  We propose that effective field theories for nuclei and nuclear matter
comprise of "double decimation": (1) the chiral symmetry decimation (CSD) and
(2) Fermi liquid decimation (FLD). The Brown-Rho scaling recently identified as
the parametric dependence intrinsic in the "vector manifestation" of hidden
local symmetry theory of Harada and Yamawaki results from the first decimation.
This scaling governs dynamics down to the scale at which the Fermi surface is
formed as a quantum critical phenomenon. The next decimation to the top of the
Fermi sea where standard nuclear physics is operative makes up the Fermi liquid
decimation. Thus nuclear dynamics is dictated by two fixed points, namely, the
vector manifestation fixed point and the Fermi liquid fixed point. It has been
a prevalent practice in nuclear physics community to proceed with the second
decimation only, assuming density independent masses. We show why most nuclear
phenomena can be reproduced by theories using either density-independent, or
density-dependent masses, a grand conspiracy of nature that is an aspect that
could be tied to the Cheshire-Cat phenomenon in hadron physics. We identify
what is left out in the Fermi liquid decimation that does not incorporate the
CSD. Experiments such as the dilepton production in relativistic heavy ion
reactions, which are specifically designed to observe effects of dropping
masses, could exhibit large effects from the reduced masses. However they are
compounded with effects that are not directly tied to chiral symmetry. We
discuss a recent STAR/RHIC observation where BR scaling can be singled out in a
pristine environment.
