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

Motivations Charmonium decays as a probe for non-perturbative QCD mechanisms Several exisiting puzzles in low-lying vector 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   h c  0 … … Conjecture: These puzzles could be related to non- pQCD mechanisms in charmonium decays due to intermediate D meson loops. Several well-known puzzles in charmonium decays

 Charmonium spectrum

 c (2980) J/  (3096) 0  (L=0,S=0)1  (L=0,S=1) Mass (MeV)  c (2980)  Light mesons , , K*K, … D  D threshold OZI rule violating transition  ’(3686)  ”(3770) 1  (L=2,S=1)  Open-charm effects in charmonium decays 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.

 (3770) non-D  D decay -- Evidence for intermediate D meson contributions to charmonium decays

Particle Data Group 2008

  (3770) non-D  D decay Experimental discrepancies: Exclusive D  D cross sections are measured at BES and CLEO-c:

CLEO-c: BES-II: non-D  D branching ratio can be up to 15% The lower bound suggests the maximum of non- D  D b.r. is about 6.8%.

Inclusive non-D  D hadronic cross sections from BES

In theory Theoretical discrepancies:

 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 pQCD calculation: BR(non-D  D) < 5% Q: How about the long-range non-pQCD mechanisms?

 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?

 Recognition of long-range transition mechanisms in spectrum studies See talk by E. Swanson at Charmed Exotics, Bad Honnef, Germany and T. Barnes and E. Swanson, PRC77, (2008) Li, Meng and Chao, PRD80, (2009) Hadronic loop contributions as unquenched effects in charmonium spectrum

 Recognition of long-range transition mechanisms in  (3770) non-D  D decays c c* M1 M2  (3770) g M1 M2  (3770) Short-range pQCD transition Long-range OZI evading transition

 (3770) decays to vector and pseudoscalar via D  D and D  D* + c.c. rescatterings Zhang, Li and Zhao, Phys. Rev. Lett. 102, (2009)

Transition amplitude can thus be decomposed as: The V  VP transition has only one single coupling of anti-symmetric tensor form Short-range pQCD amp. Long-range non- pQCD amp.

Effective Lagrangians for meson couplings Coupling constants:

i) Determine long-range parameter in  (3770)  J/  .  (3770) J/    The cut-off energy for the divergent meson loop integral can be determined by data, and then extended to other processes.  Soft  production   -  mixing is considered  a form factor is needed to kill the loop integral divergence

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 isospin- violating  (3770)  J/  0 experiences a destructive interference between the s and t channel.  There exists a strong correlation between the SOZI parameter g S and phase angle .  It is essential to have precise measurement of all the VP channels, i.e. , K*  K+c.c. etc.

 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. … More evidences are needed …

 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: [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: , PRL2009]  An analogue to the  (3770) non-D  D decay: the  (1020) non-K  K decay [see Li, Zhao and Zou, PRD77, (2008); Li, Zhang and Zhao, JPG36, (2009)].  ……

“  puzzle” and “12% rule”

pQCD expectation of the ratio between J/  and  ' annihilation: “  puzzle” R(  ) = c J/ ,  ' g c c* ** J/ ,  ' c* Large “12% rule” violation in  ! J PC = 1   0.2 %  “  puzzle” and “12% rule”

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” …

Comparable !? Branching ratios for  V P Particle Data Group

3g “12% rule” will not hold if EM, and/or other possible transitions are important. c c* V P J/  g c c* V P J/  **  +/  EM + Long-range int.

 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.

V  P coupling: V  * coupling: Transition amplitude:  EM transitions in VMD

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   All the relevant data are available ! IV. Form factors Corrections to the V  *P vertices:   P

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.  parameter is determined by assuming the dominance of EM transition in isospin-violated channels. It should be refitted when strong isospin violation is included. R th (%) R exp (%)

 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: Form factor to take into account hadron size effects: with reflects the strong decay coupling strength.

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 OZI- rule-evading mechanisms? Mechanisms suppressing the   VP strong decays should be clarified!

Open-charm effects as an OZI-rule evading mechanism J/  (  ) c cc  00 D DD D* Interferences among the single OZI, EM and intermediate meson loop transitions are unavoidable.  Mechanism suppressing the strong decay amplitudes of   VP

J/  (  )   t-channel J/  (  )   V     s-channel Decomposition of OZI evading long-range loop transitions D DD DD D D*  … … Zhang, Li and Zhao, [hep-ph]; Li and Zhao, PLB670, 55(2008)

Recognition of interferences Property of the anti-symmetric tensor coupling allows a parametrization: Zhao, Li, and Chang, [hep-ph]. In order to account for the “  puzzle”, a destructive phase between andis favored.

Not include sign.

 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. Some features about the open charm

 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.

Thanks !

Puzzles in J/ ,     c, (   c ) -- Further evidence for intermediate D meson contributions to the M1 transitions

c   c  J/  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 a naïve quark model c   c  cc 

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

J/  cc  Tree level effective Lagrangian 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: J/  cc  DD D D*  J/  c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