# Second Order QCD Corrections, Electron Positron Annihilation

• The projections are summed over all final state polarizations, whereas the matrixelements are not.
• ```Pij=(pi+pj)2, (i,j=1,2,3,4) Pi5=(p5-pi)2, (i=1,2,3,4) Q2 = s = p52```
• The scalar integrals ` B0, C0, D0 ` are defined Appendix D of T. Matsuura, S.C. van der Marck, and W.L. van Neerven, Nucl. Phys. B319 (1989) 570.
• ```Ca = 3 Cf = 4/3```
• `[e_q]` equals the charge of the detected quark.
`[e_Q]` equals the charge of the quark which is not detected.
The axial couplings `[a_q]` and `[a_Q]` are similar.
• `n = 4 + eps`
• `fi(i,j) = 1/(i + j * eps/2)`

• ```$p$5 = p1 + p2 + p3, s = p52 > 0, p12 = p22 = p32 = 0 ```

First Order:
• $V --> qqg$, (Matrix element, Asymmetry matrix element, polarized matrix element)
• Second Order:
• $V --> qqg$, (FL,q, FT,q, F3,q, G1,q, FL,g, FT,g, G1,g, Matrix element, Asymmetry matrix element, polarized matrix element)

• ```$p$5 = p1 + p2 + p3 + p4, s = p52 > 0, p12 = p22 = p32 = p42 = 0 ```

Second Order:
• $V --> qqg g$, (FL,q, FT,q, F3,q, G1,q, FL,g, FT,g, G1,g, Matrix element, Asymmetry matrix element, Polarized matrix element)

• Second Order:
• $V --> qqqq$, (FL, FT, F3, G1)
• Matrix elements (non-identical quarks, extra contributions due to identical quarks).
• Asymmetry matrix elements (non-identical quarks, extra contributions due to identical quarks).
• Polarized matrix elements (non-identical quarks, extra contributions due to identical quarks).