141 Chapter 6: Heavy Quark Photon Production Radiation Figure 6.1: The two diagrams contributing to the 0 th order in opacity pho- ton/gluon radiation spectrum. Note the inclusion of the radiation from the away side jet, which is usually ignored in pQCD calculations. where we have taken M$_{0}$ ( p + k, p $^{′}$) ≈ M$_{0}$ ( p, p ′ + k ) ≈ M$_{0}$ in the small x , soft radiation limit. Most pQCD calculations ignore the away-side jet; one can easily see that the second term in Eq. (6.8), corresponding to the inclusion of the second diagram in Fig. 6.1, is crucial for preserving the Ward identity [234]. Simultaneously dropping the /k in the numerator and the m$_{γ}$ in the denominator (consistent with the soft photon limit) exactly reproduces the classical Proca result. We note that assuming M$_{0}$ commutes with /ϵ $^{∗}$/k and retaining m$_{γ}$ = 0 in the denominator of Eq. (6.8) results in a dN$_{pQCD}$/d $^{3}$k with leading order identical to Eq. (6.4) but with (1 − x ) 2 → (1 − x/ 2) 2 as the prefactor of the m$_{γ}$ in the numerator and (1 − x ) 2 → (1 − x ) as the prefactor of the m$_{γ}$ in the denominator.