Exclusive quarkonium production or decay in soft gluon factorization
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Springer
Received: January 16, Revised: April 1, Accepted: April 14, Published: May 5,
2020 2020 2020 2020
Rong Li,a Yu Fengb and Yan-Qing Mac,d,e a
School of Science, Xi’an Jiaotong University, Xi’an 710049, China b Department of Physics, College of Basic Medical Sciences, Army Medical University, Chongqing 400038, China c School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China d Center for High Energy Physics, Peking University, Beijing 100871, China e Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
E-mail: [email protected], [email protected], [email protected] Abstract: In this paper, we study the application of the recently proposed soft gluon factorization (SGF) to exclusive quarkonium production or decay. We find that in the nonrelativistic QCD factorization framework there are too many nonperturbative parameters. Thanks to the factorization of kinematical physics from dynamical physics, the SGF significantly reduces the number of nonperturbative parameters. Therefore, the SGF can improve our predictive power of exclusive quarkonium production or decay. By applying to ηc + γ production at B-factories, our result is the closest one to data among all theoretical calculations. Keywords: QCD Phenomenology, Phenomenological Models ArXiv ePrint: 1911.05886
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)009
JHEP05(2020)009
Exclusive quarkonium production or decay in soft gluon factorization
Contents 1
2 Factorization formula for exclusive processes 2.1 From inclusive formula to exclusive formula 2.2 Definition of nonperturbative matrix elements 2.3 Factorization formula at the amplitude level 2.4 Perturbative matching 2.5 Factorization formula for quarkonium exclusive decay
2 2 2 3 4 5
3 Applications 3.1 Leading order calculation of e+ e− → ηc + γ 3.2 Leading order calculation of ηc → γγ 3.3 Numerical result
6 6 8 8
4 Comparison with NRQCD factorization and the Belle’s measurement
9
5 Summary and outlook
1
11
Introduction
The study of heavy quarkonium production or decay is useful to understand both perturbative and nonperturbative physics of QCD. In the past two decades, the widely used theory for quarkonium physics is the non-relativistic quantum chromodynamics (NRQCD) factorization [1], which factorizes processes to perturbatively calculable hard parts multiplied by nonperturbative long-distance matrix elements (LDMEs). Because LDMEs are simply numbers, the NRQCD factorization has strong predictive power. However, recent studies reveal that NRQCD factorization encounters some difficulties in describing inclusive quarkonium production data. In ref. [2], it was argued that the difficulties of NRQCD may be caused by the bad convergence of relativistic expansion. To overcome this problem, a new factorization method called soft gluon factorization (SGF) was proposed [2]. In this method, a series of relativistic corrections can be resummed to all orders and thus a b
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