Applications of the light-cone distribution amplitudes for quakonia 南昌大学 第八届全国高能物理大会 1 Based on Yu Jia & DSY, NPB814, 217 (2009); in preparation Graduate University of the CAS Deshan Yang

Outline 南昌大学 第八届全国高能物理大会 2 1.Introduction & Motivation 2.Example 1 – 3.Example 2 – 4.Summary

Exclusive QCD Processes 南昌大学 第八届全国高能物理大会 3 History: in , Brodsky et al when, the form-factor can be factorized Where the light-cone distribution amplitude (LCDA) can be defined as The same LCDA can appear in the factorization formulae in other exclusive processes, such as pion electro-magnetic form-factor and B exclusive hadronic decays.

The LCDA for quarkonium 南昌大学 第八届全国高能物理大会 4 Definition: 1981, Chernyak & Zhintnisky  Could be used in procecesses  Different from the LCDAs of light mesons, it can be calculated perturbatively.  The RGE running is governed by the Brodsky-Lepage equation

Charmonium production at B factories 南昌大学 第八届全国高能物理大会 5  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;

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 南昌大学 第八届全国高能物理大会 6

Salute to those guys 南昌大学 第八届全国高能物理大会 7 Non-pert. quantities!Kill renormalization scale dependence Gong, QWG2008

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 南昌大学 第八届全国高能物理大会 8

Light-cone framework Ma and Si, PRD 2004;Bonder and Chernyak, PLB 2005;Braguta, arXiv: [hep-ph] From Ma and Si, PRD 2004; 南昌大学 第八届全国高能物理大会 9 Fit to the expr.!LCDA: Non-pert. quantities!Lead to end-point singularity!

Motivations 南昌大学 第八届全国高能物理大会 10 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

Exclusive single quarkonium production 南昌大学 第八届全国高能物理大会 11

Refactorization 南昌大学 第八届全国高能物理大会 12 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;

Example-1: 南昌大学 第八届全国高能物理大会 13 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,

One-loop level 南昌大学 第八届全国高能物理大会 14 Sang, Chen, arXiv: ; Li, He, Chao arXiv:

Leading regions 南昌大学 第八届全国高能物理大会 15  Hard Region:  Collinear region:  Anti-collinear region:  Potential region:  Soft region:  Ultra-soft region: NRQCD regions Non-perturbative

Form factor 南昌大学 第八届全国高能物理大会 16 NRQCD: Collinear factorization:  Hard-kernel: at tree level  Light-cone distribution amplitude Ma and Si, PRD 2006; Bell and Feldmann, JHEP 2007;

RGE for LCDA 南昌大学 第八届全国高能物理大会 17 Brodsky-Lepage kernel: Resum the leading logrithms where

Resummation in moment space 南昌大学 第八届全国高能物理大会 18 Both LCDA and Brodsky-Lepage kernel can be expanded in Gegenbauer polynomial In moment space, the LL resummed form-factor is

Truncated LL approximation 南昌大学 第八届全国高能物理大会 19 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: ; Li, He, Chao arXiv: Braaten, PRD 1981;Ma and Si, PRD 2006; Bell and Feldmann, JHEP 2007;

Comparisons 南昌大学 第八届全国高能物理大会 20 LL 2-loop LL 1-loop LL

NLO results (preliminary) 南昌大学 第八届全国高能物理大会 21 Braaten, PRD 1981; Ma and Si, PRD 2006; Bell and Feldmann, JHEP 2007;  Hard Part  Collinear Part  Total Results Sang, Chen, arXiv: ; Li, He, Chao arXiv:

Example-2: 南昌大学 第八届全国高能物理大会 22 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

Comparisons 南昌大学 第八届全国高能物理大会 23 1-loop LL 2-loop LL LL

Summary 南昌大学 第八届全国高能物理大会 24  The LCDA can be used to refactoriz NRQCD short-distance coefficients in the single heavy quarkonium exclusive production at very large center energy collision;  The RG running of LCDA can be used to re-sum the large single logarithm;  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 radiative corrections with loss of m/Q suppressed corrections;

南昌大学 第八届全国高能物理 大会