  This White Paper briefly reviews the present status of the muon (g-2)
experiment and the physics motivation for a new effort. The present comparison
between experiment and theory indicates a tantalizing $3.4 \sigma$ deviation.
An improvement in precision on this comparison by a factor of 2--with the
central value remaining unchanged--will exceed the ``discovery'' threshold,
with a sensitivity above $6 \sigma$. The 2.5-fold reduction improvement goal of
the new Brookhaven E969 experiment, along with continued steady reduction of
the standard model theory uncertainty, will achieve this more definitive test.
  Already, the (g-2) result is arguably the most compelling indicator of
physics beyond the standard model and, at the very least, it represents a major
constraint for speculative new theories such as supersymmetry or extra
dimensions. In this report, we summarize the present experimental status and
provide an up-to-date accounting of the standard model theory, including the
expectations for improvement in the hadronic contributions, which dominate the
overall uncertainty. Our primary focus is on the physics case that motivates
improved experimental and theoretical efforts. Accordingly, we give examples of
specific new-physics implications in the context of direct searches at the LHC
as well as general arguments about the role of an improved (g-2) measurement. A
brief summary of the plans for an upgraded effort complete the report.
