142 Chapter 6: Heavy Quark Photon Production Radiation 6.3 Size of Effects We wish to investigate quantitatively the effect of these extra terms on the 0 th order energy loss. To do so we enforce physicality by restricting the x and k integration limits so that the emitted photon has E$_{γ}$ ≥ m$_{g}$ and leaves the jet with E$_{jet}$ ≥ M$_{Q}$ . For ease of comparison with [305] we set µ = . 5 GeV and α = . 5 fixed. One can see from Fig. 6.2 the large (50-150%) effect on Δ E/E of including the overall prefactor of (1 − x ) $^{2}$. Filling in the “dead cone” makes only a small difference to the energy lost (5-20%); this is a surprise as the “dead cone” is the usual naive justification for heavy quarks having smaller radiative energy loss than light quarks. (a) (b) Figure 6.2: (Color online) 0 th order radiative energy loss for (a) charm and (b) bottom quarks. All results are to leader order (LO) in 1 /E $^{+}$. One sees that the largest effect (50-150%) comes from including the (1 − x ) 2 prefactor and that filling in the “dead cone” with the massive photon is a rather small one (5-20%). Comparison with m$_{γ}$ = 0 yields the magnitude of the LO Ter-Mikayelian effect (10-40%).