= Yukawa scalar self-energy pole coefficients
{c}
{title2=$\widehat\tau_2^{(1)}=-y^2(4p^2+24M^2)/(\varepsilon16\pi^2)+O(1)$}
For one four-component <Dirac field> with scalar interaction $-y\bar\psi\psi\phi$ 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 $J=2/(\varepsilon16\pi^2)$ and $I=-2M^2/(\varepsilon16\pi^2)$. The local <pole> then requires both <wavefunction renormalization> and a scalar <mass counterterm>.
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