Color-kinematics duality in one-loop four-gluon amplitudes with matter

Abstract

Four-point one-loop nonsupersymmetric pure Yang-Mills amplitudes with the\nduality between color and kinematics manifest have been constructed in previous\nwork. Here, we extend the discussion to fermions and scalars circulating in the\nloop with all external gluons. This gives another nontrivial loop-level example\nshowing that the duality between color and kinematics holds in\nnonsupersymmetric gauge theory. The construction is valid in any spacetime\ndimension and written in terms of formal polarization vectors. We also convert\nthese expressions into a four-dimensional form with explicit external helicity\nstates. Using this, we compare our results to one-loop duality-satisfying\namplitudes that are already present in literature.\n