200 Appendix D: Formation Time and Brick Estimates The energy of the gluon in the quark’s rest frame is then k 0 ′ = γ ( k 0 − βk $^{z}$). Boosting the formation time, Eq. (D.1), back to the lab frame will dilate the time by γ ; therefore in the lab where for the last line we have taken k 0 ≃ k z so that Eq. (D.3) reproduces [290]. For a quark of mass M and an emitted gluon of mass m$_{g}$ with momenta τ$_{f}$ = 1 k 0 − βk z (D.2) ≃ λ 1 − β , (D.3) p = ( $^{√}$M 2 + (1 − x ) $^{2}$p2 z + k $^{2}$, (1 − x ) p$_{z}$, − k ) (D.4) k = $^{(√}$m 2 g + x $^{2}$p2 z + k $^{2}$, xp$_{z}$ , k $^{)}$, (D.5) τ$_{f}$ ≃ 2 x (1 − x ) $^{2}$p$_{z}$ k $^{2}$[1 − 2 x (1 − x )] + (1 − x ) $^{2}$m2 g + x $^{2}$M2 (D.6) τ$_{f}$ ≃ 2(1 − x ) $^{2}$p$_{z}$ x ( k 2 + M $^{2}$) , (D.7) the formation time to lowest order (assuming large p$_{z}$ and small k ) is this agrees with [447] in the limit of small- x considered there. Note that using Eq. (D.3) one finds (also for large p$_{z}$ and small k ) which agrees with Eq. (D.6) in the large- x Bethe-Heitler limit.