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The renormalization that relates a coupling "a" associated with a distinctrenormalization group beta function in a given theory is considered.Dimensional regularization and mass independent renormalization schemes areused in this discussion. It is shown how the renormalization $a^*=a+x_2a^2$ isrelated to a change in the mass scale $\mu$ that is induced by renormalization.It is argued that the infrared fixed point is to be a determined in arenormalization scheme in which the series expansion for a physical quantity$R$ terminates.

Renormalization Scheme Dependence and the Renormalization Group Beta Function