  In this paper, we study the behavior of the transmission zeros in the closed
Aharonov-Bohm(AB) interferometer with an embedded scattering center in one arm
and the corresponding change in the transmission phase when the time-reversal
symmetry is broken by magnetic fields. Specifically, we consider three embedded
scattering centers: one discrete energy level, a double-barrier well, and a
$t$-stub. We find the followings from our model study: (i) The transmission
zeros are real when the AB flux is an integer or a half-integer multiple of the
flux quantum, and the transmission phase jumps by $\pi$ at the zeros. (ii) The
transmission zeros become complex or are shifted off the real-energy axis when
the magnetic AB flux is not an integer or a half-integer multiple of the flux
quantum, and the transmission phase evolves continuously. (iii) The distance of
the zeros from the real-energy axis or the imaginary part of the transmission
zeros is sinusoidal as a function of the magnetic AB phase. We suggest the
experimental setup which can test our results.
