  We investigate the phase diagram and the mechanism for the sign problem to
appear in finite density QCD at strong coupling in a combined framework of the
auxiliary field Monte-Carlo (AFMC) and the chiral angle fixing (CAF) methods.
When bosonizing meson hopping terms in the effective action, we need to
introduce imaginary number coefficients, which leads to a complex phase in
numerical simulations. By using the cut-off technique, we quantitatively show
that high momentum modes of auxiliary fields mainly contribute to the weight
cancellation; Cutting-off high-momentum auxiliary field modes does not modify
order parameters but suppresses statistical weight cancellation, when we choose
the cut-off parameter appropriately.
