Commensurate scale relations in quantum chromodynamics
- Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)
- Department of Physics, University of Maryland, College Park, Maryland 20742 (United States)
The application of this procedure to relate known physical observables in QCD gives rather simple results. In particular, we find that up to light-by-light-type corrections all terms involving {zeta}{sub 3}, {zeta}{sub 5}, and {pi}{sup 2} in the relation between the annihilation ratio {ital R}{sub {ital e}}{sup +}{ital e}{sup {minus}} and the Bjorken sum rule for polarized electroproduction are automatically absorbed into the renomalization scales. The final series has simple coefficients which are independent of color: {cflx @}ga{sub {ital g}1}({ital Q})={cflx @}ga{sub {ital R}}({ital Q}{sup *}){minus}{cflx @}ga{sub {ital R}}{sup 2}({ital Q}{sup **}) +{cflx @}ga{sub {ital R}}{sup 3}({ital Q}{sup ***}), where {cflx @}ga=(3{ital C}{sub {ital F}})/(4{pi}){alpha}. The coefficients in the commensurate scale relation can be identified with those obtained in conformally invariant gauge theory. In the conformally invariant limit, this result agrees with a previous analysis by Broadhurst and Kataev, and coincides with Crewther`s relation, which establishes a nontrivial connection between {ital R}{sub {ital e}}{sup +}{ital e}{sup {minus}} and the Bjorken sum rule.
- Research Organization:
- Stanford Linear Accelerator Center
- DOE Contract Number:
- AC03-76SF00515; FG02-93ER40762
- OSTI ID:
- 26069
- Journal Information:
- Physical Review, D, Journal Name: Physical Review, D Journal Issue: 7 Vol. 51; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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