  Disjoint regions of the latticized, massless scalar field vacuum become
separable at large distances beyond the entanglement sphere, a distance that
extends to infinity in the continuum limit. Through numerical calculations in
one-, two- and three-dimensions, the radius of an entanglement sphere is found
to be determined by the highest momentum mode of the field supported across the
diameter, $d$, of two identical regions. As a result, the long-distance
behavior of the entanglement is determined by the short-distance structure of
the field. Effective field theories (EFTs), describing a system up to a given
momentum scale $\Lambda$, are expected to share this feature, with regions of
the EFT vacuum separable (or dependent on the UV-completion) beyond a distance
proportional to $\Lambda$. The smallest non-zero value of the entanglement
negativity supported by the field at large distances is conjectured to be
$\mathcal{N}_{{ {\cal N}\hskip-0.55em /}} \sim e^{-\Lambda d}$, independent of
the number of spatial dimensions. This phenomenon may be manifest in
perturbative QCD processes.
