Boosted Higgs-pair production associated with large $E_T^{miss}$: a signal of $Z^{\mathrm{\prime }}$

Non-resonant production of Higgs-pair via heavy intermediate states may be a distinctive signature for extended discrete symmetries when accompaied by large missing transvers energy. We discuss $T$-parity as an example of such symmetry within the Littlest Higgs Model, where a new heavy gauge boson $Z^{\mathrm{\prime }}$, the $T$-odd partner of SM $Z$-boson, predominately decays into to a Higgs boson and a dark matter candidate $\chi$. In essence, $T$-parity stablises simultaneously both the Higgs mass and the dark matter. Production via $pp\rightarrow Z’ Z’\rightarrow 2h 2\chi$ may therefore yield important clues about symmetries connecting the Higgs and dark sectors. This paper makes a case for the search for this channel at the LHC by studying its discovery potential. It is demonstrated that in situations where a large $Z^{\mathrm{\prime }}-\chi$ mass gap results in a boosted topology, the jet-substructure technique can be leveraged to reach the required significance for discovery in the $2h\to 2\gamma 2b$ decay mode.