= Disconnected scalar three-point tadpole
In a theory with interaction $-g\varphi^\dagger\varphi\phi$, the neutral correlator $\langle T\varphi^\dagger(x)\varphi(y)\phi(z)\rangle$ contains a connected three-leg contraction and, unless subtracted, the disconnected product of a free complex-field propagator with the induced one-point function of $\phi$. At first order the latter is proportional to $-igD_0(x-y)D_0(0)\int d^4wD_m(z-w)$. Vacuum-bubble normalization alone does not remove it. Normal ordering, a vanishing-tadpole condition, or taking the connected correlator does.
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