Probing the gravitational scale via running gauge couplings

According to a recent paper by Robinson and Wilczek, the leading gravitational corrections to the running of gauge couplings tend to reduce the values of the couplings at energies below the gravitational scale, defined to be the energy above which gravity becomes strongly interacting. If the physical gravitational scale is sufficiently low, as conjectured in certain extra-dimension models, this behavior of the gauge couplings can be measured in future high energy experiments, providing a way to determine where the gravitational scale lies. We estimate that measurements of the fine structure constant at the Large Hadron Collider and the proposed International Linear Collider energies can probe the gravitational scale up to several hundred TeV, which will be the most stringent test that can be obtained in the conceivable future.