One-loop QCD amplitudes in the Feynman-diagram gauge

Scattering amplitudes for the massless QCD process, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>q</a:mi><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mo stretchy="false">→</a:mo><a:msup><a:mi>q</a:mi><a:mo>′</a:mo></a:msup><a:msup><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mo>′</a:mo></a:msup></a:math>, are calculated in the one-loop order in the Feynman-Diagram (FD) gauge, where gluons are quantized on the light cone with opposite direction of the three-momenta. We find non-decoupling of the Faddeev-Popov ghosts and nonconventional UV singularities in dimensional regularization. The known QCD amplitudes with asymptotic freedom are reproduced only after summing propagator and vertex corrections. By quantizing gluons in the Feynman gauge on the FD gauge background, we obtain the one-loop improved FD gauge amplitudes.