Qiang Zhao

1
Institute of High Energy Physics, CAS
The role of intermediate meson loops in
charmonium decays

• Qiang Zhao
• Institute of High Energy Physics, CAS
• and Theoretical Physics Center for Science
  Facilities (TPCSF), CAS

Effective Field Theories in Particle and Nuclear
Physics, KITPC/ITP-CAS, August 03-Sept. 11, 2009
2
Motivations

• Charmonium decays as a probe for non-perturbative
  QCD mechanisms
• Several exisiting puzzles in low-lying vector
  charmonium decays

3
Several well-known puzzles in charmonium decays

• ?(3770) non-D?D decay
• ?? puzzle in J/?, ?? ? VP decay
• M1 transition problem in J/?, ?? ? ? ?c, (? ?c?)
  
• Isospin-violating decay of ??? J/? ?0, and ???
  hc?0

Conjecture These puzzles could be related to
non-pQCD mechanisms in charmonium decays due to
intermediate D meson loops.
4

• Charmonium spectrum

5

• Open-charm effects in charmonium decays

?(3770)
D?D threshold
?(3686)
Mass (MeV)
?c(2980) ?
J/?(3096)
?c(2980)
OZI rule violating transition
Light mesons ??, ??, KK,
The open D?D threshold is close to ?(3686) and
?(3770), which suggests that these two states
will experience or suffer the most from the open
channel effects. Nevertheless, such effects
behave differently in the kinematics below or
above the threshold.
0?? (L0,S0)
1?? (L0,S1)
1?? (L2,S1)
6
?(3770) non-D?D decay -- Evidence for
intermediate D meson contributions to charmonium
decays
7
Particle Data Group 2008
8
Particle Data Group 2008
9
Particle Data Group 2008
10

• ?(3770) non-D?D decay

• Experimental discrepancies

Exclusive D?D cross sections are measured at BES
and CLEO-c
11
BES-II non-D?D branching ratio can be up to 15
CLEO-c
The lower bound suggests the maximum of non-D?D
b.r. is about 6.8.
12
Inclusive non-D?D hadronic cross sections from
BES
13

• Theoretical discrepancies

In theory
14
pQCD calculation BR(non-D?D) lt 5

• Short-range pQCD transition
• Color-octet contributions are included
• 2S-1D state mixings are small
• NLO correction is the same order of magnitude as
  LO.
• Results do not favor both CLEO and BES

Q How about the long-range non-pQCD mechanisms?
15

• Recognition of possible long-range transition
  mechanisms

• pQCD (non-relativistic QCD)
• If the heavy c?c are good constituent degrees of
  freedom, c and ?c annihilate at the origin of the
  (c?c) wavefunction. Thus, pQCD should be
  dominant.
• If pQCD is dominant in ?(3770) ? light hadrons
  via 3g exchange, the OZI rule will be respected.
• ? ?(3770) non-D?D decay will be suppressed.

• Non-pQCD
• Are the constituent c?c good degrees of freedom
  for ?(3770) ? light hadrons? Or is pQCD dominant
  at all?
• If not, how the OZI rule is violated?
• Could the OZI-rule violation led to sizeable
  ?(3770) non-D?D decay?
• How to quantify it?

16

• Recognition of long-range transition mechanisms
  
• in spectrum studies

Hadronic loop contributions as unquenched effects
in charmonium spectrum
See talk by E. Swanson at Charmed Exotics, Bad
Honnef, Germany and T. Barnes and E. Swanson,
PRC77, 055206 (2008) Li, Meng and Chao, PRD80,
014012(2009)
17

• Recognition of long-range transition mechanisms
  
• in ?(3770) non-D?D decays

M1
g
c
M1
?(3770)
?(3770)
M2
c
M2
Long-range OZI evading transition
Short-range pQCD transition
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?(3770) decays to vector and pseudoscalar via D?D
and D?D c.c. rescatterings
Zhang, Li and Zhao, Phys. Rev. Lett. 102, 172001
(2009)
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The V ? VP transition has only one single
coupling of anti-symmetric tensor form
Transition amplitude can thus be decomposed as
Long-range non-pQCD amp.
Short-range pQCD amp.
20

• Effective Lagrangians for meson couplings

Coupling constants
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i) Determine long-range parameter in ?(3770) ?
J/? ?.
?(3770)
J/?
?(3770)
J/?
?
?

• Soft ? production
• ?-?? mixing is considered
• a form factor is needed to kill the loop
  integral divergence

The cut-off energy for the divergent meson loop
integral can be determined by data, and then
extended to other processes.
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ii) Determine short-range parameter combing
?(3770) ? ?? and ?(3770) ? ??.
Relative strengths among pQCD transition
amplitudes
23
iii) Predictions for ?(3770) ? VP.
24
X. Liu, B. Zhang and X.Q. Li, PLB675, 441(2009)
25

• Remarks

• The t-channel transition is much more important
  than the s channel.
• The s-channel can be compared with Rosners
  ?(2S)-?(1D) mixing.
• The only sizeable s channel is in ?(3770) ?
  J/??. It adds to the t-channel amplitude
  constructive. In contrast, the isospin-violating
  ?(3770) ? J/??0 experiences a destructive
  interference between the s and t channel.
• There exists a strong correlation between the
  SOZI parameter gS and phase angle ?.
• It is essential to have precise measurement of
  all the VP channels, i.e. ??, K?Kc.c. etc.

26

• More evidences are needed

• In most cases, the estimate of loop
  contributions will suffer from cut-off
  uncertainties. Thus, one should look for
  systematic constraints on the model uncertainties
  in all relevant processes.

27

• Coherent study of the ?(3686) ? VP is needed. In
  particular, It is important to investigate the
  meson loop effects in the problems of e.g. ??
  puzzle, J/? and ?(3686) radiative decay. see
  e.g. Zhao, Li and Chang, PLB645, 173(2007) Li,
  Zhao, and Chang, JPG (2008) Zhao, Li and Chang,
  arXiv0812.4092hep-ph, and work in progress
• The relevant isospin-violating channels as a
  correlation with the OZI-rule violation (OZI-rule
  evading) process, e.g. ? ? J/? ?0. Guo, Hanhart,
  and Meissner, arXiv0907.0521, PRL2009
• An analogue to the ?(3770) non-D?D decay the
  ?(1020) non-K?K decay see Li, Zhao and Zou,
  PRD77, 014010(2008) Li, Zhang and Zhao, JPG36,
  085008(2009).

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?? puzzle and 12 rule
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• ?? puzzle and 12 rule

• 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
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• 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
• Suzuki possible hadronic excess in ?(2S) decay
• 3. Others

Recent review by Yuan et al.
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Branching ratios for J/? (c?c) ? V P
Same order of magnitude !

• What accounts for such a large isospin
  violation?
• Implications of the ?? puzzle

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Branching ratios for ??? V P
Particle Data Group
Comparable !?
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/? EM Long-range int.
3g
?
?
/? EM Long-range int.
3g

• 12 rule will not hold if EM, and/or other
  possible transitions are important.

V
V
g
c
c
?
J/?
J/?
P
P
c
c
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• The property of antisymmetric VVP coupling
  suggests that one can investigate the origin of
  the ?? puzzle between the strong and EM
  transitions.
• The EM transition can be investigated by vector
  meson dominance (VMD) model.
• The strong transition amplitude contributes to
  both isospin-conserved and isospin-violated
  transitions.

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• EM transitions in VMD

V?P coupling
V? coupling
Transition amplitude
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I. Determine gV?P in V ? ? P
?
V
P
37
II. Determine e/fV in V ? e e-
e
?
V
e-
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III. Determine gP?? in P ? ??
?
P
?
IV. Form factors
Corrections to the V?P vertices
All the relevant data are available !
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V. Isospin-violated channel
We determine the cut-off energy ? in the form
factor by fitting the experimental branching
ratios for the isospin-violating J/? and ??
decays. By taking the branching ratio
fractions, it shows that the 12 rule is
approximately satisfied.
Rth() Rexp()
? parameter is determined by assuming the
dominance of EM transition in isospin-violated
channels. It should be refitted when strong
isospin violation is included.
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• Parameterize the strong decay transition

• Fig. (a) Contributions from short-range
  interactions
• Fig. (b) Contributions from long-range
  interactions with the double OZI-rule violation
• Possible glueball components inside I0 mesons

Short-range dominant, single OZI process
Long-range dominant, double OZI process
41
Parameterized strong decay amplitudes
reflects the strong decay coupling strength.
Form factor to take into account hadron size
effects
with
42
Fitting results including EM transitions
Zhao, Li and Chang, PLB645, 173(2007) Li, Zhao,
and Chang, JPG (2008)
43
Branching ratio fraction R including EM and
strong transitions Zhao, Li and Chang, PLB645,
173(2007), Li, Zhao, and Chang, JPG (2008)
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• Unanswered questions

• What is the origin of the strong coupling
  suppression on the ?? ? VP?
• What is the role played by long-range
  interactions?
• What is the correlation between the long-range
  interaction with the OZI-rule-evading mechanisms?

Mechanisms suppressing the ?? ? VP strong decays
should be clarified!
45

• Mechanism suppressing the strong decay
  amplitudes of ?? ? VP

Open-charm effects as an OZI-rule evading
mechanism
D
?
J/? (??)
c
D
?0
?c
?D

• Interferences among the single OZI, EM and
  intermediate meson loop transitions are
  unavoidable.

46
Decomposition of OZI evading long-range loop
transitions
D
?
J/? (??)
?
?D
?
?
D
J/? (??)
J/? (??)
V
?
?
?
D
?D
?
?
t-channel
s-channel
Zhang, Li and Zhao, 0902.1300hep-ph Li and
Zhao, PLB670, 55(2008)
47
Recognition of interferences
Property of the anti-symmetric tensor coupling
allows a parametrization
In order to account for the ?? puzzle, a
destructive phase between
and
is favored.
Zhao, Li, and Chang, 0812.4092hep-ph.
48
Not include sign.
49
Some features about the open charm

• The intermediate meson loops will contribute to
  the real part of the couplings since both J/? and
  ?? are below the open charm threshold.
• Since the ?? has a mass which is closer to the
  open D?D threshold, its amplitude via the D?D
  loop will be qualitatively larger than J/? due to
  near-threshold effects.
• Similar behavior due to intermediate D?D(D) and
  D?D(D) loops also shows up in a coherent study
  of J/? and ??? ??c and ?? ? ???c. (Li Zhao,
  PLB670, 55(2008))
• Light intermediate meson loops are strongly
  suppressed due to large off-shell effects.

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• Summary

• Open D?D channel effects seems to be essential
  for understanding some of the puzzles in the
  low-lying charmonium decays.
• ?(3770) non-D?D decays
• ?? puzzle in J/?, ? ? VP
• M1 transition problem in J/?, ?? ? ? ?c, (?
  ?c?)
• Isospin violating decay of ?? ?J/??0
• However, the quantitative calculations are
  sensitive to cut-off energy and exhibit
  model-dependent aspects.
• Systematic examinations of such a mechanism in
  different circumstances are necessary.
• Experimental data from BES, CLEO-c, KLOE, and
  B-factories will further clarify those issues.

51
Thanks !
52
Puzzles in J/?, ?? ? ? ?c, (? ?c?) -- Further
evidence for intermediate D meson contributions
to the M1 transitions
53

• M1 transition in a naïve quark model

?
c ?
c ?
J/?
?c
?c ?
?c ?

• M1 transition flips the quark spin
• The initial and final q?q states are in the same
  multiplet
• The initial and final q?q states have the same
  spatial wavefunction

54
M1 transition in the relativised Godfrey-Isgur
model

• Relativistic corrections, e.g. finite size
  corrections
• Form of long-rang force is unknown
• Sensitivities to the quark masses and details of
  the potential
• ?? ? ? ?c is also allowed (hindered transition)

55
NRQCD, higher-order corrections, relativistic
quark model, Lattice QCD
Relativistic quark model, Ebert et al.
predictions are sensitivity to Lorentz structure
of the quark potentials
56
Tree level effective Lagrangian
?
?c
J/?
In terms of effective coupling, the correction is
to the VVP coupling form factors.
57

• Intermediate meson exchange with effective
  Lagrangians

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(No Transcript)
59

• Vertex couplings are determined by available
  experi. Info.

60
Contact diagrams
with
61

• Results and discussions

Overall transition amplitude
?
?
D
D
?c
J/?
J/?
?D
?c
62

• Small imaginary amplitudes
• The real part is supposed to cancel the M1
  amplitude
• Simultaneous account of the J/?, ??? ? ?c with
  the same cut-off energy ?
• Prediction for ??? ? ??c