  By the unitarity cut method, analytic expressions of one-loop coefficients
have been given in spinor forms. In this paper, we present one-loop
coefficients of various bases in Lorentz-invariant contraction forms of
external momenta. Using these forms, the analytic structure of these
coefficients becomes manifest. Firstly, coefficients of bases contain only
second-type singularities while the first-type singularities are included
inside scalar bases. Secondly, the highest degree of each singularity is
correlated with the degree of the inner momentum in the numerator. Thirdly, the
same singularities will appear in different coefficients, thus our explicit
results could be used to provide a clear physical picture under various limits
(such as soft or collinear limits) when combining contributions from all bases.
