Interference contributions to gluon initiated heavy Higgs production in the Two-Higgs-Doublet Model

We discuss the production of a heavy neutral Higgs boson of a CP-conserving Two-Higgs-Doublet Model in gluon fusion and its decay into a four-fermion final state, $gg (\rightarrow VV) \rightarrow e^+e^-\mu^+\mu^-/e^+e^-\nu_l\bar\nu_l$. We investigate the interference contributions to invariant mass distributions of the four-fermion final state and other relevant kinematical observables. The relative importance of the different contributions is quantified for the process in the on-shell approximation, $gg\rightarrow ZZ$. We show that interferences of the heavy Higgs with the light Higgs boson and background contributions are essential for a correct description of the differential cross section. Even though they contribute below $\mathcal{O}(10\%)$ to those heavy Higgs signal cross sections, to which the experiments at the Large Hadron Collider were sensitive in its first run, we find that they are sizeable in certain regions of the parameter space that are relevant for future heavy Higgs boson searches. In fact, the interference contributions can significantly enhance the experimental sensitivity to the heavy Higgs boson.