FeynCalc manual (development version)

Twist2CounterOperator

Twist2CounterOperator[p, mu, nu, a, b, 5] is a special routine for particular QCD calculations.

Also available: Twist2CounterOperator[p, 7], Twist2CounterOperator[p1,p2,{p3,mu,a}, 1] (p1: incoming quark momentum, p3: incoming gluon (count1)).

See also

Overview, Twist2GluonOperator.

Examples

Twist2CounterOperator[p, mu, nu, a, b, 5]

12ε((1)m+1)CAgs2Snδab((8m12m+1+8m+28m1)gmu  nu(Δp)m+(8m24m+1+24m+24m1)p2ΔmuΔnu(Δp)m2+(6m+16m+116m+2+6m1)(Δp)m1(pmuΔnu+Δmupnu))-\frac{1}{2 \varepsilon }\left((-1)^m+1\right) C_A g_s^2 S_n \delta ^{ab} \left(\left(\frac{8}{m}-\frac{12}{m+1}+\frac{8}{m+2}-\frac{8}{m-1}\right) g^{\text{mu}\;\text{nu}} (\Delta \cdot p)^m+\left(\frac{8}{m}-\frac{24}{m+1}+\frac{24}{m+2}-\frac{4}{m-1}\right) p^2 \Delta ^{\text{mu}} \Delta ^{\text{nu}} (\Delta \cdot p)^{m-2}+\left(-\frac{6}{m}+\frac{16}{m+1}-\frac{16}{m+2}+\frac{6}{m-1}\right) (\Delta \cdot p)^{m-1} \left(p^{\text{mu}} \Delta ^{\text{nu}}+\Delta ^{\text{mu}} p^{\text{nu}}\right)\right)

Twist2CounterOperator[p, 7]

((1)m+1)(2m1m+12m1)CFgs2SnγΔ(Δp)m1ε\frac{\left((-1)^m+1\right) \left(\frac{2}{m}-\frac{1}{m+1}-\frac{2}{m-1}\right) C_F g_s^2 S_n \gamma \cdot \Delta (\Delta \cdot p)^{m-1}}{\varepsilon }

Twist2CounterOperator[p1, p2, {p3, mu, a}, 1]

((1)m+1)(2m1m+12m1)Tags3ΔmuSn(CA2CF)γΔ((Δ  p1)m1Δ  p1+Δ  p2((Δ  p2))m1Δ  p1+Δ  p2)2ε-\frac{\left((-1)^m+1\right) \left(\frac{2}{m}-\frac{1}{m+1}-\frac{2}{m-1}\right) T^a g_s^3 \Delta ^{\text{mu}} S_n \left(C_A-2 C_F\right) \gamma \cdot \Delta \left(\frac{(\Delta \cdot \;\text{p1})^{m-1}}{\Delta \cdot \;\text{p1}+\Delta \cdot \;\text{p2}}-\frac{(-(\Delta \cdot \;\text{p2}))^{m-1}}{\Delta \cdot \;\text{p1}+\Delta \cdot \;\text{p2}}\right)}{2 \varepsilon }