Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

5 QCD5.1 Feynman Rules∵ full account requires another full set of lectures∴ just a few SU(N) formulae– generators T a and totally anti symmetric structure constants f abc :(summations for c = 1, 2, . . . , (N 2 c − 1) implied).– normalization and contractions[T a , T b ] = if abc T c (146)tr (T a T b ) = 1 2 δ ab• physical degrees of freedom: quarks and gluons:(147a)T a T a = C F · 1 = N2 C − 1 · 12N C(147b)f acd f bcd = C F · δ ab(147c)k, µ, app ′ = igγ µ T a (148)• triple gluon couplings1gf a1 a 2 a 3g µ1 µ 2(k 1 µ 3− k 2 µ 3)23=+gf a1 a 2 a 3g µ2 µ 3(k 2 µ 1− k 3 µ 1)+gf a1 a 2 a 3g µ3 µ 1(k 3 µ 2− k 1 µ 2)(• quartic gluon couplings21−ig 2 f a1 a 2 bf a3 a 4 b×(g µ1 µ 3g µ4 µ 2− g µ1 µ 4g µ2 µ 3)=−ig 2 f a1 a 3 bf a4 a 2 b×(g µ1 µ 4g µ2 µ 3− g µ1 µ 2g µ3 µ 4)(3 4−ig 2 f a1 a 4 bf a2 a 3 b×(g µ1 µ 2g µ3 µ 4− g µ1 µ 3g µ4 µ 2)• Faddeev-Popov ghosts appear only in loop diagrams31