1. Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 1 Based on Yu Jia & DSY, NPB814, 217 (2009) Graduate University of the CAS Deshan Yang

2. Outline 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 2 1.Introduction & Motivations 2.Refactorization of NRQCD coefficients 3.Example 1 – 4.Example 2 – 5.Summary

3. Charmonium production at B factories 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 3  Exlusive quarknium production at B-factories Abe et al (Belle Collaboration), PRL 2002; Aubert et al (BaBar Collaboration), PRD 2005;  Suprises for theorists LONRQCD: Braaten and Lee, PRD 2003; PRD 2005; Liu, He and Chao, PLB 2003; Hagiwara, Kou and Qiao, PLB 2003;

4. Battlefield for NRQCD guys  NLO QCD Corrections: K~ 2 Zhang, Gao, Chao, PRL 2006; Gong, Wang, PRD 2008;  Relativistic Corrections: K~ 2 Bodwin, Kang, Kim, Lee, Yu, AIP Conf. Proceeding 2007; He, Fan, Chao, PRD 2007;  Triumph? Confusions? Questions?  Perturbation stability  Non-relativistic vs. Relativistic 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 4

5. Salute to those guys 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 5 Non-pert. quantities!Kill renormalization scale dependence Gong, QWG2008

6. NRQCD factorization For single quarkonium production  : NRQCD operator with definite velocity power counting  multi-scale problem: Q>>m  stability of the perturbation: large log(Q/m) may need the resummation. 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 6

7. Light-cone framework Ma and Si, PRD 2004;Bonder and Chernyak, PLB 2005;Braguta, arXiv:0811.2640[hep-ph] From Ma and Si, PRD 2004; 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 7 Fit to the expr.!LCDA: Non-pert. quantities!Lead to end-point singularity!

8. Motivations 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 8 Large logs in NRQCD short-distance coefficients could ruin the perturbation! Large logs in NRQCD short-distance coefficients could ruin the perturbation! 1 How to harmonize LC factorization and NRQCD factorization? How to harmonize LC factorization and NRQCD factorization? 2 Understand the mechanisms to heavy quarkonium exclusive production! Understand the mechanisms to heavy quarkonium exclusive production! 3 Key

9. Inclusive quarkonium production at hadron collider 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 9 J.W.Qiu’s talk at this program Absent from electron-positron collider! Less complications! Perturbative region could be furthur fined into two regions!

10. Exclusive single quarkonium production 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 10

11. Refactorization 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 11 At the leading power of velocity,  The hard kernel is the same as the similar process in which the quarkonium is replaced by a flavor singlet light meson.  Since, the LCDA of bounded heavy quark and anti-quark can be calculated perturbatively. Ma and Si, PRD 2006; Bell and Feldman 2007;

12. Example-1: 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 12 Amplitude up to leading power of velocity: The short-distance contribution is parameterized as The equivalent computation is to calculate the on-shell heavy quark anti-quark pair with equal momentum and the same quantum number as the quarkonium. At the tree level,

13. One-loop level 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 13

14. Leading regions 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 14  Hard Region:  Collinear region:  Anti-collinear region:  Potential region:  Soft region:  Ultra-soft region:

15. Form factor 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 15 NRQCD: Collinear factorization:  Hard-kernel: at tree level  Light-cone distribution amplitude

16. RGE for LCDA 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 16 Brodsky-Lepage kernel: Resum the leading logrithms where

17. Resummation in moment space 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 17 Both LCDA and Brodsky-Lepage kernel can be expanded in Gegenbauer polynomial In moment space, the LL resummed form-factor is

18. Truncated LL approximation 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 18 In momentum space, solve the RGE recursively, at two-loop level, we have which is equivalent to the expressions in moment space

19. Comparisons 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 19 LL 2-loop LL 1-loop LL

20. Example-2: 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 20 Amplitude up to the lowest order of velocity: The short-distance contribution is parameterized as The factorization formula for the form-factor involves the twist-2 LCDA for transversely polarized quark pair which corresponding B-L kernel is

21. Comparisons 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 21 1-loop LL 2-loop LL LL

22. Summary 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics 22  For the single heavy quarkonium exclussive production at very large center energy collision, it is possible to derive the refactorization formula for the relevant NRQCD short-distance coefficients;  In the two examples we showed, the LL resummation does not lead to large corrections in the accessible ernergy;  However, the refactorization property of the NRQCD short-distance coefficients may offer an easier way to obtain the higher order radioactive corrections with price of m/Q suppressed corrections;  For the double charmonium production, double logarithm appears with the overall m/Q suppression at one-loop level. However we do not know how to resum such logarithm with the aid of B-L equations.

23. 23 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics