Chiral weak-current trace contraction ($T^{\alpha \beta }(a,b)T_{\alpha \beta }(c,d)$)

For massless momenta, define $T^{\alpha \beta }(a,b)=\mathrm{Tr}[/a{\gamma }^{\alpha }(1-{\gamma }^5)/b{\gamma }^{\beta }(1-{\gamma }^5)]$. 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.