Anatomy of the sign-problem in heavy-dense QCD

QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential. Results are validated using those from a reweighting approach where the latter can produce a significant signal-to-noise ratio. We confirm the particle-hole symmetry at low temperatures, find a strong sign problem at intermediate values of the chemical potential, and an inverse Silver Blaze feature for chemical potentials close to the onset value: here, the phase-quenched theory underestimates the density of the full theory.