  The anomalous magnetic moment (g-2) of the muon was measured with a precision
of 0.54 ppm in Experiment 821 at Brookhaven National Laboratory. A difference
of 3.2 standard deviations between this experimental value and the prediction
of the Standard Model has persisted since 2004; in spite of considerable
experimental and theoretical effort, there is no consistent explanation for
this difference. This comparison hints at physics beyond the Standard Model,
but it also imposes strong constraints on those possibilities, which include
supersymmetry and extra dimensions. The collaboration is preparing to relocate
the experiment to Fermilab to continue towards a proposed precision of 0.14
ppm. This will require 20 times more recorded decays than in the previous
measurement, with corresponding improvements in the systematic uncertainties.
We describe the theoretical developments and the experimental upgrades that
provide a compelling motivation for the new measurement.
