Analyzing Power Law Extensions of Newtonian Gravity Using Differential Force Measurements

Abstract

The Standard Model is not a complete description of reality; it omits the existence of dark matter, dark energy, and an explanation as to why no CP violation has been observed. However, some of these phenomena could be explained through a new force mediated by a new boson. If such a boson were massless it would result in a power law potential and if massive the interaction would be Yukawa-like. A previous experiment employing the interactions of a micromechanical oscillator attached to spherical test mass was successful in placing the best limits on a mass–mass Yukawa-like interaction, but the data were never analyzed in the context of a power law. Here, those data are analyzed considering a power law for powers n = 1–5 where n is the number of boson exchanges. The results show that the limits obtained through power law analysis of these data are not better than the currently accepted limits. A discussion of an experiment design capable of producing better limits on power law extensions to the Standard Model is presented, and suggests that a micromechanical-oscillator-based experiment remains capable of improving the limits by at least one order of magnitude.