FCLoopAddAuxiliaryMass[expr, {k1, k2, ...},-m^2,n] adds
auxiliary mass term m^2 to the
propagators in the list that depend on loop momenta
k1, k2, .... For n=0 the
mass is added directly.
For n>0 the function applies the
exact identity from arXiv:hep-ph/9711266,
known as infrared rearrangement, n
times. The option Last allows to add a flag to the last
term in the expression as a check that it does not contribute to the
physical results.
Overview, FeynAmpDenominatorCombine.
FCLoopAddAuxiliaryMass[{FAD[k + p]}, {k}, -M^2, 2]\left\{\frac{1}{(k+p)^2}\to -\frac{M^2}{((k+p)^2-M^2+i \eta )^2}+\frac{1}{((k+p)^2-M^2+i \eta )}+\frac{M^4}{((k+p)^2+i \eta ).((k+p)^2-M^2+i \eta )^2}\right\}
FCLoopAddAuxiliaryMass[{denHead[FAD[k + p]]}, {k}, -M^2, 2, Head -> denHead]\left\{\text{denHead}\left(\frac{1}{(k+p)^2}\right)\to -\frac{M^2}{((k+p)^2-M^2+i \eta )^2}+\frac{1}{((k+p)^2-M^2+i \eta )}+\frac{M^4}{((k+p)^2+i \eta ).((k+p)^2-M^2+i \eta )^2}\right\}
FCLoopAddAuxiliaryMass[{denHead[FAD[k + p]]}, {k}, -M^2, 2, Head -> denHead, "MassHead" -> auxM]\left\{\text{denHead}\left(\frac{1}{(k+p)^2}\right)\to \frac{\text{auxM}\left(-M^2\right)^2}{((k+p)^2+i \eta ).((k+p)^2-M^2+i \eta )^2}+\frac{\text{auxM}\left(-M^2\right)}{((k+p)^2-M^2+i \eta )^2}+\frac{1}{((k+p)^2-M^2+i \eta )}\right\}
FCLoopAddAuxiliaryMass[{denHead[FAD[k + p]]}, {k}, -M^2, 3, Head -> denHead, "MassHead" -> auxM, Last -> flag]\left\{\text{denHead}\left(\frac{1}{(k+p)^2}\right)\to \frac{\text{flag} \;\text{auxM}\left(-M^2\right)^3}{((k+p)^2+i \eta ).((k+p)^2-M^2+i \eta )^3}+\frac{\text{auxM}\left(-M^2\right)^2}{((k+p)^2-M^2+i \eta )^3}+\frac{\text{auxM}\left(-M^2\right)}{((k+p)^2-M^2+i \eta )^2}+\frac{1}{((k+p)^2-M^2+i \eta )}\right\}
FCLoopAddAuxiliaryMass[{denHead[FAD[{k + p, M}]]}, {k}, -M^2, 0, Head -> denHead]\left\{\text{denHead}\left(\frac{1}{(k+p)^2-M^2}\right)\to \frac{1}{(k+p)^2-M^2}\right\}