Scalar bubble integral
= Scalar bubble integral
{title2=$B(P)$}
The <loop momentum> integral with two massive <quantum field theory propagators> is
$$
B(P)=\int\frac{d^dq}{(2\pi)^d}\frac{1}{(q^2+m^2)((q+P)^2+m^2)}.
$$
Its momentum dependence gives a one-loop <self-energy> in <cubic scalar field theory> and a quartic effective vertex in <quartic scalar field theory>.