  Heavy scalar and pseudoscalar resonance searches through the $gg\rightarrow
S\rightarrow t\bar t$ process are challenging due to the peculiar behavior of
the large interference effects with the standard model $t\bar t$ background.
Such effects generate non-trivial lineshapes from additional relative phases
between the signal and background amplitudes. We provide the analytic
expressions for the differential cross sections to understand the interference
effects in the heavy scalar signal lineshapes. We extend our study to the case
of CP-violation and further consider the effect of bottom quarks in the
production and decay processes. We also evaluate the contributions from
additional particles to the gluon fusion production process, such as stops and
vector-like quarks, that could lead to significant changes in the behavior of
the signal lineshapes. Taking into account the large interference effects, we
perform lineshape searches at the LHC and discuss the importance of the
systematic uncertainties and smearing effects. We present projected
sensitivities for two LHC performance scenarios to probe the $gg\rightarrow S
\rightarrow t\bar t$ channel in various models.
