= Scalar triangle Feynman integral
{title2=$C=\int\frac{d^4\ell}{(2\pi)^4}\frac1{D_0D_1D_2}$}
In mostly-minus signature, take $D_j=(\ell+r_j)^2-m^2+i0$. <Feynman parameters> and a momentum shift give
$$
C=-\frac{i}{16\pi^2}\int_{x_j\ge0}dx_0dx_1dx_2\,\delta(1-\textstyle\sum_jx_j)\left[m^2-\sum_{i<j}x_ix_j(r_i-r_j)^2-i0\right]^{-1}.
$$
For massive internal lines this is ultraviolet finite in four dimensions. Physical external kinematics can still create threshold cuts, encoded by the <Feynman i-epsilon prescription>.
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