Twist2QuarkOperator

Description

Twist2QuarkOperator[p] or Twist2QuarkOperator[p,_,_] yields the quark-antiquark operator (p is momentum in the direction of the incoming quark). Twist2QuarkOperator[{p,q}] yields the 2-quark operator for non-zero momentum insertion (p is momentum in the direction of the incoming quark). Twist2QuarkOperator[{p1,___}, {p2,___}, {p3, mu, a}] or Twist2QuarkOperator[p1,_,_, p2,_,_, p3,mu,a] is the quark-antiquark-gluon operator, where p1 is the incoming quark, p2 the incoming antiquark and p3 denotes the incoming gluon momentum. Twist2QuarkOperator[{p1}, {p2}, {p3, mu, a}, {p4, nu, b}] or Twist2QuarkOperator[{p1,___}, {p2,___}, {p3, mu, a}, {p4, nu, b}] or Twist2QuarkOperator[p1,_,_, p2,_,_, p3,mu,a, p4, nu, b] gives the Quark-Quark-Gluon-Gluon-operator. The setting of the option Polarization (unpolarized: 0; polarized: 1) determines whether the unpolarized or polarized operator is returned

Polarized case, zero-momentum insertion

Quark-antiquark operator.

Quark-antiquark-gluon operator.

Quark-antiquark-gluon-gluon operator.

Unpolarized case, zero-momentum insertion

Quark-antiquark operator.

Quark-antiquark-gluon operator.

Quark-antiquark-gluon-gluon operator.

This shows the FeynCalcExternal (FCE) form.

Polarized case, non-zero momentum insertion

With the setting ZeroMomentumInsertion -> False a non-zero momentum is assumed to flow into the operator vertex.

This is the Feynman rule associated with the quark-antiquark operator, where p is the momentum of the incoming quark and q the momentum of the antiquark. The momentum flowing into the operator vertex is thus -p-q.

This is the quark-antiquark-gluon operator vertex.

This shows the FeynCalcExternal form.

Unpolarized case, non-zero momentum insertion

Quark-antiquark operator.

Quark-antiquark-gluon operator.

Converted from the Mathematica notebook Twist2QuarkOperator.nb