Twist2GluonOperator

Description

Twist2GluonOperator[{p, mu, a}, {nu, b}] or Twist2GluonOperator[p, {mu, a}, {nu, b}] or Twist2GluonOperator[p, mu,a, nu,b] yields the 2-gluon operator (p is ingoing momentum corresponding to Lorentz index mu). Twist2GluonOperator[{p,mu,a}, {q,nu,b}, {k,la,c}] or Twist2GluonOperator[ p,mu,a , q,nu,b , k,la,c ] gives the 3-gluon operator. Twist2GluonOperator[{p,mu,a}, {q,nu,b}, {k,la,c}, {s,si,d}] or Twist2GluonOperator[p,mu,a , q,nu,b , k,la,c , s,si,d] yields the 4-Gluon operator. The dimension is determined by the option and Dimension. The setting of the option Polarization (unpolarized: 0; polarized: 1) determines whether the unpolarized or polarized feynman rule is returned. With the setting Explicit to False the color-structure and the (1+(-1)^OPEm) (for polarized: (1-(-1)^OPEm)) is extracted and the color indices are omitted in the arguments of Twist2GluonOperator.

See also:  Twist2QuarkOperator.

Polarized case, zero-momentum insertion

SetOptions[Twist2GluonOperator,  Polarization  ->  1, 
      Explicit -> False,  ZeroMomentumInsertion  ->  True]

2-gluon legs

Twist2GluonOperator[p, {μ, a}, {ν, b}]

Twist2GluonOperator[p, {μ, a}, {ν, b}, 
      Explicit -> True]

Twist2GluonOperator[p, {μ}, {ν}]

Twist2GluonOperator[p, {μ}, {ν}, Explicit -> True]

3-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, 
      Explicit -> True]

4-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}, {s, σ, d}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, {s, σ}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, {s, σ}, 
      Explicit -> True]

Unpolarized case, zero-momentum insertion

SetOptions[Twist2GluonOperator, Polarization -> 0, 
      ZeroMomentumInsertion -> True]

2-gluon legs

Twist2GluonOperator[p, {μ, a}, {ν, b}]

Twist2GluonOperator[p, {μ, a}, {ν, b}, 
      Explicit -> True]

Twist2GluonOperator[p, {μ}, {ν}]

Twist2GluonOperator[p, {μ}, {ν}, Explicit -> True]

3-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, 
      Explicit -> True]

4-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}, {s, σ, d}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, {s, σ}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, {s, σ}, 
      Explicit -> True]

Advanced Examples

The setting All for Explicit performs the sums.

SetOptions[Twist2GluonOperator,  Polarization  ->  1,  
      Explicit -> All];

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}];

Polarized case, non-zero-momentum insertion

SetOptions[Twist2GluonOperator,  Polarization  ->  1, 
      ZeroMomentumInsertion -> False]

2-gluon legs

Twist2GluonOperator[{p, q}, {μ, a}, {ν, b}]

3-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}]

4-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}, {s, σ, d}, Explicit -> False]

Unpolarized case, non-zero-momentum insertion

SetOptions[Twist2GluonOperator,  Polarization  ->  0, 
      ZeroMomentumInsertion -> False]

2-gluon legs

Twist2GluonOperator[{p, q}, {μ, a}, {ν, b}]

3-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}];

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}]

Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, 
      Explicit -> True]

4-gluon legs

Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, 
        c}, {s, σ, d}, Explicit -> False]

Suppress the lengthy output.

Short[
      Twist2GluonOperator[{p, μ}, {q, ν}, {r, ρ}, {s, σ}, 
        Explicit -> True], 6]

The setting Explicit -> All performs the sums.

SetOptions[Twist2GluonOperator,  Polarization  ->  1,  
      Explicit -> All];

Short[
      Twist2GluonOperator[{p, μ, a}, {q, ν, b}, {r, ρ, c}], 
      5]