246 Appendix F: Heavy Quark Production Radiation Derivation F.3 Comparison F.3.1 Full Result: Massive Field, Charge, with Recoil We wish to make a connection to the zeroth order radiation emitted from the production of a hard parton at midrapidity. To that end, let’s consider the massive quark and field configuration first. Using Ivan’s notation: a four- vector is not bold-faced (e.g. p , k ), a three-vector is bold-faced with a vector symbol (e.g. ⃗ p , ⃗ k ), and a transverse two-vector is bold-faced without a vector symbol (e.g. p , k ). Minkowski four-vectors are written with parentheses, (); light-cone four-vectors with brackets, []. In this notation our momenta of interest are In order to compute the Proca result we must convert these into three vectors. Doing so faithfully and using these in Eq. (F.80) yields to lowest order, when expanding in powers of 1 /E $^{+}$, where C = $^{(}$2(2 π ) 3 ) − 1 is a constant that will be have the same value for p = [ M$_{Q}$, M$_{Q}$, 0 ] (F.88) p ′ = [(1 − x ) E $^{+}$, k 2 + M 2 Q (1 − x ) E $_{+}$, − k ] (F.89) k = [ xE $^{+}$, k 2 + m 2 γ xE + , k ] . (F.90) dE d $^{3}$k = C 4(1 − x ) 2 $^{(}$k 2 + (1 − x ) $^{2}$m2 γ ) $^{(}$k 2 + (1 − x ) $^{2}$m2 γ + x $^{2}$M 2 Q ) $_{2}$, (F.91)