MICROSCOPE limits for new long-range forces and implications for unified theories
Résumé
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 [εQQ+εBB+εLL]e, involving B-L in a grand-unified theory, presumably through B-L-.61Q, 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 εB+εL/2, times a combination involving mostly εL. 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 εB-L or εL, 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 [εQQ+εB-L(B-L)]e or [εQQ+εLL]e should verify |εB-L| or |εL|<.8 10-24, and a force coupled to [εQQ+εBB]e, |εB|<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.