  Disordered and hyperuniform structures of densely packed spheres near and at
jamming are characterized by vanishing of long-wavelength density fluctuations,
or equivalently by long-range power-law decay of the direct correlation
function (DCF). We focus on previous simulation results that exhibit
degradation of hyperuniformity in jammed structures while maintaining the
long-range nature of the DCF to a certain length scale. Here we demonstrate
that a field-theoretic formulation of the stochastic density functional theory
is relevant to explore the degradation mechanism. The strong-coupling expansion
method of the stochastic density functional theory is developed to obtain the
metastable chemical potential considering intermittent fluctuations in dense
packings. The metastable chemical potential yields an analytical form of the
metastable DCF that has a short-range cutoff inside the sphere while retaining
the long-range power-law behavior. It is confirmed that the metastable DCF
provides zero-wavevector limit of structure factor in quantitative agreement
with the previous simulation results of degraded hyperuniformity. We can also
predict the emergence of soft modes localized at the particle scale from
plugging this metastable DCF into the linearized Dean-Kawasaki equation, a
stochastic density functional equation.
