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WIP - Add support for 1-loop PaVe's that can be described using Package-X functions having different Weights. #4

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WIP - Add support for 1-loop PaVe's that can be described using Package-X functions having different Weights. #4

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72 changes: 66 additions & 6 deletions Interfaces/PackageX.m
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Original file line number Diff line number Diff line change
Expand Up @@ -252,12 +252,31 @@ what D is (e.g. 4-2 Epsilon). The default value is 1. \
PaXContinuedDiLog[{x1_?NumericQ, a1_?NumericQ}, {x2_?NumericQ, a2_?NumericQ}]:=
X`ContinuedDiLog[{x1,a1},{x2,a2}]/; paxLoaded;

(* Extra PaVe reduction *)
PaVeEx::usage="";

(* TODO: Reduction formula with non-zero indices *)
reduceGenPaVe[GenPaVe[(*inds_List*)inds:{(0)..}, lst:{{0,_}, ({_,_} ...)}], opts:OptionsPattern[]]:=
Module[{packList = Tally@lst},
(* Reduce only if we actually have less than 4 different propagators, otherwise just transform into standard PaVe[]. *)
If[Length@packList <= 4,
PaVeEx[Sequence@@inds, ExpandScalarProduct@FeynCalc`Package`momentumRoutingDenner[Drop[packList[[All,1,1]],1],Pair[#1,#1]&],
Power[#, 2]& /@ packList[[All,1,2]], Weights->packList[[All,2]]],
ToPaVe2@PaVeOrder@PaVe[Sequence@@inds, ExpandScalarProduct@FeynCalc`Package`momentumRoutingDenner[Drop[lst[[All,1]],1],Pair[#1,#1]&],
Power[#, 2]& /@ lst[[All,2]], Sequence@@Join[{PaVeAutoReduce->False,PaVeAutoOrder->OptionValue[PaVeAutoOrder]},FilterRules[{opts},FilterRules[Options[PaVe],Except[PaVeAutoOrder|PaVeAutoReduce]]]]]
]
];

(* Anything else is ignored *)
reduceGenPaVe[x_, OptionsPattern[]]:= x;


(* FeynCalc->Package-X conversion of scalar products *)
momConv[x_] :=
FCE[ExpandScalarProduct[MomentumCombine[x]]];

toPackageX[pref_, q_]:=
pref /; FreeQ2[pref,Join[{q},FeynCalc`Package`PaVeHeadsList]];
pref /; FreeQ2[pref,Join[{q},FeynCalc`Package`PaVeHeadsList,{PaVeEx}]];

(* FeynCalc->Package-X conversion for A0, B0, B1, B00, B11 and C0.
Notice that additional (2Pi)^(D-4) prefactor that comes from different
Expand All @@ -276,44 +295,83 @@ Notice that additional (2Pi)^(D-4) prefactor that comes from different
(2 Pi)^(-2*(X`Eps)) pref X`PVA[0, PowerExpand[Sqrt[m]]]/;
FreeQ[pref,q] && FreeQ[m, Complex];

toPackageX[pref_. PaVeEx[0, {}, {m_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVA[0, PowerExpand[Sqrt[m]], opts]/;
FreeQ[pref,q] && FreeQ[m, Complex];

toPackageX[pref_. PaVe[inds__, {}, {m_}, OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVA[Count[{inds},0]/2, PowerExpand[Sqrt[m]]]/;
FreeQ[pref,q] && FreeQ[m, Complex] && EvenQ[Count[{inds},0]] && {inds}=!={0};

toPackageX[pref_. PaVeEx[inds__, {}, {m_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVA[Count[{inds},0]/2, PowerExpand[Sqrt[m]], opts]/;
FreeQ[pref,q] && FreeQ[m, Complex] && EvenQ[Count[{inds},0]] && {inds}=!={0};

(* 2-point functions *)
toPackageX[pref_. PaVe[0, {mom1_}, {m1_, m2_}, OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVB[0, 0, momConv[mom1], PowerExpand[Sqrt[m1]],
PowerExpand[Sqrt[m2]]]/;FreeQ[pref,q] && FreeQ[{m1,m2}, Complex];

toPackageX[pref_. PaVeEx[0, {mom1_}, {m1_, m2_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVB[0, 0, momConv[mom1], PowerExpand[Sqrt[m1]],
PowerExpand[Sqrt[m2]], opts]/;FreeQ[pref,q] && FreeQ[{m1,m2}, Complex];

toPackageX[pref_. PaVe[inds__, {mom1_}, {m1_, m2_}, OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVB[Count[{inds},0]/2, Count[{inds},1], momConv[mom1], PowerExpand[Sqrt[m1]],
PowerExpand[Sqrt[m2]]]/;FreeQ[pref,q] && FreeQ[{m1,m2}, Complex] &&
(EvenQ[Count[{inds}, 0]] || Count[{inds}, 0] === 0) && {inds}=!={0};

toPackageX[pref_. PaVeEx[inds__, {mom1_}, {m1_, m2_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVB[Count[{inds},0]/2, Count[{inds},1], momConv[mom1], PowerExpand[Sqrt[m1]],
PowerExpand[Sqrt[m2]], opts]/;FreeQ[pref,q] && FreeQ[{m1,m2}, Complex] &&
(EvenQ[Count[{inds}, 0]] || Count[{inds}, 0] === 0) && {inds}=!={0};

(* 3-point functions *)
toPackageX[pref_. PaVe[0, {mom1_, mom1min2_, mom2_}, {m1_, m2_, m3_}, OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVC[0, 0, 0, momConv[mom1], momConv[mom1min2], momConv[mom2],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]]]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3}, Complex];

toPackageX[pref_. PaVeEx[0, {mom1_, mom1min2_, mom2_}, {m1_, m2_, m3_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVC[0, 0, 0, momConv[mom1], momConv[mom1min2], momConv[mom2],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]], opts]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3}, Complex];

toPackageX[pref_. PaVe[inds__, {mom1_, mom1min2_, mom2_}, {m1_, m2_, m3_}, OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVC[Count[{inds},0]/2, Count[{inds},1], Count[{inds},2], momConv[mom1], momConv[mom1min2], momConv[mom2],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]]]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3}, Complex] && (EvenQ[Count[{inds}, 0]] || Count[{inds}, 0] === 0);

toPackageX[pref_. PaVeEx[inds__, {mom1_, mom1min2_, mom2_}, {m1_, m2_, m3_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVC[Count[{inds},0]/2, Count[{inds},1], Count[{inds},2], momConv[mom1], momConv[mom1min2], momConv[mom2],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]], opts]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3}, Complex] && (EvenQ[Count[{inds}, 0]] || Count[{inds}, 0] === 0);

(* 4-point functions *)
toPackageX[pref_. PaVe[0, {mom1_, mom1min2_, mom2min3_, mom3_, mom2_, mom1min3_}, {m1_, m2_, m3_, m4_}, OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVD[0, 0, 0, 0,
momConv[mom1], momConv[mom1min2], momConv[mom2min3], momConv[mom3], momConv[mom2], momConv[mom1min3],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]], PowerExpand[Sqrt[m4]]]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3,m4}, Complex];

toPackageX[pref_. PaVeEx[0, {mom1_, mom1min2_, mom2min3_, mom3_, mom2_, mom1min3_}, {m1_, m2_, m3_, m4_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVD[0, 0, 0, 0,
momConv[mom1], momConv[mom1min2], momConv[mom2min3], momConv[mom3], momConv[mom2], momConv[mom1min3],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]], PowerExpand[Sqrt[m4]], opts]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3,m4}, Complex];

toPackageX[pref_. PaVe[inds__, {mom1_, mom1min2_, mom2min3_, mom3_, mom2_, mom1min3_}, {m1_, m2_, m3_, m4_}, OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVD[Count[{inds},0]/2, Count[{inds},1], Count[{inds},2], Count[{inds},3],
momConv[mom1], momConv[mom1min2], momConv[mom2min3], momConv[mom3], momConv[mom2], momConv[mom1min3],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]], PowerExpand[Sqrt[m4]]]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3,m4}, Complex] && (EvenQ[Count[{inds}, 0]] || Count[{inds}, 0] === 0);

toPackageX[pref_. PaVeEx[inds__, {mom1_, mom1min2_, mom2min3_, mom3_, mom2_, mom1min3_}, {m1_, m2_, m3_, m4_}, opts:OptionsPattern[]], q_]:=
(2 Pi)^(-2*(X`Eps)) pref X`PVD[Count[{inds},0]/2, Count[{inds},1], Count[{inds},2], Count[{inds},3],
momConv[mom1], momConv[mom1min2], momConv[mom2min3], momConv[mom3], momConv[mom2], momConv[mom1min3],
PowerExpand[Sqrt[m1]], PowerExpand[Sqrt[m2]], PowerExpand[Sqrt[m3]], PowerExpand[Sqrt[m4]], opts]/;
FreeQ[pref,q] && FreeQ[{m1,m2,m3,m4}, Complex] && (EvenQ[Count[{inds}, 0]] || Count[{inds}, 0] === 0);


PaXEvaluateUVIRSplit[expr_, opts:OptionsPattern[]]:=
PaXEvaluateUVIRSplit[expr, dummyLoopMom, opts];
Expand Down Expand Up @@ -448,11 +506,13 @@ Notice that additional (2Pi)^(D-4) prefactor that comes from different
(* First of all, let us convert all the scalar integrals to PaVe functions: *)
FCPrint[1,"PaXEvaluate: Applying ToPaVe/ToPaVe2.", FCDoControl->paxVerbose];
If[OptionValue[ToPaVe],
ex = expr//ToPaVe[#,q,PaVeAutoReduce->False,
ex = expr//ToPaVe[#,q, GenPaVe->True, PaVeAutoReduce->False,
PaVeAutoOrder -> OptionValue[PaVeAutoOrder]]&//ToPaVe2,
ex = expr//ToPaVe2
];

(* Attempt further reduction in case same propagators are repeated more than once *)
ex = ex /. gpv:_GenPaVe :> reduceGenPaVe[gpv, PaVeAutoReduce->False, PaVeAutoOrder -> OptionValue[PaVeAutoOrder]];

(* Since we care only for the scalar integrals, we need
only the second element from the list returned by FCLoopSplit.
Expand All @@ -461,7 +521,7 @@ Notice that additional (2Pi)^(D-4) prefactor that comes from different
like 1/p.p B0[p.p,m^2,m^2] will be expanded in a wrong way *)

FCPrint[1,"PaXEvaluate: Applying FCLoopSplit.", FCDoControl->paxVerbose];
fclsOutput = FCLoopSplit[ex,Join[{q}],PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {X`PVA, X`PVB, X`PVC, X`PVD}]];
fclsOutput = FCLoopSplit[ex,Join[{q}],PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {PaVeEx, X`PVA, X`PVB, X`PVC, X`PVD}]];
If [fclsOutput[[3]]=!=0 || fclsOutput[[4]]=!=0,
Message[PaXEvaluate::tens]
];
Expand Down Expand Up @@ -494,7 +554,7 @@ Notice that additional (2Pi)^(D-4) prefactor that comes from different
FCPrint[1,"PaXEvaluate: Applying FCLoopIsolate.", FCDoControl->paxVerbose];

check=FCLoopIsolate[FCReplaceD[tmp, dim->4-2*Epsilon], {q}, FCI->True, Head->loopIntegral,
PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {X`PVA, X`PVB, X`PVC, X`PVD, Epsilon},paxSeriesVars]];
PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {PaVeEx, X`PVA, X`PVB, X`PVC, X`PVD, Epsilon},paxSeriesVars]];
FCPrint[3,"PaXEvaluate: After FCLoopIsolate: ",check, FCDoControl->paxVerbose];


Expand All @@ -507,13 +567,13 @@ Notice that additional (2Pi)^(D-4) prefactor that comes from different

FCPrint[1,"PaXEvaluate: Applying FCLoopIsolate.", FCDoControl->paxVerbose];
ints=FCLoopIsolate[tmp, {q}, FCI->True, Head->loopIntegral,
PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {X`PVA, X`PVB, X`PVC, X`PVD},paxSeriesVars]];
PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {PaVeEx, X`PVA, X`PVB, X`PVC, X`PVD},paxSeriesVars]];
FCPrint[3,"PaXEvaluate: After FCLoopIsolate: ",ints, FCDoControl->paxVerbose];

(* The 4th element in fclcOutput is our list of unique scalar integrals that
need to be computed. But first we need to convert them to the Pacakge X input *)
fclcOutput = FCLoopCanonicalize[ints, q, loopIntegral,FCI->True,
PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {X`PVA, X`PVB, X`PVC, X`PVD}]];
PaVeIntegralHeads->Join[FeynCalc`Package`PaVeHeadsList, {PaVeEx, X`PVA, X`PVB, X`PVC, X`PVD}]];

If[ !FreeQ2[fclcOutput,{Spinor,Polarization}],
Message[PaXEvaluate::gen, "PaXEvaluate may not pass spinors or polarization vectors to Package-X."];
Expand Down