Recent study on γγ*  ηc transition form factor and χcJ  γγ 桑 文 龙 SouthWest University, ChongQing In collaboration with Feng Feng, Yu Jia, Shuang-Ran Liang QCD Study Group 2016 workshop 2016.4.2-2016.4.4 上海交大 (SJTU)

Contents Brief introduction to NRQCD factorization NNLO QCD correction to γγ*  ηc form factor and confront the BaBar data NNLO QCD correction to χcJ  γγ and confront the BESIII data Summaries

Nonrelativistic QCD (NRQCD): the modern effective field theory to tackle heavy quarkonium Caswell, Lepage (1986); Bodwin, Braaten, Lepage (1995) This scale separation is usually referred to as NRQCD factorization. The NRQCD short-dist. coefficients can be computed in perturbation theory, order by order

production at hadron colliders …… NRQCD gains popularity in quarkonium physics (see Brambilla et al. EPJC 2011 for a recent review) Nowadays, NRQCD becomes an important approach to tackle various quarkonium production and decay processes charmonium: bottomonium: Exemplified by at B factories production at hadron colliders ……

The underlying problems Most of the NRQCD successes based on the NLO QCD predictions. However, the NLO QCD corrections are often large: Zhang et.al. Gong et.al. Campbell et.al. Mackenzie et.al. … …

Question: How about the convergence of the QCD correction? So calculating the higher order QCD correction is very necessary to test NRQCD predictions!

Investigation on γγ*  ηc form factor Experiment BaBar Collaboration: Phys.Rev. D81 (2010) 052010 Babar measures the transition form factor in the momentum transfer range from 2 to 50 GeV2.

Investigation on γγ*  ηc form factor Experiment BaBar Collaboration: Phys.Rev. D81 (2010) 052010

Investigation on γγ*  ηc form factor Experiment BaBar Collaboration: Phys.Rev. D81 (2010) 052010 The solid curve is from a simple monopole fit: The dotted curve is from pQCD prediction Feldmann and Kroll, Phys. Lett. B 413, 410 (1997)

Investigation on γγ*  ηc form factor Previous investigation factorization: Feldmann et.al., Cao and Huang Lattice QCD: Dudek et.al., J/ψ -pole-dominance: Lees et.al., QCD sum rules: Lucha et.al., light-front quark model: Geng et.al., All yield predictions compatible with the data, at least in the small Q2 range. So far, so good. Unlike γγ*  π0 , there is no open puzzle here

Investigation on γγ*  ηc form factor Our motivations Model-independent method is always welcome. In the normalized form factor, nonperturbative NRQCD matrix element cancels. Therefore, our predictions are free from any freely adjustable parameters! Is LO NRQCD prediction enough? The momentum transferred is not large enough, we are not bothered by the large logarithmic resummation. Jia and Yang

Investigation on γγ*  ηc form factor Theoretical descriptions Definition for form factor: NRQCD factorization defines: Factorization scale Short-distance coefficient We are going to compute it!

Investigation on γγ*  ηc form factor Theoretical descriptions Upon general consideration, the SDC can be written as IR pole matches anomalous dimension of NRQCD pseudo-scalar density RGE invariance

Investigation on γγ*  ηc form factor Theoretical calculation Tree-level SDC NLO QCD correction

Investigation on γγ*  ηc form factor Feynman diagrams Numer of diagrams 2 8 108 12

Investigation on γγ*  ηc form factor NNLO corrections At , the value of is compatible with asymptotic behavior in Jia, Yang, NPB 2009 Light-by-light UV/IR finite regular Reproduce known NNLO corr. to ηc->γγ Czarnecki et al. 2001

Investigation on γγ*  ηc form factor NNLO corrections Contribution from lbl is not always negligible!

γγ*  ηc : NNLO prediction seriously fails to describe data! Investigation on γγ*  ηc form factor Theory vs Experiment Our Prediction is free of any nonperturbative parameters! γγ*  ηc : NNLO prediction seriously fails to describe data!

Investigation on γγ*  ηc form factor Prediction to γγ*  ηb Convergence of perturbation series is rather good. Wait for CEPC/ILC to test our prediction?

Investigation on c0,2 2γ Experiment  BESIII gives updated measurements: (BESIII, PRD, 2012) Decay width of c0  2 γ Ratio of decay width of c2  2 γ to that of c0  2 γ Ratio of the two-photon widths for helicity λ= 0 and helicity λ= 2 components in c2  2 γ

Investigation on c0,2 2γ Various theoretical predictions  Review of previous theoretical works Numerous work based on phenomenological models R. Barbieri, R. Gatto, R. Kogerler (PLB, 1976) L. Bergstrom, G. Hulth, H. Snellman (Z. Phys. C, 1983) Z. P. Li, F. E. Close, T. Barnes (PRD, 1991) H. W. Huang, C. F. Qiao, K. T. Chao (PRD, 1996) S. N. Gupta, J. M. Johnson, W. W. Repko (PRD, 1996) G. L. Wang (PLB, 2007) C. W. Hwang, R. S. Guo (PRD, 2010) … … … Lattice QCD prediction for c0 2 γ by J. Dudek and R. Edwards (PRL 2006), obtains partial width of , based on the algorithm proposed by X. D. Ji and C. W. Jung (PRL 2001; PRD, 2001)

Investigation on c0,2 2γ NRQCD formula According to the NRQCD factorization The short-distance coefficients can be systematically expanded

Investigation on c0,2 2γ NRQCD formula

Investigation on c0,2 2γ NRQCD calculation

Investigation on c0,2 2γ NRQCD calculation

Investigation on c0,2 2γ Theory vs Experiment (BESIII, PRD, 2012) By assuming HQSS, we predict

Investigation on c0,2 2γ Theory vs Experiment

Investigation on c0,2 2γ Theory vs Experiment Giving up HQSS

Summaries The NNLO NRQCD predictions to γγ*  ηc form factor and c0,2 2γ fail to explain the experiment! The convergence of QCD expansions for the short-distance coefficients is poor! NRQCD predictions should be tested at high order!

Thanks for your attention!