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We present an extension to next-to-leading order in the strong coupling constant g of the AMY effective kinetic approach to the energy loss of high momentum particles in the quark-gluon plasma. At leading order, the transport of jet-like particles is determined by elastic scattering with the thermal constituents, and by inelastic collinear splittings induced by the medium. We reorganize this description into collinear splittings, high-momentum-transfer scatterings, drag and diffusion, and particle conversions (momentum-preserving identity-changing processes). We show that this reorganized description remains valid to NLO in g, and compute the appropriate modifications of the drag, diffusion, particle conversion, and inelastic splitting coefficients. In addition, a new kinematic regime opens at NLO for wider-angle collinear bremsstrahlung. These semi-collinear emissions smoothly interpolate between the leading order high-momentum-transfer scatterings and collinear splittings. To organize the calculation, we introduce a set of Wilson line operators on the light-cone which determine the diffusion and identity changing coefficients, and we show how to evaluate these operators at NLO.

The putative recent indication of an unidentified 3.55 keV X-ray line in certain astrophysical sources is taken as a motivation for an improved theoretical computation of the cosmological abundance of 7.1 keV sterile neutrinos. If the line is interpreted as resulting from the decay of Warm Dark Matter, the mass and mixing angle of the sterile neutrino are known. Our computation then permits for a determination of the lepton asymmetry that is needed for producing the correct abundance via the Shi-Fuller mechanism, as well as for an estimate of the non-equilibrium spectrum of the sterile neutrinos. The latter plays a role in structure formation simulations. Results are presented for different flavour structures of the neutrino Yukawa couplings and for different types of pre-existing lepton asymmetries, accounting properly for the charge neutrality of the plasma and incorporating approximately hadronic contributions.