Final State Gluon Emission in Deep-Inelastic Scattering at Next-to-Leading Twist

A detailed reanalysis of the single gluon emission rate at next-to-leading twist is carried out. As was the case in prior efforts, the problem is cast in the framework of deep-inelastic scattering (DIS) of an electron off a large nucleus. The quark produced in the interaction propagates through the remaining nucleus and engenders scattering and gluon radiation, which is calculated in the limit of one re-scattering. This medium induced single gluon emission rate forms the basis of several energy loss calculations in both DIS and heavy-ion collisions. Unlike prior efforts, a complete transverse momentum gradient expansion of the hadronic tensor, including $N_c$ suppressed terms, phase terms and finite gluon momentum fraction terms, ignored previously, is carried out. These terms turn out to be surprisingly large. In contrast to prior efforts, the full next-to-leading twist gluon emission kernel is found to be positive definite and slowly increasing with the exchanged transverse momentum. Phenomenological consequences of these new contributions are discussed.