Complex rational Ruijsenaars model. The two-particle case

We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit ω₁ + ω₂ → 0 (or b → i in 2d CFT) and investigate the two-particle case in detail. Corresponding wave functions are described by complex hypergeometric functions in the Mellin–Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter Q-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special ω₁ − ω₂ → 0 (or b → 1) limit. Additionally, two new degenerations to the complex Calogero–Sutherland type models are described.