MICROSCOPE limits for new long-range forces and implications for unified theories

Abstract

Many theories beyond the standard model involve an extra U (1 ) gauge group. The resulting gauge boson U , in general mixed with the Z and the photon, may be massless or very light and very weakly coupled. It may be viewed as a generalized dark photon interacting with matter through a linear combination [ɛ_QQ +ɛ_BB +ɛ_LL ]e , involving B -L in a grand-unified theory, presumably through B -L -.61 Q , inducing effectively a very small repulsive force between neutrons. This new force, if long-ranged, may manifest through apparent violations of the equivalence principle. They are approximately proportional to ɛ_B+ɛ_L/2 , times a combination involving mostly ɛ_L. New forces coupled to B -L or L should lead to nearly opposite values of the Eötvös parameter δ , and to almost the same limits for ɛ_{B -L} or ɛ_L, as long as no indication for δ ≠0 is found. We derive new limits from the first results of the MICROSCOPE experiment testing the equivalence principle in space. A long-range force coupled to [ɛ_QQ +ɛ_{B -L}(B -L )]e or [ɛ_QQ +ɛ_LL ]e should verify |ɛ_{B -L}| or |ɛ_L|<.8 10^-24 , and a force coupled to [ɛ_QQ +ɛ_BB ]e , |ɛ_B|<5 10^-24. We also discuss, within supersymmetric theories, how such extremely small gauge couplings g " , typically ≲10^-24, may be related to a correspondingly large ξ " D " term associated with a huge initial vacuum energy density, ∝1 /g "² . The corresponding hierarchy between energy scales, by a factor ∝1 /√{g " }≳10¹² , involves a very large scale ∼ 10¹⁶ GeV , that may be associated with inflation, or supersymmetry breaking with a very heavy gravitino, leading to possible values of δ within the experimentally accessible range.