Perturbative approach to the infrared gluon propagator in the maximal Abelian gauge

Abstract

The inclusion of a mass-like term for the gluon in Yang-Mills theories quantized in the Landau gauge has proven to be an effective way of reproducing lattice results for gauge-fixed correlation functions within perturbative computations. Since those quantities are gauge dependent, it is natural to question how general this prescription is for describing the infrared behavior of gluon and Faddeev-Popov ghost propagators in different gauges. In this work, we provide a systematic investigation of this issue in the maximal Abelian gauge, which cannot be deformed into the Landau gauge and has been investigated in gauge-fixed lattice simulations. We compute the one-loop non-Abelian and diagonal gluon propagators and perform fits to lattice data in the case of $SU(2)$. Our results show that the transverse component of the non-Abelian gluon propagator as well as the diagonal gluon propagator, are in good agreement with lattice data in the infrared.

Figures (8)

• Figure 1: One-loop diagrams that contribute to $\langle A_\mu(p)A_\nu(-p) \rangle$
• Figure 2: One-loop diagrams that contribute to $\langle A^a_\mu(p)A^b_\nu(-p) \rangle$
• Figure 3: Gluon dressing of the diagonal transverse propagator in the MAG for the $SU(2)$ gauge group. The results of the present work (Green line) are compared with lattice data of Bornyakov:2003ee (Orange stars).
• Figure 4: Gluon dressing of the off-diagonal transverse propagator in the MAG for the $SU(2)$ gauge group. The results of the present work (Blue line) are compared with lattice data of Bornyakov:2003ee (Red crosses).
• Figure 5: Transverse gluon propagator in the MAG for the $SU(2)$ gauge group. The results of the present work are compared with lattice data of Bornyakov:2003ee. For the diagonal transverse propagator: Green line (present work) and Orange stars (lattice data). For the off-diagonal transverse propagator: Blue line (present work) and Red crosses (lattice data).