Yukawa scalar self-energy pole coefficients (${\hat{\tau }}_2^{(1)}=-y^2(4p^2+24M^2)/(\epsilon 16{\pi }^2)+O(1)$)

For one four-component Dirac field with scalar interaction $-y\bar{\psi }\psi \varphi$ and the mostly-plus propagator convention, the fermion loop numerator is $4[M^2-k\cdot (k-p)]$. Reduce it to a bubble and tadpole: $-4y^2[(2M^2+p^2/2)J-I]$. Dimensional regularization gives pole parts $J=2/(\epsilon 16{\pi }^2)$ and $I=-2M^2/(\epsilon 16{\pi }^2)$. The local pole then requires both wavefunction renormalization and a scalar mass counterterm.