= Solution
An <on-shell renormalization scheme> fixes the mass parameter at the physical <pole mass> and fixes the renormalized field by the chosen pole residue. Its <counterterms> include finite contributions needed to enforce those conditions. A coupling is likewise defined by a specified physical amplitude or mass-shell condition.
The <minimal subtraction scheme> removes only poles in the dimensional regulator. The <modified minimal subtraction scheme>, which is the overbarred scheme in the PDF, removes the accompanying universal combination $\log4\pi-\gamma_E$ as well. In $D=4-\epsilon$, the one-loop subtraction is proportional to
$$
\boxed{\Delta_{\overline{\rm MS}}=\frac2\epsilon-\gamma_E+\log4\pi.}
$$
\b[A subtraction-scheme mass is a running parameter and generally differs from the physical mass]. Finite redefinitions relate the schemes while leaving physical quantities unchanged. The overbar is essential for the stated finite formula in part (d).
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