FCLoopExtract[expr, {q1, q2, ...}, loopHead] exctracts
loop integrals that depend on q1, q2, ... from the given
expression. The output is given as a list of three entries. The first
one contains part of the original expression that consists of irrelevant
loop integrals and terms that are free of any loop integrals. The second
entry contains relevant loop integrals, where each integral is wrapped
into loopHead. The third entry is a list of all the unique
loop integrals from the second entry and can be used as an input to
another function. Note that if loop integrals contain free indices,
those will not be canonicalized.
FCI[GSD[q - p1] . (GSD[q - p2] + M) . GSD[p3] SPD[q, p2] FAD[q, q - p1, {q - p2, m}]]
FCLoopExtract[%, {q}, loopInt]\frac{(\text{p2}\cdot q) (\gamma \cdot (q-\text{p1})).(M+\gamma \cdot (q-\text{p2})).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}
\left\{0,((\gamma \cdot \;\text{p1}).(\gamma \cdot \;\text{p2}).(\gamma \cdot \;\text{p3})-M (\gamma \cdot \;\text{p1}).(\gamma \cdot \;\text{p3})) \;\text{loopInt}\left(\frac{\text{p2}\cdot q}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right)+M \;\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot q).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right)-\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot \;\text{p1}).(\gamma \cdot q).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right)-\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot q).(\gamma \cdot \;\text{p2}).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right)+\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot q).(\gamma \cdot q).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right),\left\{\text{loopInt}\left(\frac{\text{p2}\cdot q}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right),\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot q).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right),\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot \;\text{p1}).(\gamma \cdot q).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right),\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot q).(\gamma \cdot \;\text{p2}).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right),\text{loopInt}\left(\frac{(\text{p2}\cdot q) (\gamma \cdot q).(\gamma \cdot q).(\gamma \cdot \;\text{p3})}{q^2.(q-\text{p1})^2.\left((q-\text{p2})^2-m^2\right)}\right)\right\}\right\}