Examining the Lagrangian we see that this is precisely the situation in which there are no derivatives in the vertices, hence the one-loop bubble integrals in standard perturbation theory are finite. In fact, as one might expect, it can be seen that the difference between the two results comes precisely from rational terms that appear as a result of regularization. Notice that the form of these terms is such that they are proportional to tree-level graphs. Therefore, introducing separate couplings $h_1=h c_1$ and $h_2=h c_2$ and shifting them in as follows $$\begin{aligned}
\label{2shift}
 h_1 &\to h_1 + \frac{{h_2}^2}{\pi}& h_2&\to h_2 -\frac{3 {h_2}^2}{\pi}\end{aligned}$$ we can recover the perturbative result. In this sense, the difference can be understood as a regularization-scheme ambiguity. On the other hand one may ask if performing unitarity cuts in $d = 2-2\epsilon$ dimensions [@vanNeerven:1985xr; @Bern:1995db] could give rise to these rational terms and resolve this discrepancy. We leave the study of this formalism for future investigation.

In this work we would like to explore an alternative avenue, which is to focus on integrable theories. Integrable theories possess hidden symmetries that heavily constrain the scattering theory – $(i)$ there can be no particle production, $(ii)$ the set of 