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 (ε_Q Q + ε_B B+ε_L L) 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 ε_B+ε_L/2, times a combination involving mostly ε_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 ε_{B-L} or ε_L, as long as no indication for δ\neq 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 (ε_Q Q + ε_{B-L} (B-L)) e or (ε_Q Q + ε_L L) e should verify |ε_{B-L}| or |ε_L| < .8 10^{-24}, and a force coupled to (ε_Q Q + ε_B B) e, |ε_B| < 5 10^{-24}. We also discuss, within supersymmetric theories, how such extremely small gauge couplings g", typically \simle 10^{-24}, may be related to a correspondingly large ξ"D" term associated with a huge initial vacuum energy density, \propto 1/g"^2. The corresponding hierarchy between energy scales, by a factor \propto 1/\sqrt g" \simge 10^{12}, involves a very large scale ~ 10^{16} 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.

13 pages. Phys. Rev. D, in press. Journal version, with systematic and statistical errors combined in quadrature

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