Renormalization-scheme dependence of the strong coupling constant in quantum chromodynamics

Quantum chromodynamics (QCD) lacks a limit analogous to the Thomson limit of quantum electrodynamics (QED) for defining its coupling constant. Nevertheless, the strong coupling constant in QCD can be determined from measurable quantities in an approximately scheme-independent manner as $-q^2\to \infty$. At finite $q^2$, however, high-order terms in the renormalization-group functions introduce scheme-dependent terms into ${\alpha }_s\left(q^2\right)$. A recently suggested method for estimating high-order terms in solutions of Callan-Symanzik equation, which is similar in nature to techniques employed in QED, enables us to determine the size of these scheme-dependent terms. We also discuss a modified minimal-subtraction (MS) scheme which is very appealing. It has the same $\beta$ function as the MS scheme (to all orders) but it equals the momentum-subtraction (MOM) scheme up to two-loop calculations and differs from it at higher orders. We denote this scheme as MOM.