Transcript Manifestation of intermediate meson loop effects in charmonium decays Qiang Zhao

Institute of High Energy Physics, CAS
Manifestation of intermediate
meson loop effects in charmonium
decays
Qiang Zhao
Institute of High Energy Physics, CAS
and Theoretical Physics Center for Science
Facilities (TPCSF), CAS
The 5-th International Conference on Quarks and Nuclear Physics,
Beijing, Sept. 22, 2009
Motivations
• Charmonium decays as a probe for
non-perturbative QCD mechanisms
• Several exisiting puzzles in low-lying
vector charmonium decays
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 nonpQCD mechanisms in charmonium decays due to
intermediate D meson loops.

Charmonium spectrum
 Open-charm effects in charmonium decays
Mass (MeV)
”(3770)
DD threshold
’(3686)
c(2980) 
c(2980)
J/(3096)
OZI rule violating transition
Light mesons
The open DD threshold is close to (3686) and (3770), which
, , K*K, …
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
(L=0,S=0)
1 (L=0,S=1) 1 (L=2,S=1)
(3770) non-DD decay
-- Evidence for intermediate D meson
contributions to charmonium decays
Particle Data Group 2008
Particle Data Group 2008
Particle Data Group 2008
 (3770) non-DD decay
 Experimental discrepancies:
Exclusive DD cross sections are measured at BES and CLEO-c:
BES-II: non-DD branching ratio can be up to 15%
CLEO-c:
The lower bound suggests the maximum of nonDD b.r. is about 6.8%.
Inclusive non-DD hadronic cross sections from BES
 Theoretical discrepancies:
In theory
pQCD calculation:
BR(non-DD) < 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
 NNLO ?
Q: How about the long-range
non-pQCD mechanisms?
 Recognition of possible long-range transition
mechanisms
pQCD (non-relativistic QCD):
Non-pQCD:
If the heavy cc are good
constituent degrees of freedom, c
and c annihilate at the origin of
the (cc) wavefunction. Thus,
NRQCD should be valid.
Are the constituent cc good
degrees of freedom for (3770) 
light hadrons? Or is pQCD
dominant at all?
pQCD is dominant in (3770)
 light hadrons via 3g exchange,
hence the OZI rule will be
respected.
 (3770) non-DD decay
will be suppressed.
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?
 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)
 Recognition of long-range transition mechanisms
in (3770) non-DD decays
Short-range pQCD transition
via single OZI (SOZI) process
c
g
M1
M1
(3770)
(3770)
c*
Long-range OZI evading transition
M2
M2
(3770) decays to vector and pseudoscalar via DD
and DD* + c.c. rescatterings
Y.-J. Zhang, G. Li and Q. Zhao, Phys. Rev. Lett. 102, 172001 (2009)
The V  VP transition has only one single
coupling of anti-symmetric tensor form
Transition amplitude can thus be decomposed as:
Long-range nonpQCD amp.
Short-range
pQCD amp.
 Effective Lagrangians for meson couplings
Coupling constants:
i) Determine long-range parameter in (3770)  J/ .
(3770)
(3770)
J/
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.
ii) Determine short-range parameter combing (3770)  
and (3770)  .
Relative strengths among pQCD transition amplitudes:
iii) Predictions for (3770)  VP.
X. Liu, B. Zhang and X.Q. Li, PLB675, 441(2009)
 Remarks
 The t-channel transition is much more important than the s
channel.
 The s-channel can be compared with Rosner’s (2S)-(1D)
mixing.
 The only sizeable s channel is in (3770)  J/. It adds to
the t-channel amplitude constructive. In contrast, the isospinviolating (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*K+c.c. etc.
 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. …
 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, arXiv:0812.4092[hep-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, arXiv:0907.0521, 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)].
 ……
“ puzzle” and “12% rule”

“ puzzle” and “12% rule”
• pQCD expectation of
the ratio between J/
and ' annihilation:
• “ puzzle”
 0.2 %
R() =
Large “12% rule” violation in  !
JPC = 1
c
J/, '
c*
g
c
J/, '
c*
*
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.
Branching ratios for J/ (cc)  V P
Same order
of magnitude !
• What accounts for such a large isospin violation?
• Implications of the “ puzzle” …
Branching ratios for  V P
Comparable !?


+/ EM + Long-range int.
3g
+/ EM + Long-range int.
3g
• “12% rule” will not hold if EM, and/or other possible
transitions are important.
c
g
V
*
V
J/
J/
c*
c
P
c*
P
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.

EM transitions in VMD
VP coupling:
V* coupling:
Transition amplitude:
I. Determine g
VP
in V   P

V
P
II. Determine e/f
V
in V  e+ e-
V
*
e+
e-
III. Determine g
P
in P  

P

IV. Form factors
Corrections to the V*P vertices:
All the relevant data are available !
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.

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 I=0 mesons
Short-range dominant,
single OZI process
Long-range dominant,
double OZI process
Parameterized strong decay amplitudes:
reflects the strong decay
coupling strength.
Form factor to take into account hadron size effects:
with
Fitting results
including EM
transitions
Zhao, Li and Chang,
PLB645, 173(2007)
Li, Zhao, and Chang, JPG
(2008)
Branching ratio fraction “R” including EM and strong
transitions
Zhao, Li and Chang, PLB645, 173(2007), Li, Zhao, and Chang, JPG (2008)

Unanswered questions
i)
What is the origin of the
strong coupling
suppression on the  
VP?
ii) What is the role played by
long-range interactions?
iii) What is the correlation
between the long-range
interaction with the OZIrule-evading mechanisms?
Mechanisms suppressing the   VP strong
decays should be clarified!
Mechanism suppressing the strong
decay amplitudes of   VP

Open-charm effects as an OZI-rule evading mechanism

D
J/ ()
c
D*
c
D
0
• Interferences among the single OZI, EM and
intermediate meson loop transitions are unavoidable.
Decomposition of OZI evading long-range loop
transitions
D

D

J/ ()


J/ () D

D*
D
t-channel

J/ ()
…
V


s-channel
Zhang, Li and Zhao, 0902.1300[hep-ph]; Li and Zhao, PLB670, 55(2008)
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, 0812.4092[hep-ph].
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.

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 Bfactories will further clarify those issues.
Thanks !
Puzzles in J/,    c, ( c)
-- Further evidence for intermediate D
meson contributions to the M1
transitions
 M1 transition in a naïve quark model

c
c
c
J/
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
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)
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
Tree level effective Lagrangian

J/
c
In terms of effective coupling, the correction is to the VVP coupling
form factors.
• Intermediate meson exchange with effective Lagrangians
• Vertex couplings are determined by available experi. Info.
Contact diagrams
with
 Results and discussions
Overall transition amplitude:


D
J/
c
D*
J/
D
c
 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