213 Appendix E: Standard pQCD Results The first relation is proved as follows: The second line comes from using { γ $^{µ}$, γ$^{ν}$} = 2 g $^{µν}$; the third line results from the Dirac equation, ¯ u ( p )( / p + m ) = 0. The proof of the conjugate relation follows the exact same line of reasoning. ¯ u ( p $^{′}$) γ · ϵ $^{∗}$( / p ′ + m ) = ¯ u ( p $^{′}$) γ $^{µ}$ϵ ∗ $_{µ}$( γ $^{ν}$p ′ ν + m ) = ¯ u ( p $^{′}$) $^{(}$2 ϵ ∗ · p ′ − ( / p ′ + m ) γ · ϵ ∗ ) = ¯ u ( p $^{′}$)2 p ′ $^{µ}$ϵ ∗ $_{µ}$. (E.12) E.2.2 Diagrammatic Calculation, Massless Photon and Quark Monojet Figure E.1: Zeroth order radiation diagram. The blob on the left represents the factorized production of the hard quark.