content_image/308590.jpg content_image/308591.jpg
the rest of this section. There are two interesting features in this result that are different from Magda’s zeroth order massive QCD result (ignoring the additional difference from the error in her published result that she corrected in her thesis). The first is the overall factor of (1 − x ) 2 that does not reproduce Ivan’s massless result, which is C/ k $^{2}$. While this may be swept under the rug as 1 − x ≈ 1 in the small- x limit, we will actually recover this overall factor below. The other difference is the (1 − x ) $^{2}$m2 γ term in the numerator: this cannot be ignored. Nevertheless this filling in of the “dead cone” in the massive field case is not so far-fetched; the additional longitudinal polarization could easily create a mode to emit radiation collinearly. 

Plugging the above momenta into Eq. (F.87) and expanding in powers of 1 /E $^{+}$, the lowest order QFT calculation gives 

<img src='content_image/308590.jpg'>

exactly reproducing the classical limit. This gives us quite a bit of confidence in our results. 

## F.3.2 Massive Field and Charge, No Recoil 

Interestingly the result when there is no recoil, 

<img src='content_image/308591.jpg'>

