QED one-loop running-mass to pole-mass conversion ($m_{\overline{\mathrm{MS}}}(\mu )=m_{\mathrm{pole}}[1-\frac{e^2}{16{\pi }^2}(5+3\log ({\mu }^2/m_{\mathrm{pole}}^2))]+O(e^4)$)

In quantum electrodynamics, the modified minimal subtraction scheme running mass differs from the perturbative pole mass by a finite correction. The displayed relation follows by evaluating the renormalized fermion self-energy at the mass shell and imposing a zero of the inverse Dirac propagator. The sign assigned to the self-energy insertion must be matched to its denominator convention; changing that naming convention does not change the conversion. A wave-function coefficient counterterm and multiplicative mass renormalization are also distinct: the coefficient of the mass term includes both at first order.