Closed-form decomposition of one-loop massive amplitudes

We present formulas for the coefficients of 2-, 3-, 4-, and 5-point master integrals for one-loop massive amplitudes. The coefficients are derived from unitarity cuts in $D$ dimensions. The input parameters can be read off from any unitarity-cut integrand, as assembled from tree-level expressions, after simple algebraic manipulations. The formulas presented here are suitable for analytical as well as numerical evaluation. Their validity is confirmed in two known cases of helicity amplitudes contributing to $gg\to gg$ and $gg\to gH$, where the masses of the Higgs and the fermion circulating in the loop are kept as free parameters.