Comment on Fast-slow mode coupling instability for coasting beams in the presence of detuning impedance

In this comment we show untenability of key points of the recent article of N. Biancacci, E. Metral and M. Migliorati [Phys. Rev. Accel. Beams 23, 124402 (2020)], hereafter the Article and the Authors. Specifically, the main Eqs. (23), suggested to describe mode coupling, are shown to be unacceptable even as an approximation. The Article claims the solution of this pair of equations to be in excellent agreement with the pyHEADTAIL simulations for CERN PS, which is purportedly demonstrated by Fig. 6. Were it really so, it would be a signal of a mistake in the code. However, the key part of the simulation results is not actually shown, and the demonstrated agreement has all the features of an illusion.