FeynHelpers manual (development version)

KiraCreateConfigFiles[topo, sectors, path] can be used to generate Kira configuration files (integralfamilies.yaml and kinematics.yaml) from an FCTopology or list thereof. Here sectors is a list of sectors need to be reduced, e.g. {{1,0,0,0}, {1,1,0,0}, {1,1,1,0}} etc.

The functions creates the corresponding yaml files and saves them in path/topoName/config. Using KiraCreateConfigFiles[{topo1, topo2, ...}, {sectors1, sectors2, ...}, path] will save the scripts to path/topoName1, path/topoName2 etc. The syntax KiraCreateConfigFiles[{topo1, topo2, ...}, {sectors1, sectors2, ...}, {path1, path2, ...}] is also possible.

If the directory specified in path/topoName does not exist, it will be created automatically. If it already exists, its content will be automatically overwritten, unless the option OverwriteTarget is set to False.

It is also possible to supply a list of GLIs instead of sectors. In that case FCLoopFindSectors will be used to determine the top sector for each topology.

The syntax KiraCreateConfigFiles[{topo1, topo2, ...}, {sectors1, sectors2, ...}, path] or KiraCreateConfigFiles[{topo1, topo2, ...}, {glis1, glis2, ...}, path] is also allowed. This implies that all config files will go into the corresponding subdirectories of path, e.g. path/topoName1/config, path/topoName2/config etc.

The mass dimension of all kinematic variables should be specified via the option KiraMassDimensions e.g. as in {{m1->1},{M->1},{msq->2}}.

If the amplitude originally contained any external momenta that were eliminated using momentum conservation, .e.g. by replacing k_2 by P-k_1 for P=k_1+k_2, those momenta must be nevertheless specified via the option KiraImplicitIncomingMomenta.

See also

Examples

topo = FCTopology["asyR1prop2Ltopo01310X11111N1", {SFAD[{p1, 0}], 
    SFAD[{p3, mg^2}], SFAD[{{0, 2*p3 . q}}], 
    SFAD[{(p1 + q), mb^2}], SFAD[{{0, p1 . p3}}]}, 
   {p1, p3}, {q}, {Hold[SPD][q, q] -> mb^2}, {}]

\text{FCTopology}\left(\text{asyR1prop2Ltopo01310X11111N1},\left\{\frac{1}{(\text{p1}^2+i \eta )},\frac{1}{(\text{p3}^2-\text{mg}^2+i \eta )},\frac{1}{(2 (\text{p3}\cdot q)+i \eta )},\frac{1}{((\text{p1}+q)^2-\text{mb}^2+i \eta )},\frac{1}{(\text{p1}\cdot \;\text{p3}+i \eta )}\right\},\{\text{p1},\text{p3}\},\{q\},\left\{\text{Hold}[\text{SPD}][q,q]\to \;\text{mb}^2\right\},\{\}\right)

fileName = KiraCreateConfigFiles[topo, {{1, 1, 1, 1, 1}}, 
    FileNameJoin[{$FeynCalcDirectory, "Database"}], KiraMassDimensions -> {mb -> 1, mg -> 1}];

fileName[[1]] // FilePrint

(*integralfamilies:
  - name: asyR1prop2Ltopo01310X11111N1
    loop_momenta: [p1, p3]
    top_level_sectors: [b11111]
    propagators:
      - [ "p1", 0]
      - [ "p3", "mg^2"]
      - { bilinear: [ [ "2*p3", "q"], 0] }
      - [ "p1 + q", "mb^2"]
      - { bilinear: [ [ "p1", "p3"], 0] }*)

fileName[[2]] // FilePrint

(*kinematics:
  incoming_momenta: [q]
  outgoing_momenta: [q]
  momentum_conservation: []
  kinematic_invariants:
    - [mb, 1]
    - [mg, 1]
  scalarproduct_rules:
    - [ [ q, q],mb^2]*)

topos = {
   FCTopology["asyR3prop2Ltopo01310X11111N1", {SFAD[{{-p1, 0}, {0, 1}, 1}], SFAD[{{-p3, 0}, {mg^2, 1}, 1}], SFAD[{{0, 2*p3 . q}, {0, 1}, 1}], 
     SFAD[{{0, 2*p1 . q}, {0, 1}, 1}], SFAD[{{-p1 + p3, 0}, {0, 1}, 1}]}, {p1, p3}, {q}, {Hold[SPD][q, q] -> mb^2}, {}], 
   FCTopology["asyR1prop2Ltopo01310X11111N1", {SFAD[{{-p1, 0}, {0, 1}, 1}], SFAD[{{-p3, 0}, {mg^2, 1}, 1}], SFAD[{{0, 2*p3 . q}, {0, 1}, 1}], 
      SFAD[{{-p1 - q, 0}, {mb^2, 1}, 1}], SFAD[{{0, -p1 . p3}, {0, 1}, 1}]}, {p1, p3}, {q}, {Hold[SPD][q, q] -> mb^2}, {}] 
   }

\left\{\text{FCTopology}\left(\text{asyR3prop2Ltopo01310X11111N1},\left\{\frac{1}{(\text{p1}^2+i \eta )},\frac{1}{(\text{p3}^2-\text{mg}^2+i \eta )},\frac{1}{(2 (\text{p3}\cdot q)+i \eta )},\frac{1}{(2 (\text{p1}\cdot q)+i \eta )},\frac{1}{((\text{p3}-\text{p1})^2+i \eta )}\right\},\{\text{p1},\text{p3}\},\{q\},\left\{\text{Hold}[\text{SPD}][q,q]\to \;\text{mb}^2\right\},\{\}\right),\text{FCTopology}\left(\text{asyR1prop2Ltopo01310X11111N1},\left\{\frac{1}{(\text{p1}^2+i \eta )},\frac{1}{(\text{p3}^2-\text{mg}^2+i \eta )},\frac{1}{(2 (\text{p3}\cdot q)+i \eta )},\frac{1}{((-\text{p1}-q)^2-\text{mb}^2+i \eta )},\frac{1}{(-\text{p1}\cdot \;\text{p3}+i \eta )}\right\},\{\text{p1},\text{p3}\},\{q\},\left\{\text{Hold}[\text{SPD}][q,q]\to \;\text{mb}^2\right\},\{\}\right)\right\}

{GLI["asyR3prop2Ltopo01310X11111N1", {1, 1, 1, 1, 2}], GLI["asyR1prop2Ltopo01310X11111N1", {1, 1, 1, 1, 2}]}

\left\{G^{\text{asyR3prop2Ltopo01310X11111N1}}(1,1,1,1,2),G^{\text{asyR1prop2Ltopo01310X11111N1}}(1,1,1,1,2)\right\}

fileNames = KiraCreateConfigFiles[topos, {GLI["asyR3prop2Ltopo01310X11111N1", {1, 1, 1, 1, 2}], GLI["asyR1prop2Ltopo01310X11111N1", {1, 1, 1, 1, 2}]}, 
   FileNameJoin[{$FeynCalcDirectory, "Database"}], KiraMassDimensions -> {mb -> 1, mg -> 1}]

\left( \begin{array}{cc} \;\text{/home/vs/.Mathematica/Applications/FeynCalc/Database/asyR3prop2Ltopo01310X11111N1/config/integralfamilies.yaml} & \;\text{/home/vs/.Mathematica/Applications/FeynCalc/Database/asyR3prop2Ltopo01310X11111N1/config/kinematics.yaml} \\ \;\text{/home/vs/.Mathematica/Applications/FeynCalc/Database/asyR1prop2Ltopo01310X11111N1/config/integralfamilies.yaml} & \;\text{/home/vs/.Mathematica/Applications/FeynCalc/Database/asyR1prop2Ltopo01310X11111N1/config/kinematics.yaml} \\ \end{array} \right)

FilePrint[fileNames[[1]][[1]]]

(*integralfamilies:
  - name: asyR3prop2Ltopo01310X11111N1
    loop_momenta: [p1, p3]
    top_level_sectors: [b11111]
    propagators:
      - [ "p1", 0]
      - [ "p3", "mg^2"]
      - { bilinear: [ [ "2*p3", "q"], 0] }
      - { bilinear: [ [ "2*p1", "q"], 0] }
      - [ "-p1 + p3", 0]*)

FilePrint[fileNames[[1]][[2]]]

(*kinematics:
  incoming_momenta: [q]
  outgoing_momenta: [q]
  momentum_conservation: []
  kinematic_invariants:
    - [mb, 1]
    - [mg, 1]
  scalarproduct_rules:
    - [ [ q, q],mb^2]*)

FilePrint[fileNames[[2]][[1]]]

(*integralfamilies:
  - name: asyR1prop2Ltopo01310X11111N1
    loop_momenta: [p1, p3]
    top_level_sectors: [b11111]
    propagators:
      - [ "p1", 0]
      - [ "p3", "mg^2"]
      - { bilinear: [ [ "2*p3", "q"], 0] }
      - [ "-p1 - q", "mb^2"]
      - { bilinear: [ [ "-p1", "p3"], 0] }*)

FilePrint[fileNames[[2]][[2]]]

(*kinematics:
  incoming_momenta: [q]
  outgoing_momenta: [q]
  momentum_conservation: []
  kinematic_invariants:
    - [mb, 1]
    - [mg, 1]
  scalarproduct_rules:
    - [ [ q, q],mb^2]*)