= Chiral weak-current trace contraction
{title2=$T^{\alpha\beta}(a,b)T_{\alpha\beta}(c,d)$}
For massless momenta, define $T^{\alpha\beta}(a,b)=\operatorname{Tr}[\not a\gamma^\alpha(1-\gamma^5)\not b\gamma^\beta(1-\gamma^5)]$. The <gamma matrix trace identities> and the antisymmetric tensor contraction give $T^{\alpha\beta}(a,b)T_{\alpha\beta}(c,d)=256(a\cdot c)(b\cdot d)$. Reversing an antiquark's spinor order changes the momentum pairing and creates the $(1-y)^2$ angular factor in a <weak charged-current quark scattering> rate.
Back to article page
