QCDFeynmanRuleConvention fixes the sign convention in the QCD Feynman rules for the ghost propagator and the ghost-gluon vertex.This is done by setting the value of QCDFeynmanRuleConvention[GhostPropagator] and QCDFeynmanRuleConvention[GluonGhostVertex].
The default values are 1 for both, which corresponds to the convention used in most books. Setting them to -1 enforces the convention that can be found e.g. in the book “Applications of Perturbative QCD” by R. Field.
Overview, GluonGhostVertex, GhostPropagator.
Enforce the convention as in “Applications of Perturbative QCD” by R. Field.
QCDFeynmanRuleConvention[GhostPropagator] = -1;
QCDFeynmanRuleConvention[GluonGhostVertex] = -1;GHP[p, a, b] // Explicit-\frac{i \delta ^{ab}}{p^2}
GGV[{p, \[Mu], a}, {q, \[Nu], b}, {k, \[Rho], c}] // Explicitg_s k^{\mu } f^{abc}
Back to the standard convention.
QCDFeynmanRuleConvention[GhostPropagator] = 1
QCDFeynmanRuleConvention[GluonGhostVertex] = 11
1
GHP[p, a, b] // Explicit\frac{i \delta ^{ab}}{p^2}
GGV[{p, \[Mu], a}, {q, \[Nu], b}, {k, \[Rho], c}] // Explicitg_s \left(-k^{\mu }\right) f^{abc}