Dip or nothingness of a Higgs resonance from the interference with a complex phase

We show that new resonance shapes -- a pure dip, nothingness and an enhanced pure peak -- can be produced from the interference between resonance and continuum with a relative phase. Production conditions of those new shapes are derived based on a general parameterization of the interference. The narrow width approximation is modified to work with the non-zero imaginary part of interference, and the correction factor can characterize the resonance shape. We demonstrate that the new resonance shapes of heavy Higgs bosons, $H^0$ and $A^0$ in the Type II aligned two Higgs doublet model, generally show up in $gg \to H^0/A^0 \to t\bar{t}$ as well as $b\bar{b}$ and $\gamma \gamma$ channels. The pure $A^0$ resonance dip in the $t\bar{t}$ channel is a particularly interesting signal as it can be probed well by the current search techniques that do not even take into account interferences; the high-luminosity LHC 14 TeV can perhaps probe a large part of its parameter space.