 Tadpole contribution to a cubic-theory two-point function

Use $-g{\varphi }^3/3!$ and $D=6-2ϵ$ with $m>0$. In an unshifted vacuum, the one-loop mean field has pole $v_{\mathrm{div}}=-g{m}^2/[4(4\pi {)}^3ϵ]$. Attaching it to a cubic vertex gives the connected but one-particle-reducible two-point insertion $(-ig)v_{\mathrm{div}}=i{g}^2{m}^2/[4(4\pi {)}^3ϵ]$. It supplements the proper bubble unless a tadpole subtraction sets the renormalized mean field to zero. A disconnected product of two one-point functions is a separate two-loop term and is not a propagator insertion.

// Target: relativistic-quantum-field.bigb