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

See also:  Twist2GluonOperator.

Examples

Polarized case, zero-momentum insertion

SetOptions[Twist2QuarkOperator, Polarization -> 1, 
      ZeroMomentumInsertion -> True]

Quark-antiquark operator.

t1 = Twist2QuarkOperator[p]

Quark-antiquark-gluon operator.

t2 = Twist2QuarkOperator[{p}, {q}, {k, μ, a}]

Quark-antiquark-gluon-gluon operator.

t3 = 
      Twist2QuarkOperator[{p}, {q}, {k, μ, a}, {r, ν, b}]

Unpolarized case, zero-momentum insertion

SetOptions[Twist2QuarkOperator,  Polarization -> 0, 
      ZeroMomentumInsertion -> True]

Quark-antiquark operator.

t4 = Twist2QuarkOperator[p]

Quark-antiquark-gluon operator.

t5 = Twist2QuarkOperator[{p}, {q}, {k, μ, a}]

Quark-antiquark-gluon-gluon operator.

t6 = 
      Twist2QuarkOperator[{p}, {q}, {k, μ, a}, {r, ν, b}]

This shows the FeynCalcExternal (FCE) form.

Twist2QuarkOperator[p] // FCE // StandardForm

Twist2QuarkOperator[{p}, {q}, {k, μ, a}, Explicit -> All, 
      Polarization -> 0]

Twist2QuarkOperator[{p}, {q}, {k, μ, a}, {r, ν, b}, 
      Explicit -> All, Polarization -> 0]

Polarized case, non-zero momentum insertion

SetOptions[Twist2QuarkOperator, Polarization -> 1, 
      ZeroMomentumInsertion -> False]

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.

t1 = Twist2QuarkOperator[{p, q}]

This is the quark-antiquark-gluon operator vertex.

t2 = Twist2QuarkOperator[{p}, {q}, {k, μ, a}]

This shows the FeynCalcExternal form.

StandardForm[FCE[t2]]

Unpolarized case, non-zero momentum insertion

SetOptions[Twist2QuarkOperator, Polarization -> 1, 
      ZeroMomentumInsertion -> False]

Quark-antiquark operator.

t4 = Twist2QuarkOperator[{p, q}]

Quark-antiquark-gluon operator.

t5 = Twist2QuarkOperator[{p}, {q}, {k, μ, a}]

Clear[t1, t2, t3, t4, t5, t6];