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

Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production. Graduate University of the CAS Deshan Yang. Based on Yu Jia & DSY, NPB814, 217 (2009); in preparation. Outline. Introduction & Motivations Refactorization of NRQCD coefficients Example 1 –

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

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  1. Refactorizing NRQCDshort-distance coefficients in exclusive quarkonium production Graduate University of the CAS Deshan Yang Based on Yu Jia & DSY, NPB814, 217 (2009); in preparation 2009.12.2 Center of High Energy Physics, Peking University

  2. Outline Introduction & Motivations Refactorization of NRQCD coefficients Example 1 – Example 2 – Summary 2009.12.2 Center of High Energy Physics, Peking University

  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; 2009.12.2 Center of High Energy Physics, Peking University

  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 2009.12.2 Center of High Energy Physics, Peking University

  5. Salute to those guys Gong, QWG2008 Non-pert. quantities! Kill renormalization scale dependence 2009.12.2 Center of High Energy Physics, Peking University

  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. 2009.12.2 Center of High Energy Physics, Peking University

  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! 2009.12.2 Center of High Energy Physics, Peking University

  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 2009.12.2 Center of High Energy Physics, Peking University

  9. Inclusive quarkonium production at hadron collider J.W.Qiu’s talk at KITPC-EFT program Absent from electron-positron collider! Less complications! Perturbative region could be furthur fined into two regions! 2009.12.2 Center of High Energy Physics, Peking University

  10. Exclusive single quarkonium production 2009.12.2 Center of High Energy Physics, Peking University

  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 Feldmann, JHEP 2007; 2009.12.2 Center of High Energy Physics, Peking University

  12. Example-1: • NRQCD factorization 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, 2009.12.2 Center of High Energy Physics, Peking University

  13. One-loop level  Sang, Chen, arXiv:0910.4071; Li, He, Chao arXiv:0910.4155 2009.12.2 Center of High Energy Physics, Peking University

  14. Leading regions • Hard Region: • Collinear region: • Anti-collinear region: • Potential region: • Soft region: • Ultra-soft region: NRQCD regions Non-perturbative 2009.12.2 Center of High Energy Physics, Peking University

  15. Form factor • NRQCD: • Collinear factorization: • Hard-kernel: • at tree level • Light-cone distribution amplitude Ma and Si, PRD 2006; Bell and Feldmann, JHEP 2007; 2009.12.2 Center of High Energy Physics, Peking University

  16. RGE for LCDA Brodsky-Lepage kernel: Resum the leading logrithms where 2009.12.2 Center of High Energy Physics, Peking University

  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 2009.12.2 Center of High Energy Physics, Peking University

  18. Truncated LL approximation In momentum space, solve the RGE recursively, at two-loop level, we have (neglecting mixing) which is consistent with the NRQCD calculation Actually, we even got the correct NLO results by summing up the hard part and collinear part. (see below). Sang, Chen, arXiv:0910.4071; Li, He, Chao arXiv:0910.4155 Braaten, PRD 1981;Ma and Si, PRD 2006; Bell and Feldmann, JHEP 2007; 2009.12.2 Center of High Energy Physics, Peking University

  19. Comparisons LL 2-loop LL 1-loop LL 2009.12.2 Center of High Energy Physics, Peking University

  20. NLO results (preliminary) • Hard Part • Collinear Part • Total Results Braaten, PRD 1981; Ma and Si, PRD 2006; Bell and Feldmann, JHEP 2007; Sang, Chen, arXiv:0910.4071; Li, He, Chao arXiv:0910.4155 2009.12.2 Center of High Energy Physics, Peking University

  21. Example-2: • NRQCD factorization 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 2009.12.2 Center of High Energy Physics, Peking University

  22. Comparisons 1-loop LL 2-loop LL LL 2009.12.2 Center of High Energy Physics, Peking University

  23. Summary • For the single heavy quarkoniumexclusive 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 energy; • However, the refactorization property of the NRQCD short-distance coefficients may offer an easier way to obtain the higher order radiativecorrections 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 know that it is impossible to resum such logarithm with the aid of B-L equations. 2009.12.2 Center of High Energy Physics, Peking University

  24. 谢谢！ 2009.12.2 Center of High Energy Physics, Peking University

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