  Heavy-Dense QCD (HDQCD) is a popular theory to investigate the sign problem
in quantum field theory. Besides its physical applications, HDQCD is relatively
easy to implement numerically: the fermionic degrees of freedom are integrated
out, and the fermion determinant factorises into local ones. The theory has a
sign problem, the severeness of which depends on the value of the chemical
potential, which makes this theory ideal to test the reach of new algorithms.
We use the LLR approach to obtain the probability distribution of the phase of
the fermion determinant. Our goal is the calculation of the phase factor
expectation value, which appears as Fourier transform of this probability
distribution. We here propose a new and systematic moment expansion for this
phase factor. We compare the answer from the moment expansion order by order
with the exact answer. We find that this expansion converge quickly and works
very well in the strong sign problem region.
