  We address the recently-observed unexpected behavior of Aharonov-Bohm
oscillations in the electronic Mach-Zehnder interferometer that was realized
experimentally in a quantum Hall system [1]. We argue that the measured lobe
structure in the visibility of oscillations and the phase rigidity result from
a strong long-range interaction between two adjacent counter-propagating edge
states, which leads to a resonant scattering of plasmons. The visibility and
phase shift, which we expressed in terms of the transmission coefficient for
plasmons, can be used for the tomography of edge states.
