= QED one-loop running-mass to pole-mass conversion
{c}
{title2=$m_{\overline{\rm MS}}(\mu)=m_{\rm pole}[1-\tfrac{e^2}{16\pi^2}(5+3\log(\mu^2/m_{\rm pole}^2))]+O(e^4)$}
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.
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