The understanding of the origin of dark matter has great importance for cosmology and particle physics. Several interesting extensions of the standard model dealing with solution of this problem motivate the concept of hidden sectors consisting of SU
(3)xSU(2)_LxU(1)_Y singlet fields. Among these models, the mirror matter model is certainly one of the most interesting. The model explains the origin of parity violation in weak interactions, it could also explain the baryon asymmetry of the Universe and provide a natural ground for the explanation of dark matter. The mirror matter could have a portal to our world through photon-mirror photon mixing (epsilon). This mixing would lead to orthopositronium (o-Ps) to mirror orthopositronium oscillations, the experimental signature of which is the apparently invisible decay of o-Ps. In this paper, we describe an experiment to search for the decay o-Ps -> invisible in vacuum by using a pulsed slow positron beam and a massive 4pi BGO crystal calorimeter. The developed high efficiency positron tagging system, the low calorimeter energy threshold and high hermiticity allow the expected sensitivity in mixing strength to be epsilon about 10^-9, which is more than one order of magnitude below the current Big Bang Nucleosynthesis limit and in a region of parameter space of great theoretical and phenomenological interest. The vacuum experiment with such sensitivity is particularly timely in light of the recent DAMA/LIBRA observations of the annual modulation signal consistent with a mirror type dark matter interpretation.
