Abstract
We study the spin chain model which captures the one-loop spectral problem of a prototypical example of an N=2 SCFT in four dimensions. Up to date, this spin chain model remains unfathomable; the standard coordinate Bethe Ansatz does not lead to a solution from three magnons on, as the Yang-Baxter equation is not satisfied by the two-magnon scattering coefficients. In this paper, we find a long-range solution to the eigenvalue problem for three magnons. Remarkably, the scattering coefficients of particular subclasses of our solution, together with the position-dependent corrections, obey an infinite tower of modified Yang-Baxter equations. Our method of solving the three-magnon problem is interesting in its own right and generalizes the standard coordinate Bethe Ansatz approach to cases where the permutation symmetry is broken.