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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
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

outline
Outline

Introduction & Motivations

Refactorization of NRQCD coefficients

Example 1 –

Example 2 –

Summary

2009.12.2 Center of High Energy Physics, Peking University

charmonium production at b factories
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

battlefield for nrqcd guys
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

salute to those guys
Salute to those guys

Gong, QWG2008

Non-pert. quantities!

Kill renormalization scale dependence

2009.12.2 Center of High Energy Physics, Peking University

nrqcd factorization
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

light cone framework
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

motivations
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

inclusive quarkonium production at hadron collider
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

exclusive single quarkonium production
Exclusive single quarkonium production

2009.12.2 Center of High Energy Physics, Peking University

refactorization
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

example 1
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

one loop level
One-loop level

 Sang, Chen, arXiv:0910.4071; Li, He, Chao arXiv:0910.4155

2009.12.2 Center of High Energy Physics, Peking University

leading regions
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

form factor
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

rge for lcda
RGE for LCDA

Brodsky-Lepage kernel:

Resum the leading logrithms

where

2009.12.2 Center of High Energy Physics, Peking University

resummation in moment space
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

truncated ll approximation
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

comparisons
Comparisons

LL

2-loop LL

1-loop LL

2009.12.2 Center of High Energy Physics, Peking University

nlo results preliminary
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

example 2
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

comparisons1
Comparisons

1-loop LL

2-loop LL

LL

2009.12.2 Center of High Energy Physics, Peking University

summary
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

slide24

谢谢!

2009.12.2 Center of High Energy Physics, Peking University