Revisiting some long-standing puzzles in charmonium decays Institute of High Energy Physics, CAS Revisiting some long-standing puzzles in charmonium decays Qiang Zhao Institute of High Energy Physics, CAS and Theoretical Physics Center for Science Facilities (TPCSF), CAS Contributors: G. Li, X.-H. Liu, and Y.-J. Zhang 3rd FCPPL Conference, Lyon, April 7-10, 2010

Motivations Charmonium decays as a probe for non-perturbative QCD mechanisms pQCD helicity selection rule is badly violated Several exisiting puzzles in low-lying vector charmonium decays could be related with non-perturbative mechanisms.

Several well-known puzzles in charmonium decays (3770) non-DD decay “ puzzle” in J/,   VP decay Large c  VV branching ratios M1 transition problem in J/,    c, ( c) Isospin-violating decay of  J/ 0, and  hc0 Even more … … Conjecture: These puzzles could be related to non-pQCD mechanisms in charmonium decays due to intermediate D meson loops. The intermediate meson loop transition could be a mechanism for the evasion of the helicity selection rule.

Charmonium spectrum

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 , , K*K, … 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 (L=0,S=0) 1 (L=0,S=1) 1 (L=2,S=1)

Outline Introduction to the helicity selection rule Long-distance contribution from intermediate meson loop (IML) transitions (3770) non-DD decays “ puzzle” c1→VV, c2→VP, c, c0, hc BB (X.-H. Liu, talk in the satellite meeting) Summary

Helicity selection rule Base on the pQCD quark-gluon interaction, the asymptotic behavior of exclusive hadronic processes has a power-counting as follows: Chernyark and Zitnitsky, Phys. Rept. 112, 173 (1984); Brodsky and Lepage, PRD24, 2848 (1981). The QCD leading twist will contribute when 1+2=0, while the next to leading order contribution will be suppressed by a factor of 2QCD/mc2

Helicity selection rule An alternative description of this selection rule with the quantum number named “naturalness” The selection rule requires that Take the process J/ VP as an example In the rest frame of initial state, it requires V=0 at leading twist accuracy. V can be approximately expressed as a linear combination of the final state momenta, which then results in a vanishing amplitude.

S- and P-wave charmonium exclusive decays (3770) (3770) non-DD decays into VP “ puzzle”-related Feldmann and Kroll, PRD62, 074006 (2000) PDG2008 The helicity selection rule seems to be violated badly in charmonium decays!

(3770) non-DD decay -- IML as a mechanism for evading the helicity selection rule

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:

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

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 ? 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, NRQCD should be valid. 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. 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 (3770) non-DD decays Short-range pQCD transition via single OZI (SOZI) process Long-range OZI evading transition g M1 c M1 (3770) (3770) c* M2 M2

(3770) decays to vector and pseudoscalar via DD and DD. + c. c (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)

Long-range non-pQCD amp. 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.

Effective Lagrangians for meson couplings Coupling constants:

i) Determine long-range parameter in (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:

iii) Predictions for (3770)  VP.

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 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 for the meson loop contributions 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 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)]. Helicity selection rule evasions in c1  VV and c2  VP. [see Liu and Zhao, PRD81, 014017 (2010)] Helicity selection rule evasions in c, c0, hc BB. [ Liu and Zhao, arXiv: 1004.0496[hep-ph]. ] Other cases where the helicity selection rule is violated.

Thanks !