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## Qiang Zhao Institute of High Energy Physics, CAS

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Institute of High Energy Physics, CAS

Puzzles in charmonium decays

Qiang Zhao

Institute of High Energy Physics, CAS

and Theoretical Physics Center for Science Facilities (TPCSF), CAS

USCT, Hefei, July 9, 2009

Outline

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

Several well-known puzzles in charmonium decays

- “ puzzle” in J/, VP decay
- M1 transition problem in J/, c, ( c)
- (3770) non-DD decay
- Isospin-violating decay of J/ 0
- Hidden cc state with I=1, e.g. Z(4430), and other exotic configurations
- Scalar a0(980)-f0(980) mixing in J/ f0(980) 0
- Glueball search in charmonium hadronic decays

- “ puzzle” in J/, VP decay
- M1 transition problem in J/, c, ( c)
- (3770) non-DD decay
- Isospin-violating decay of J/ 0
- Hidden cc state with I=1, e.g. Z(4430), and other exotic configurations
- Scalar a0(980)-f0(980) mixing in J/ f0(980) 0
- Glueball search in charmonium hadronic decays

These puzzles could be related to non-pQCD mechanisms in charmonium decays.

Focus of hadron physics

- Complexity of QCD in the non-perturbative regime

exotic hadrons (glueball, hybrid, multiquarks …)

- Lattice QCD, QCD sum rules, effective theory… Phenomenological tools
- Break-down certain problems
- Experimental information: Light hadron spectroscopy (JLab, ELSA, MAMI, ERSF, Spring-8); Heavy quarkonium hadronic and EM decays (BES, CLEO-c, Belle, BaBar, LHC…)

A probe of strong QCD dynamics

q

Meson

c

glue

q

J/

q

qq Meson

hybrid

glueball

c

q

- Glue-rich intermediate states
- Ideal for the search for exotic states (hybrid, glueball …)
- Quark-gluon interaction in light hadron production

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

= (uu + dd)/2

= ss

V=

(I=0)

(I=0)

c

c

J/

J/

uudd

(I=0)

qq (I=1)

c

c

ss(I=0)

- OZI rule violations
- Isospin violations

Open-charm effects in charmonium decays

”(3770)

DD threshold

’(3686)

Mass (MeV)

c(2980)

J/(3096)

c(2980)

OZI rule violating transition

Light mesons

, , K*K, …

0 (L=0,S=0)

1 (L=0,S=1)

1 (L=2,S=1)

J/(3096)

(3770)

Mass axial

(3686)

The open DD threshold is close to (3686) and (3770), which suggests that these two states will experience or suffer the most from the open channel effects.

However, such effects behave differently in the kinematics below or above the threshold.

-- Evidence for intermediate D meson contributions to charmonium decays

- Experimental discrepancies:

Exclsusive DD cross sections are measured at BES and CLEO-c:

BES-II: non-DD branching ratio can be up to 15%

CLEO-c:

The lower bound suggests the maximum of non-DD b.r. is about 6.8%.

In theory

pQCD calculation: BR(non-DD) < 5%

- Short-range pQCD transition;
- Color-octet contributions are small;
- 2S-1D state mixings are small;
- NLO correction is the same order of magnitude as LO.

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

Recognition of long-range transition mechanisms

- pQCD (non-relativistic QCD):
- If the heavy cc are good constituent degrees of freedom, c and c annihilate at the origin of the (cc) 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-DD decay will be suppressed.

- Non-pQCD:
- Are the constituent cc 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-DD decay?
- How to quantify it?

Recognition of long-range transition mechanisms

in spectrum studies

Implies S=0 and S=1 c.o.g.

degenerate for L > 0.

(Not true for vector confinement.)

1. Success of potential quark model

OGE + Linear confinement; spin-dependent force is perturbative.

Unquench the naïve quark model scenario

B

A

A

C

T. Barnes and E. Swanson, PRC77, 055206 (2008)

For the states A in a given Ni and Li multiplet,

“These hold to all orders if there are no final state interactions in the continuum channels.”

Also by Tornqvist

Mass shift and cc-bar probabilities for low-lying charmonium states due to couplings to two-meson continua.

Recognition of long-range transition mechanisms

in (3770) non-DD decays

M1

g

c

M1

(3770)

(3770)

M2

c*

M2

(3770) decays to vector and pseudoscalar via DD and DD* + c.c. rescatterings

Zhang, Li and Zhao, Phys. Rev. Lett. 102, 172001 (2009)

The V VP transition has only one single form of coupling as anti-symmetric tensor

Transition amplitude can thus be decomposed as:

Long-range non-pQCD amp.

Short-range pQCD amp.

Effective Lagrangians for meson couplings

Coupling constants:

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.

ii) Determine short-range parameter combing (3770) and (3770) .

Relative strengths among pQCD transition amplitudes:

- 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 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 . By varying , but keeping the rate unchanged (i.e., gS will be changed), we obtain a lower bound for the sum of branching ratios, 0.41%.
- It is essential to have precise measurement of all the VP channels, i.e. , K*K+c.c. etc.

- Coherent study of the (3686) VP is important for clarifying the role played by long-range transition mechanisms, in particular, the open-charm effects.
- It is essential to quantify (3770) VT, VS, etc.
- It is important to investigate the meson loop effects in other processes, 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]
- It is important to investigate the relevant isospin-violating channels as a correlation with the OZI-rule violation (OZI-rule evading) process. [Wu, Zhao and Zou, PRD75, 114012(2007)]
- An analogue to the (3770) non-DD decay: the (1020) non-KK decay [see Li, Zhao and Zou, PRD77, 014010(2008); Li, Zhang and Zhao, JPG in press].
- ……

- 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*

- 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 …

Recent review by Yuan et al.

Branching ratios for J/ (cc) V P

Same order of magnitude !

- What accounts for such a large isospin violation?
- Implications of the “ puzzle” …

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*

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.

P

IV. Form factors

Corrections to the V*P vertices:

All the relevant data are available !

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(%)

- Note:
- The short-distant 3g transition is suppressed.
- 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

Branching ratio fraction “R” including EM and strong transitions

Zhao, Li and Chang, PLB645, 173(2007), Li, Zhao, and Chang, JPG (2008)

- 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!

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.

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, 0902.1300[hep-ph]; Li and Zhao, PLB670, 55(2008)

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 DD threshold, its amplitude via the DD loop will be qualitatively larger than J/ due to near-threshold effects.
- Similar behavior due to intermediate DD(D*) and DD*(D) loops also shows up in a coherent study of J/ and cand c. (Li & Zhao, PLB670, 55(2008))
- Light intermediate meson loops are strongly suppressed due to large off-shell effects.
- Open charm effects are essential for understanding " non-DD decays (Zhang, Li & Zhao, PRL102, 172001(2009))

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

J/

c

c

c

- M1 transition flips the quark spin
- The initial and final qq states are in the same multiplet
- The initial and final qq 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,…

Relativistic quark model, Ebert et al. :

predictions are sensitivity to Lorentz structure of the quark potentials

Tree level effective Lagrangian

c

J/

In terms of effective coupling, the correction is to the VVP coupling form factors.

with

- 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

- Open DD channel effects are essential for understanding a lot of puzzles in low-lying charmonium decays.
- It contains rich information about the strong QCD dynamics via a correlation between the OZI evading and long-range interactions, and also isospin violations.
- “ puzzle” in J/, ’ VP
- M1 transition problem in J/, c, ( c)
- (3770) non-DD decays
- ……
- Experimental data from BES, CLEO-c, KLOE, and B-factories will further clarify those issues.

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