skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A Prediction for the 4-Loop beta Function in QCD

Abstract

We predict that the four-loop contribution {beta}{sub 3} to the QCD {beta} function in the {ovr MS} prescription is given by {beta}{sub 3} {approx_equal} 23,600(900) - 6,400(200) N{sub f} + 350(70)N{sub f}{sup 2} + 1.5 N{sub f}{sup 3}, where N{sub f} is the number of flavours and the coefficient of N{sub f}{sup 3} is an exact result from large-N{sub f} expansion. In the phenomenologically-interesting case N{sub f} = 3, we estimate {beta}{sub 3} = (7.6 {+-} 0.1) x 10{sup 3}. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) {Phi}{sup 4} theory, and on variations in the details of our estimation method, which goes beyond conventional Pade approximants by estimating and correcting for subasymptotic deviations from exact results.

Authors:
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (US)
OSTI Identifier:
813118
Report Number(s):
SLAC-PUB-9826
TRN: US200315%%351
DOE Contract Number:  
AC03-76SF00515
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 14 May 2003
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; FORECASTING; QUANTUM CHROMODYNAMICS

Citation Formats

Samuel, Mark A. A Prediction for the 4-Loop beta Function in QCD. United States: N. p., 2003. Web. doi:10.2172/813118.
Samuel, Mark A. A Prediction for the 4-Loop beta Function in QCD. United States. https://doi.org/10.2172/813118
Samuel, Mark A. 2003. "A Prediction for the 4-Loop beta Function in QCD". United States. https://doi.org/10.2172/813118. https://www.osti.gov/servlets/purl/813118.
@article{osti_813118,
title = {A Prediction for the 4-Loop beta Function in QCD},
author = {Samuel, Mark A},
abstractNote = {We predict that the four-loop contribution {beta}{sub 3} to the QCD {beta} function in the {ovr MS} prescription is given by {beta}{sub 3} {approx_equal} 23,600(900) - 6,400(200) N{sub f} + 350(70)N{sub f}{sup 2} + 1.5 N{sub f}{sup 3}, where N{sub f} is the number of flavours and the coefficient of N{sub f}{sup 3} is an exact result from large-N{sub f} expansion. In the phenomenologically-interesting case N{sub f} = 3, we estimate {beta}{sub 3} = (7.6 {+-} 0.1) x 10{sup 3}. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) {Phi}{sup 4} theory, and on variations in the details of our estimation method, which goes beyond conventional Pade approximants by estimating and correcting for subasymptotic deviations from exact results.},
doi = {10.2172/813118},
url = {https://www.osti.gov/biblio/813118}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed May 14 00:00:00 EDT 2003},
month = {Wed May 14 00:00:00 EDT 2003}
}