# Four point function with complex momenta?

It is well known that the four-point function $$\int_{\mathbb{R}^{3,1}}\frac {d^4 q}{((q+p_1)^2-i\epsilon)((q+p_2)^2-i\epsilon)((q+p_3)^2-i\epsilon)((q+p_4)^2-i\epsilon)}$$ can be computed using the volume of a certain ideal tetrahedron (See for example Davydychev, Delbourgo, J.Math.Phys.39:4299-4334,1998). Is there any generalization to the case when $$p_1, p_2, p_3, p_4$$ are complexified momentas in $$\mathbb{R}^{3,1}+ i\mathbb{R}^{3,1}$$?