Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production

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

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

3. Charmonium production at B factories • 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; 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics

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

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

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

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; Fit to the expr.! LCDA: Non-pert. quantities! Lead to end-point singularity! 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics

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

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

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

11. Refactorization • 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; 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics

12. Example-1: 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, 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics

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

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

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

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

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

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

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

20. Example-2: 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 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics

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

22. Summary • 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. 2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics

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