Proton Decay, Black Holes, and Large Extra Dimensions

We consider proton decay in theories that contain large extra dimensions. If virtual black hole states are allowed by the theory, as is generally the case, then proton decay can proceed via virtual black holes. The experimental limits on the proton lifetime place strong constraints on the quantum gravity scale M_qg (the effective Planck mass). For most theories, this implies a lower bound of M_qg>10¹⁶ GeV. The corresponding bound on the size of large extra dimensions is l<10^6/n×10^-30 cm, where n is the number of such dimensions. Regrettably, for most theories this limit rules out the possibility of observing large extra dimensions at accelerators or in millimeter scale gravity experiments. Conversely, proton decay could be dominated by virtual black holes, providing an experimental probe to study stringy quantum gravity physics.