Title: Renormalization scale setting for heavy quark pair production in $e^+e^–$ annihilation near the threshold region

Abstract

Heavy fermion pair production in $e^{+}{e}^{–}$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the principle of maximum conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $v{m}_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated.

Authors:

Wang, Sheng-Quan ;

• Search DOE PAGES for author "Wang, Sheng-Quan"
• Search DOE PAGES for ORCID "0000-0002-1855-2423"

Brodsky, Stanley J. ;

• Search DOE PAGES for author "Brodsky, Stanley J."
• Search DOE PAGES for ORCID "0000-0001-8786-3172"

Wu, Xing-Gang; Di Giustino, Leonardo ;

• Search DOE PAGES for author "Di Giustino, Leonardo"
• Search DOE PAGES for ORCID "0000-0001-7746-918X"

Shen, Jian-Ming

Publication Date:

Mon Jul 06 00:00:00 EDT 2020

Research Org.:

SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC)

OSTI Identifier:

1637397

Alternate Identifier(s):

OSTI ID: 1646876

Report Number(s):

SLAC-PUB-17512
Journal ID: ISSN 2470-0010; PRVDAQ; 014005

Grant/Contract Number:  

AC02-76SF00515; KY[2017]067; 11625520; 11905056; 11705033

Resource Type:

Published Article

Journal Name:

Physical Review. D.

Additional Journal Information:

Journal Name: Physical Review. D. Journal Volume: 102 Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS