250 Appendix F: Heavy Quark Production Radiation Derivation “ k · p = 0” pole is shoved below the real axis. Since we throw away these poles anyway we know that we may safely use our previously derived equations for the radiated energy lost, Eq. (F.59) and Eq. (F.80). All we need to do is alter the p momentum appropriately before plugging in. We’d like to know whether consideration of pair production, Fig. F.3, results in an amplitude different from the usual bremsstrahlung diagrams, Fig. F.2. The amplitude from Fig. F.3 is F.4.2 QFT where we see that the sign difference between the terms no longer comes from the switch in sign of the ( p − k ) 2 vs. the ( p $^{′}$+ k ) 2 term in the denominator but rather from the opposite sign of charge. We may safely employ our previous derivation, Eqs. (F.86,F.87), using momenta associated with pair production. i M ≈ − ie ¯ u ( p $^{′}$)¯ u ( p ) γ · ϵ $^{∗}$( k )$^{[}$ i ( / p + / k + m ) ( p + k ) 2 − m 2 − i ( / p ′ + / k + m ) ( p ′ + k ) 2 − m 2 ] M$_{0}$ u · · · u, (F.103)