Search for the Production of a Long-Lived Neutral Particle Decaying within the ATLAS Hadronic Calorimeter in Association with a $Z$ Boson from $pp$ Collisions at $\sqrt{s} =$ 13  TeV

This Letter presents a search for the production of a long-lived neutral particle ($Z_d$) decaying within the ATLAS hadronic calorimeter, in association with a Standard Model (SM) $Z$ boson produced via an intermediate scalar boson, where $Z\to l^+l^-$ ($l=e,\mu$). The data used were collected by the ATLAS detector during 2015 and 2016 $pp$ collisions with a center-of-mass energy of $\sqrt{s} = 13$ TeV at the Large Hadron Collider and corresponds to an integrated luminosity of $36.1\pm0.8$ fb$^{-1}$. No significant excess of events is observed above the expected background. Limits on the production cross section of the scalar boson times its decay branching fraction into the long-lived neutral particle are derived as a function of the mass of the intermediate scalar boson, the mass of the long-lived neutral particle, and its $c\tau$ from a few centimeters to one hundred meters. In the case that the intermediate scalar boson is the SM Higgs boson, its decay branching fraction to a long-lived neutral particle with a $c\tau$ approximately between 0.1 m and 7 m is excluded with a 95% confidence level up to 10% for $m_{Z_d}$ between 5 and 15 GeV.