  It has been suggested that for QCD at finite baryon density the distribution
of the phase angle, i.e. the angle defined as the imaginary part of the
logarithm of the fermion determinant, has a simple Gaussian form. This
distribution provides the density in the density of states approach to the sign
problem. We calculate this phase angle distribution using i) the hadron
resonance gas model; and ii) a combined strong coupling and hopping parameter
expansion in lattice gauge theory. While the former model leads only to a
Gaussian distribution, in the latter expansion we discover terms which cause
the phase angle distribution to deviate, by relative amounts proportional to
powers of the inverse lattice volume, from a simple Gaussian form. We show that
despite the tiny inverse-volume deviation of the phase angle distribution from
a simple Gaussian form, such non-Gaussian terms can have a substantial impact
on observables computed in the density of states/reweighting approach to the
sign problem.
