Probing a light long-lived pseudo-scalar from Higgs decay via displaced taus at the LHC

A light (GeV mass) long-lived ($c\tau$ around dozens of millimeters) CP-odd scalar can be readily predicted in new physics models. In this work we investigate the Higgs decay into such a light scalar plus a $Z$-boson and take the aligned two-Higgs-doublet model (2HDM) as an example. This light long-lived scalar, with the dominant decay to tau leptons, will fly over a distance from the production point and present a displaced vertex in an Inner Detector of a generally purposed experiment like ATLAS or CMS. In our study we focus on the LHC experiment and perform Monte Carlo simulations for the signal and backgrounds. We demonstrate some benchmark points for the aligned 2HDM and find the signal to be detectable when the luminosity is accumulated to 300 fb$^{-1}$. So our study suggests an experimental search for this process in the ongoing LHC.