Bounds on ortho-positronium and J/psi - Y quarkonia invisible decays and constraints on hidden braneworlds in a SO(3,1)-broken 5D bulk

While our visible Universe could be a 3-brane, some cosmological scenarios consider that other3-branes could be hidden in the extra-dimensional bulk. Matter disappearance toward a hiddenbrane is mainly discussed for neutron – both theoretically and experimentally – but other particlesare poorly studied. Recent experimental results offer new constraints on positronium or quarkoniuminvisible decays. In the present work, we show how a two-brane Universe allows for such invisibledecays. We put this result in the context of the recent experimental data to constrain the braneenergy scaleMB(or effective brane thicknessM−1B) and the interbrane distancedfor a relevanttwo-brane Universe in aSO(3,1)-broken 5D bulk. Quarkonia present poor bounds compared toresults deduced from previous passing-through-walls-neutron experiments for which scenarios withMB<2.5×1017GeV andd >0.5 fm are excluded. By contrast, positronium experiments cancompete with neutron experiments depending on the matter content of each brane. To constrainscenarios up to the Planck scale, positronium experiments in vacuum cavity should be able to reachBr(o-Ps→invisible)≈10−6