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Extra Dimensions and the Muon Anomalous Magnetic Moment
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February 1, 2008
LBNL-42812
UCB-PTH-99/03
Extra Dimensions and the Muon Anomalous Magnetic Moment 1
M. L. Graesser 2
Theoretical Physics Group, Lawrence Berkeley National Laboratory
and
Department of Physics, University of California
Berkeley, California 94720
Abstract
It has been proposed recently that the scale of strong gravity can be very close to the
weak scale. Dimensions of sizes anywhere from ~mm to ~TeV?1 can be populated by
bulk gravitons, vector bosons and fermions. In this paper the one-loop correction of these
bulk particles to the muon magnetic moment (MMM) are investigated. In all the scenarios
considered here it is found that the natural value for the MMM is O(10?8?10?9). One main
result is that the contribution of each Kaluza?Klein graviton to the MMM is remarkably
finite. The bulk graviton loop implies a limit of ~ 400 GeV on the scale of strong gravity.
This could be pushed up to ~ 1 ? 2 TeV, even in the case of six extra dimensions, if the
BNL E821 experiment reaches an expected sensitivity of ~ 10?9. Limits on a bulk B ? L
gauge boson are interesting, but still allow for forces 106 ? 107 times stronger than gravity
at mm?1 distances. The correction of a bulk right-handed neutrino to the MMM in one
recent proposal for generating small Dirac neutrino masses is considered in the context of
a two Higgs doublet model, and is found to be close to 10?9. The contributions of all
these bulk particles to the MMM are (roughly) independent of both the total number of
extra dimensions and the dimension of the subspace occupied by the bulk states. Finally,
limits on the size of “small” compact dimensions gotten from the MMM and atomic parity
violation are determined and compared.
1This work was supported in part by the Director, Office of Energy Research, Office of High Energy and
Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-
76SF00098.
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