  Currently, the experimental uncertainty for the determination of the
ortho-positronium (o-Ps) decay rate is at 150 ppm precision; this is two orders
of magnitude lower than the theoretical one, at 1 ppm level. Here we propose a
new proof of concept experiment aiming for an accuracy of 100 ppm to be able to
test the second-order correction in the calculations, which is $\simeq
45\left(\frac{\alpha}{\pi}\right)^2\approx 200$ ppm. The improvement relies on
a new technique to confine the o-Ps in a vacuum cavity. Moreover, a new method
was developed to subtract the time dependent pick-off annihilation rate of the
fast backscattered positronium from the o-Ps decay rate prior to fitting the
distribution. Therefore, this measurement will be free from the systematic
errors present in the previous experiments. The same experimental setup
developed for our recent search for invisible decay of ortho-positronium is
being used. The precision will be limited by the statistical uncertainty, thus,
if the expectations are fulfilled, this experiment could pave the way to reach
the ultimate accuracy of a few ppm level to confirm or confront directly the
higher order QED corrections. This will provide a sensitive test for new
physics, e.g. a discrepancy between theoretical prediction and measurements
could hint the existence of an hidden sector which is a possible dark matter
candidate.
