  The Twin Higgs mechanism keeps the scalar sector of the Standard Model (SM)
natural while remaining consistent with the non-observation of new colored
particles at the Large Hadron Collider (LHC). In this construction the heavy
twin Higgs boson provides a portal between the SM particles and the twin
sector, but is quite challenging to discover at colliders. In the Fraternal
Twin Higgs setup, where light twin quarks are absent, we study a novel
discovery channel for the heavy twin Higgs boson by considering its decay to a
pair of light Higgs bosons, one of which subsequently decays to glueball states
in the twin sector, leading to displaced vertex signatures. We estimate the
sensitivity of existing LHC searches in this channel, and assess the discovery
potential of the high luminosity (HL) LHC. We show that the glueballs probed by
these searches are outside the sensitivity of existing searches for exotic
decays of the light Higgs boson. In addition, we demonstrate that the displaced
signals we consider probe a region of heavy Higgs masses beyond the reach of
prompt signals. We also comment on the possibility of probing the input
parameters of the microscopic physics and providing a way to test the Twin
Higgs mechanism with this channel.
