A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

In this work, we study the propagators of matter fields within the framework of the refined Gribov–Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang–Mills theory. In full analogy with the pure gluon sector of the refined Gribov–Zwanziger action, a non-local long-range term in the inverse of the Faddeev–Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov–Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hep-th]), Pereira et al. (arXiv:1605.09747 [hep-th]),the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci–Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.