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A search for a new heavy boson produced via gluon-fusion in the four-leptonchannel with missing transverse momentum or jets is performed. The search usesproton-proton collision data equivalent to an integrated luminosity of 139fb$^{-1}$ at a centre-of-mass energy of 13 TeV collected by the ATLAS detectorbetween 2015 and 2018 at the Large Hadron Collider. This study explores thedecays of heavy bosons: $R\rightarrow SH$ and $A\rightarrow ZH$, where $R$ is aCP-even boson, $A$ is a CP-odd boson, $H$ is a CP-even boson, and $S$ isconsidered to decay into invisible particles that are candidates for darkmatter. In these processes, $S\rightarrow \textrm{invisible}$ and $H\rightarrowZZ$. The $Z$ boson associated with the heavy scalar boson $H$ decays into alldecay channels of the $Z$ boson. The mass range under consideration is 390-1300(320-1300) GeV for the $R$ ($A$) boson and 220-1000 GeV for the $H$ boson. Nosignificant deviation from the Standard Model backgrounds is observed. Theresults are interpreted as upper limits at a 95% confidence level on thecross-section times the branching ratio of the heavy resonances.

Search for heavy resonances in final states with four leptons and  missing transverse momentum or jets in $pp$ collisions at $\sqrt{s} = 13$ TeV  with the ATLAS detector