content_image/303382.jpg content_image/303383.jpg content_image/303384.jpg content_image/303385.jpg content_image/303386.jpg content_image/303387.jpg
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 

<img src='content_image/303382.jpg'>

<img src='content_image/303383.jpg'>

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 

the formation time to lowest order (assuming large p$_{z}$ and small k ) is 

<img src='content_image/303384.jpg'>

<img src='content_image/303385.jpg'>

<img src='content_image/303386.jpg'>

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. 

<img src='content_image/303387.jpg'>

