FeynHelpers manual (development version)

FIREReduceLoopIntegrals

FIREReduceLoopIntegrals[glis, topos, path] performs IBP reduction of loop integral listed in glis from the families given in topos using C++ FIRE. It returns reduction tables obtained from FIRE.

Since all processes are started from the current Mathematica notebook, it can be reliably used only for simple integrals and topologies.

See also

Overview, FIRERunReduction.

Examples

glis = Get[FileNameJoin[{$FeynHelpersDirectory, "Documentation", "Examples", "glglToHH1L", "glis.m"}]];

glis // Length

(*79*)

glis[[1 ;; 5]]

(*{GLI[glglToHH1Ltopo1, {-1, 1, 1, 1}], GLI[glglToHH1Ltopo1, {0, 0, 1, 1}], GLI[glglToHH1Ltopo1, {0, 1, 0, 1}],GLI[glglToHH1Ltopo1, {0, 1, 1, 0}], GLI[glglToHH1Ltopo1, {0, 1, 1, 1}]}*)

topos = Get[FileNameJoin[{$FeynHelpersDirectory, "Documentation", "Examples", "glglToHH1L", "topos.m"}]];

topos[[1]] // FCE

\text{FCTopology}\left[\text{glglToHH1Ltopo1},\left\{\text{SFAD}\left[\left\{\{k,0\},\left\{\text{mt}^2,1\right\},1\right\}\right],\text{SFAD}\left[\left\{\{k+\text{q1},0\},\left\{\text{mt}^2,1\right\},1\right\}\right],\text{SFAD}\left[\left\{\{k+\text{p2}+\text{q1},0\},\left\{\text{mt}^2,1\right\},1\right\}\right],\text{SFAD}\left[\left\{\{k+\text{p2}+\text{q1}+\text{q2},0\},\left\{\text{mt}^2,1\right\},1\right\}\right]\right\},\{k\},\{\text{p2},\text{q1},\text{q2}\},\left\{s\to 2 \;\text{mh}^2-t-u,\text{Hold}[\text{Pair}][\text{Momentum}[\text{p1},D],\text{Momentum}[\text{p2},D]]\to \frac{1}{2} \left(2 \;\text{mh}^2-t-u\right),\text{Hold}[\text{Pair}][\text{Momentum}[\text{p1},D],\text{Momentum}[\text{q1},D]]\to -\frac{\text{mh}^2}{2}+\frac{t}{2},\text{Hold}[\text{Pair}][\text{Momentum}[\text{p1},D],\text{Momentum}[\text{q2},D]]\to -\frac{\text{mh}^2}{2}+\frac{u}{2},\text{Hold}[\text{Pair}][\text{Momentum}[\text{p2},D],\text{Momentum}[\text{p2},D]]\to 0,\text{Hold}[\text{Pair}][\text{Momentum}[\text{p2},D],\text{Momentum}[\text{q1},D]]\to -\frac{\text{mh}^2}{2}+\frac{u}{2},\text{Hold}[\text{Pair}][\text{Momentum}[\text{p2},D],\text{Momentum}[\text{q2},D]]\to -\frac{\text{mh}^2}{2}+\frac{t}{2},\text{Hold}[\text{Pair}][\text{Momentum}[\text{q1},D],\text{Momentum}[\text{q1},D]]\to \;\text{mh}^2,\text{Hold}[\text{Pair}][\text{Momentum}[\text{q1},D],\text{Momentum}[\text{q2},D]]\to -\text{mh}^2+\frac{1}{2} \left(2 \;\text{mh}^2-t-u\right),\text{Hold}[\text{Pair}][\text{Momentum}[\text{q2},D],\text{Momentum}[\text{q2},D]]\to \;\text{mh}^2\right\},\{\}\right]

dir = FileNameJoin[{$TemporaryDirectory, "Docu-Reduction-glglToHH-1L"}];

tables = FIREReduceLoopIntegrals[glis, topos, dir];

\text{FIREPrepareStartFile: }\;\text{Created }3\text{ script files.}

(*Creating config file (1/3) for glglToHH1Ltopo1 (glglToHH1Ltopo1.config)... done.
Creating config file (2/3) for glglToHH1Ltopo2 (glglToHH1Ltopo2.config)... done.
Creating config file (3/3) for glglToHH1Ltopo3 (glglToHH1Ltopo3.config)... done.

glglToHH1Ltopo1, number of loop integrals: 15
glglToHH1Ltopo2, number of loop integrals: 32
glglToHH1Ltopo3, number of loop integrals: 32

Creating LiteRed files (1/3) for glglToHH1Ltopo1... done, timing: 3.369
Creating LiteRed files (2/3) for glglToHH1Ltopo2... done, timing: 3.343
Creating LiteRed files (3/3) for glglToHH1Ltopo3... done, timing: 3.346

Creating FIRE files (1/3) for glglToHH1Ltopo1... done, timing: 6.265
Creating FIRE files (2/3) for glglToHH1Ltopo2... done, timing: 6.150
Creating FIRE files (3/3) for glglToHH1Ltopo3... done, timing: 6.392

Running reduction (1/3) for glglToHH1Ltopo1... done, timing: 0.8302
Running reduction (2/3) for glglToHH1Ltopo2... done, timing: 4.168
Running reduction (3/3) for glglToHH1Ltopo3... done, timing: 4.170

Importing reduction tables (1/3) for FileBaseName[glglToHH1Ltopo1]... done.
Importing reduction tables (2/3) for FileBaseName[glglToHH1Ltopo2]... done.
Importing reduction tables (3/3) for FileBaseName[glglToHH1Ltopo3]... done.
*)

\text{FIRECreateConfigFile: }\;\text{Created }3\text{ .config files.}

\text{FIRECreateIntegralFile: }\;\text{Created }3\text{ integral files.}

\text{FIRECreateLiteRedFiles: }\;\text{Run }3\text{ script files.}

\text{FIRECreateStartFile: }\;\text{Run }3\text{ script files.}

\text{FIRERunReduction: }\;\text{Reduced }3\text{ topologies.}

\text{FIREImportResults: }\;\text{Imported }3\text{ reduction tables.}

tables[[1 ;; 3]]

\left\{G^{\text{glglToHH1Ltopo1}}(1,1,1,1)\to G^{\text{glglToHH1Ltopo1}}(1,1,1,1),G^{\text{glglToHH1Ltopo1}}(1,1,-1,1)\to \frac{G^{\text{glglToHH1Ltopo1}}(0,0,0,1) \left(-D \;\text{mh}^2+D u+2 \;\text{mh}^2-2 u\right)}{2 \;\text{mh}^2 \;\text{mt}^2-2 \;\text{mt}^2 t}+\frac{G^{\text{glglToHH1Ltopo1}}(0,0,1,1) \left(3 \;\text{mh}^4-\text{mh}^2 t-\text{mh}^2 u-t u\right)}{\text{mh}^4-2 \;\text{mh}^2 t+t^2}+\frac{G^{\text{glglToHH1Ltopo1}}(0,1,0,1) \left(-\text{mh}^4-2 \;\text{mh}^2 t+t^2+2 t u\right)}{\text{mh}^4-2 \;\text{mh}^2 t+t^2}+\frac{G^{\text{glglToHH1Ltopo1}}(0,1,1,1) \left(\text{mh}^4-t u\right)}{\text{mh}^2-t},G^{\text{glglToHH1Ltopo1}}(1,1,0,1)\to G^{\text{glglToHH1Ltopo1}}(0,1,1,1)\right\}