FCLoopCreatePartialFractioningRules
`FCLoopCreatePartialFractioningRules[glis, topos] applies partial fraction decomposition to the given GLIs provided that the corresponding topologies contain linearly dependent propagators. The output is given as a list containing replacement rules and new topologies generated in the course of the decomposition.
See also
Overview, ApartFF, FCTopology, GLI.
Examples
glis = {
GLI["preTopoDia2", {1, 1, 0, 0, 1}],
GLI["preTopoDia1", {1, 0, 1, 1, 1}]}
{GpreTopoDia2(1,1,0,0,1),GpreTopoDia1(1,0,1,1,1)}
topos = {FCTopology["preTopoDia1", {SFAD[{{k1, 0}, {0, 1}, 1}], SFAD[{{0, mqb*k1 . nb},
{0, 1}, 1}], SFAD[{{k1, 2*gkin*meta*u0b*k1 . n}, {0, 1}, 1}],
SFAD[{{k1, 2*gkin*meta*k1 . n - meta*u0b*k1 . nb}, {2*gkin*meta^2*u0b, 1}, 1}],
SFAD[{{k1, 2*gkin*meta*u0b*k1 . n - meta*u0b*k1 . nb}, {2*gkin*meta^2*u0b^2, 1},
1}]}, {k1}, {n, nb}, {Hold[SPD][n] -> 0, Hold[SPD][nb] -> 0, Hold[SPD][n, nb] -> 2},
{}], FCTopology["preTopoDia2", {SFAD[{{k1, 0}, {0, 1}, 1}], SFAD[{{0, -(mqb*k1 . nb)}, {0, 1}, 1}], SFAD[{{k1, meta*u0b*k1 . nb}, {0, 1}, 1}], SFAD[{{k1, -2*gkin*meta*k1 . n + meta*u0b*k1 . nb}, {2*gkin*meta^2*u0b, 1}, 1}],
SFAD[{{k1, -2*gkin*meta*u0b*k1 . n + meta*u0b*k1 . nb}, {2*gkin*meta^2*u0b^2, 1},
1}]}, {k1}, {n, nb}, {Hold[SPD][n] -> 0, Hold[SPD][nb] -> 0, Hold[SPD][n, nb] -> 2},
{}]}
{FCTopology(preTopoDia1,{(k12+iη)1,(mqb(k1⋅nb)+iη)1,(k12+2gkinmetau0b(k1⋅n)+iη)1,(k12+2gkinmeta(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b+iη)1,(k12+2gkinmetau0b(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b2+iη)1},{k1},{n,nb},{Hold[SPD][n]→0,Hold[SPD][nb]→0,Hold[SPD][n,nb]→2},{}),FCTopology(preTopoDia2,{(k12+iη)1,(−mqb(k1⋅nb)+iη)1,(k12+metau0b(k1⋅nb)+iη)1,(k12+metau0b(k1⋅nb)−2gkinmeta(k1⋅n)−2gkinmeta2u0b+iη)1,(k12+metau0b(k1⋅nb)−2gkinmetau0b(k1⋅n)−2gkinmeta2u0b2+iη)1},{k1},{n,nb},{Hold[SPD][n]→0,Hold[SPD][nb]→0,Hold[SPD][n,nb]→2},{})}
FCLoopCreatePartialFractioningRules[glis, topos]
{{GpreTopoDia1(1,0,1,1,1)→−2gkinmeta2u0b2GpreTopoDia1PFR12(1,1,1)+2gkinmeta2u0b2GpreTopoDia1PFR23(1,1,1)+2gkinmeta2(u0b−1)u0bGpreTopoDia1PFR24(1,1,1)−2gkinmeta2(u0b−1)u0bGpreTopoDia1PFR25(1,1,1)},{FCTopology(preTopoDia1PFR12,{(k12+2gkinmetau0b(k1⋅n)+iη)1,(k12+2gkinmeta(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b+iη)1,(k12+2gkinmetau0b(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b2+iη)1},{k1},{n,nb},{Hold[SPD][n]→0,Hold[SPD][nb]→0,Hold[SPD][n,nb]→2},{}),FCTopology(preTopoDia1PFR23,{(k12+iη)1,(k12+2gkinmeta(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b+iη)1,(k12+2gkinmetau0b(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b2+iη)1},{k1},{n,nb},{Hold[SPD][n]→0,Hold[SPD][nb]→0,Hold[SPD][n,nb]→2},{}),FCTopology(preTopoDia1PFR25,{(k12+iη)1,(k12+2gkinmetau0b(k1⋅n)+iη)1,(k12+2gkinmeta(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b+iη)1},{k1},{n,nb},{Hold[SPD][n]→0,Hold[SPD][nb]→0,Hold[SPD][n,nb]→2},{}),FCTopology(preTopoDia1PFR24,{(k12+iη)1,(k12+2gkinmetau0b(k1⋅n)+iη)1,(k12+2gkinmetau0b(k1⋅n)−metau0b(k1⋅nb)−2gkinmeta2u0b2+iη)1},{k1},{n,nb},{Hold[SPD][n]→0,Hold[SPD][nb]→0,Hold[SPD][n,nb]→2},{})}}