Tadpole contribution to a cubic-theory two-point function (source code)

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

Use $-g\phi^3/3!$ and $D=6-2\epsilon$ with $m>0$. In an unshifted vacuum, the one-loop mean field has pole $v_{\rm div}=-gm^2/[4(4\pi)^3\epsilon]$. Attaching it to a cubic vertex gives the connected but one-particle-reducible two-point insertion $(-ig)v_{\rm div}=ig^2m^2/[4(4\pi)^3\epsilon]$. 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