loops
V ? V P is a P-wave decay, favors a dipole form
factor.
In phase
Out of phase
Exp.
Exp.
44
Summary

• 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

45
Thanks !
46
Scalar meson structures probed in charmonium
hadronic decays

• Conventional and unconventional meson
• Scalar mesons between 12 GeV
• Scalar glueball-q?q mixing
• Scalar meson production in charmonium hadronic
  decays

47
Meson spectroscopy
I) Q?Q mesons Quarks as building blocks of
hadrons meson (q?q), baryon (qqq)
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.
48
Conventional Q?Q mesons

• Mesons are bound state of Q?Q with baryon number
  B0
• The parity is given by P(?1)L1 with orbital
  angular momentum L
• The meson spin J is given by L?S lt J lt LS ,
  where S0, 1 are
• the total spin of the quarks.
• 4. Charge conjugate is defined as C(?1)LS for
  mesons made of quark
• and its own antiquark.

For light quarks u, d, and s, the SU(3) flavor
symmetry constrains the number of flavor Q?Q
multiplet 3 ? ?3 8 ? 1
3 4 1 1
49
II) Non-Q?Q mesons
Type (a) JPC are not allowed by Q?Q
configuration
For states in natural spin-parity series
P(?1)L1 (?1)J , the state must have S1 and
hence CP(?1)(LS)(L1) 1. Therefore, mesons
with natural spin-parity but CP ?1 will be
forbidden, e.g. 0?, 1?, 2?, 3?,
L

Natural 0, 1??, 2, 3??, Unnatural ( 0??),
1, 2??,3,
?
S1
L

Unnatural 0?, 1?, 2?, 3?,
?
S0
50
Exotic type 1 Mesons have the same JPC as a Q?Q,
but cannot be accommodated into the SU(3) nonet
3 ? ?3 8 ? 1
3 4 1 1
f0(1810)
f0(1790)
Mass
f0(1710)
Glueball ? Q?Q-glue mixing ?
f0(1500)
f0(1370)
?(1020)
f0(980)
??(958)
Jaffes Multiquarks? Meson molecule ?
?(782)
?/f0(600)
?(547)
0??
1??
0??
I0
51
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 ??, ??, ???, K?K,

52
f0(1370) at BES
f0(1370) ??? is dominant over K K, ??, ??? ?
nonstrange n?n
f0(1370)

• f0(1370) clearly seen in J/? ? ???, but not seen
  in J/? ? ???.

NO f0(1370)
S. Jin, Plenary talk at ICHEP04
53
f0(1710) at BES
f0(1710) ?KK is dominant. ? s?s
f0(1710)

• Clear f0(1710) peak in J/? ? ?KK.
• No f0(1710) observed in J/? ? ??? !

NO f0(1710)
S. Jin, Plenary talk at ICHEP04
54

• A flavour filter for OZI singly disconnected
  transitions

? (uudd)/?2 ? ss
V
?
?
c
c
J/?
J/?
c
c
ss
uu?dd
f0(1370)
f0(1710)
Could the exp. puzzle imply correlations between
the structure of scalars and their prod.
mechanism in J/? ? V f0 ?
55
Interest in scalar glueball search Mesons are
made of colored gluons confined by strong
interaction
q
M
c
glue
?q
J/?
q
?c
M
?q
Glue rich intermediate states
Lattice 0 1.5 1.7 GeV Exp.
Scalars f0(1370) f0(1500) f0(1710) f0(1790)
(?) f0(1810) (?)
f0
Lattice QCD prediction
Morningstar and Peardon, PRD60, 034509 (1999)
56
Glueball and Q?Q mixing in the scalar mesons
In the basis of Ggt gg, Sgt s?s, and Ngt
n?n (u?u d?d)/?2, the glueball-quarkonia
mixing can be expressed as
S
G
N
where i1,2,3, and f1,2,3 f0(1710), f0(1500)
and f0(1370), respectively.
Amsler Close, PLB353, 385(1995) PRD53,
295(1996) Close Kirk, PLB483, 345(2000).
57
Parameterization of f0 ? PP
r3 ? g0
g0
r2 ? g0
P
?
?
f0
P
Partial decay widths for f0 ? PP
Close Zhao, PRD71, 094022(2005)
58
WA102
WA102BES
f0 states
1710
S
1500
G
1370
N
Lattice QCD MG 1.5 1.7 GeV
Strong QCD character.
59
Implications of the OZI-rule violation
gg s?s n?n
0.36 0.93 0.09
?0.84 0.35 ?0.41
0.40 ?0.07 ?0.91
?
c
??
K?K
c
ss
f0(1710)
i) OZI rule on f0(1710) br(J/???
f0(1710)??K?K) gt br(J/??? f0(1710)??K?K) Exp
br(J/??? f0(1710)??K?K) / br(J/??? f0(1710)??K?K)
0.3 !
ii) OZI rule on f0(1370) br(J/???
f0(1370)??K?K)ltlt br(J/??? f0(1370)????) Exp
br(J/??? f0(1370)????) is dominant !
60
Scalar mesons production in J/? ? V f0
I) Singly disconnected diagram
II) Doubly disconnected diagram
? (ss)
? (ss)
g
c
c
g
J/?
J/?
f0 (ss)
c
f0 (nn)
c
III) Glue configuration
pQCD Okubo-Zweig-Iizuka (OZI) rule I) III)
? ? II) ?g2/4? 0.3 However, a glueball
component implies significant OZI-rule violations.
? (ss)
c
J/?
f0 (gg)
c
61
Factorization of J/? ? V f0 ? V P P
V (?, ?)
Transition amplitudes via potential V?
J/?
P
f0
III) I) II)
P
Doubly OZI disconnected
Project to the final physical states
Gluon-counting rule I) III)
62
Partial decay width for J/? ? V f0 ? V P P
?(nn)
?(ss)
c
c
J/?
J/?
G(gg)
G(gg)
c
c
Flavor-blindness of quark-gluon interaction
63
Step 1 Direct test of the OZI rule
BES Experiment br(J/??? f0(1710)??KK) (2.0 ?
0.7) ? 10?4 br(J/??? f0(1710)??KK) (13.2 ?
2.6) ? 10?4
a) OZI rule applies r ? 0
PDG estimate Rexp 0.75
b) OZI rule violated r 1
where
r 2.2
64
Step 2 Normalize the G production
Normalized glueball production b.r. ratios
Scalar decay br. ratios
65
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 ?
66
OZI violation mechanism for J/? ? V f0
c
K
K
J/?
K
c
Large J/?KK coupling Large ?KK coupling Large
f0(1710)KKbar coupling
Zhao, Zou Ma, PLB631, 22(2005), hep-ph/0508088.
67
Intermediate KK rescattering contributions to
J/? ? ? f0, ?f0
68
Factorization for ?c0,2 ? VV, PP, SS
(a)
(b)
g0
r
(c)
(d)
g0 basic gqq coupling r OZI-rule
violation R SU(3)f breaking t glueball
coupling strength
Zhao, PRD72, 074001 (2005)
69
For a typical state
the transition amplitude is factorized to be
A commonly used form factor
70
i) ?c0,2 ? V V
?c0
?c2
BES data
Predictions
The OZI violation need to be constrained by data
for ?? channel.
71
ii) ?c0,2 ? P P
Improved data for ?? channel are required.
72
iii) ?c0,2 ? f0 f0
Branching ratio fractions

• a) If OZI-rule is respected, i.e. r?0,
• will be the smallest decay channel.
• b) If OZI-rule is violated, i.e. r?1,
• will be the largest
  decay channel.

normalized
Exp. Data from BES for ?c0? f0(1710) f0(1370) ?
KK??. (PRD2005, hep-ex/0508050)
73
Factorization for ?c ? VV
BES Collaboration, PRD72, 072005(2005).
74
OZI violation mechanism for ?c ? ??
BES estimate
75
Summary-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.
76
Summary-2
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?