![Page 1: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/1.jpg)
Refactorizing NRQCD short-distance coefficients
in exclusive quarkonium production
Refactorizing NRQCD short-distance coefficients
in exclusive quarkonium production
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
11
Based on Yu Jia & DSY, NPB814, 217 (2009)
Graduate University of the CASDeshan Yang
![Page 2: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/2.jpg)
OutlineOutline
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
22
1. Introduction & Motivations
2. Refactorization of NRQCD coefficients
3. Example 1 –
4. Example 2 –
5. Summary
bee
Υh
![Page 3: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/3.jpg)
Charmonium production at B factories
Charmonium production at B factories
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
33
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;
fbBJee
fbBJeec
c
c
c
)8.26.17(]2[]/[ :BaBar
)4.38.26.25(]2[]/[ : Belle5.11.2
fbJee c )5.53.2(]/[
![Page 4: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/4.jpg)
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
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
44
![Page 5: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/5.jpg)
Salute to those guysSalute to those guys
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
55
Non-pert. quantities!
Kill renormalization scale dependence
LONLOcmsK /)/( 2
Gong, QWG2008
![Page 6: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/6.jpg)
NRQCD factorizationNRQCD factorizationFor 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
66
![Page 7: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/7.jpg)
Light-cone frameworkLight-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
77
Fit to the expr.!
LCDA: Non-pert. quantities!
Lead to end-point singularity!
![Page 8: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/8.jpg)
MotivationsMotivations
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
88
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 2vmvmms ccc
![Page 9: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/9.jpg)
Inclusive quarkonium production at hadron collider
Inclusive quarkonium production at hadron collider
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
99
J.W.Qiu’s talk at this program
Absent from electron-positron collider!Less complications!
Perturbative region could be furthurfined into two regions!
![Page 10: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/10.jpg)
Exclusive single quarkonium productionExclusive single quarkonium production
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1010
![Page 11: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/11.jpg)
RefactorizationRefactorization
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1111
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;
![Page 12: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/12.jpg)
Example-1:Example-1:
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1212
bee
Amplitude up to leading power of velocity:
The short-distance contribution is parameterized as
The equivalent computation is to calculate the on-shell heavyquark anti-quark pair with equal momentum and the samequantum number as the quarkonium. At the tree level,
![Page 13: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/13.jpg)
One-loop levelOne-loop level
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1313
![Page 14: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/14.jpg)
Leading regionsLeading regions
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1414
Hard Region:
Collinear region:
Anti-collinear region:
Potential region:
Soft region:
Ultra-soft region:
![Page 15: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/15.jpg)
Form factorForm factor
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1515
NRQCD:
Collinear factorization:
Hard-kernel:
at tree level
Light-cone distribution amplitude
![Page 16: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/16.jpg)
RGE for LCDARGE for LCDA
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1616
Brodsky-Lepage kernel:
Resum the leading logrithms
where
![Page 17: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/17.jpg)
Resummation in moment spaceResummation in moment space
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1717
Both LCDA and Brodsky-Lepage kernel can be expanded in Gegenbauer polynomial
In moment space, the LL resummed form-factor is
![Page 18: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/18.jpg)
Truncated LL approximationTruncated LL approximation
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1818
In momentum space, solve the RGE recursively, at two-looplevel, we have
which is equivalent to the expressions in moment space
![Page 19: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/19.jpg)
ComparisonsComparisons
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
1919
LL2-loop LL
1-loop LL
![Page 20: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/20.jpg)
Example-2:Example-2:
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
2020
h
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
![Page 21: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/21.jpg)
ComparisonsComparisons
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
2121
1-loop LL
2-loop LL
LL
![Page 22: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/22.jpg)
SummarySummary
2009.9.10 KITPC-EFT in Nuclear Physics & Particle Physics
2222
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.
![Page 23: Refactorizing NR Q C D short-distance coefficients in exclusive quarkonium production](https://reader035.vdocument.in/reader035/viewer/2022062802/56814573550346895db242a8/html5/thumbnails/23.jpg)
232009.9.10 KITPC-EFT in Nuclear Physics
& Particle Physics