At present, the generally a epted and widely used prop erty of multiparti le amplitudes is the absen e of simultaneous dis ontinuities of amplitudes in energy invariants of overlapping hannels. To justify this prop erty, the Steinmann relations are used. The pap er shows the presen e of su h dis ontinuities and the illegitima y of using the  teinmann relations to prove their absen e. In the ase of infrared singular parts of the amplitudes, the existen e of the simultaneous dis ontinuities is ompletely natural. But it is not limited to su h parts, and is not limited to the existen e of infrared singularities at all, but o urs also in their absen e. The pap er demonstrates the existen e of simultaneous dis ontinuities in the $s_{12}$ and $s_{23}$ hannels for the amplitude with three parti les in the nal state shown in the gure.

The existen e of simultaneous dis ontinuities means that the urrently a epted form of multi-Regge amplitudes is in orre t and should b e taken into a ount when deriving the BFKL (Balitsky-Fadin-Kuraev-Lipatov) equation in the higher approximations.

V. Fadin
JETP Letters 122, issue 4  (2025)