Ward identity in One-Loop QCD Process #284
Unanswered
mahdihoumanii
asked this question in
Q&A
Replies: 1 comment
-
Sorry, since some years I don't really have time to debug other people's diagram calculations. If a bug is suspected, I usually ask for the I can only recommend to flag the diagrams and try to see if there are gauge invariant subsets among them as well as the origin |
Beta Was this translation helpful? Give feedback.
0 replies
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Uh oh!
There was an error while loading. Please reload this page.
Uh oh!
There was an error while loading. Please reload this page.
-
Hello!
I am using the Latest version of FC and FH (10) in development version.
I am calculating QCD One-Loop qQ-> tTg amplitude where q/Qis a quark/anti-quark and t/T is a top/anti-top. Since I have a single gluon in my amplitude I should be able to say that the polarization is transverse, and if I replace the polarization vector by its momentum, the amplitude should vanish. Now, I generated the diagrams with both FeynArts and the FH QGraf interface and multiplied by a given tensor.
(Some Random SME present in the tree-level amplitude)
Tens = Spinor[-Momentum[p4, D], mt, 1] .
DiracGamma[Momentum[Polarization[p5, I], D], D] .
Spinor[Momentum[p3, D], mt, 1] Spinor[-Momentum[p2, D], 0, 1] .
DiracGamma[Momentum[p4, D], D] . Spinor[Momentum[p1, D], 0, 1];
diagsLoop[1] = InsertFields[CreateTopologies[1, 0 -> 5,
ExcludeTopologies -> {Tadpoles, WFCorrections}], {} ->
{ F[3, {1}], -F[3, {1}], F[3, {3}], -F[3, {3}], V[5]},
InsertionLevel -> {Particles}, Model -> "SMQCD",
ExcludeParticles -> {S[], V[1 | 2 | 3 | 4], F[3, {2}],
F[4, {1 | 2 | 3}]}];
diagstree[1] = InsertFields[CreateTopologies[0, 0 -> 5,
ExcludeTopologies -> {Tadpoles, WFCorrections}], {} ->
{F[3, {1}], -F[3, {1}], F[3, {3}], -F[3, {3}], V[5]},
InsertionLevel -> {Particles}, Model -> "SMQCD",
ExcludeParticles -> {S[], V[1 | 2 | 3 | 4], F[3, {2}],
F[4, {1 | 2 | 3}]}];
amploop = FCFAConvert[CreateFeynAmp[diagsLoop[1],
Truncated -> False, GaugeRules -> {_FAGaugeXi -> 1},
PreFactor -> 1],
IncomingMomenta -> {}, OutgoingMomenta -> {p1, p2, p3, p4, p5},
LorentzIndexNames -> {mu10}, DropSumOver -> True,
SUNIndexNames -> {a10}, SUNFIndexNames -> {a2, a4, a6, a8},
LoopMomenta -> {l},
ChangeDimension -> D, List -> True, SMP -> True,
UndoChiralSplittings -> True,
FinalSubstitutions -> {SMP["m_u"] -> 0 , SMP["m_t"] -> mt,
SMP["g_s"] -> gs}];
FCClearScalarProducts[];
SetMandelstam[mand, {p1, p2, p3, p4, p5}, {0, 0, mt, mt, 0}];
mandelstam = {mand[1, 5] -> s15, mand[1, 2] -> s12,
mand[2, 3] -> s23, mand[3, 4] -> s34, mand[4, 5] -> s45};
(Here I define projector operators for independent color structures)
ColorFactor[a1_, a2_, b1_, b2_, b3_] :=
SUNFDelta[a1, a2] SUNTF[{SUNIndex[b1]}, SUNFIndex[b2], SUNFIndex[b3]]
ColorOps = {ColorFactor[a8, a2, a10, a6, a4],
ColorFactor[a8, a6, a10, a2, a4], ColorFactor[a2, a4, a10, a6, a8],
ColorFactor[a4, a6, a10, a2, a8]};
ColorMat =
Table[SUNSimplify[ColorOps[[i]]*ComplexConjugate[ColorOps[[j]]],
SUNNToCACF -> False] /. SUNN -> 3, {i, 4}, {j, 4}];
Proj = Inverse[ColorMat] . ComplexConjugate[ColorOps];
ampLoop[1] =
SUNSimplify[
amploop*Proj[[3]] /. Polarization[p5, -I] :> p5 /. Glu5 -> a10 /.
Glu5 -> a10, SUNNToCACF -> False] /. SUNN -> 3;
ampLoop[2] = (ampLoop[1]*Tens /. Polarization[p5, I] :> p5 //
FermionSpinSum);
ampLoop[3] = ampLoop[2] // DiracSimplify // Simplify;
ampLoop[4] =
Monitor[Table[
TID[ampLoop[3][[i]] /. mandelstam, l, ToPaVe -> True], {i, 1,
102}], I];
When I collect all PaVe Functions, all Coefficients of functions vanish and then I am left with a coefficient of the following integrals ((D - 2) A0[mt^2] - B0[mt^2, 0, mt^2]*4 *mt^2) which will not vanish after applying //PaXEvaluate.
ToBe clear: I tried the same thing on tree-level amplitudes, and it vanished, is there something that could be wrong with how I defined the diagrams, because even with QGRAF FeynHelpers, it gave the same results.
Beta Was this translation helpful? Give feedback.
All reactions