Off-diagonal gluon mass generation and infrared Abelian dominance in the maximally Abelian gauge in lattice QCD

Abstract

We study effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian ͑MA͒ gauge. Using SU͑2͒ lattice QCD, we investigate the propagator and the effective mass of the gluon field in the MA gauge with U(1) 3 Landau gauge fixing. The Monte Carlo simulation is performed on the 12 3 ϫ24 lattice with 2.2р␤р2.4, and also on the 16 4 and 20 4 lattices with 2.3р␤р2.4. In the MA gauge, the diagonal gluon component A 3 shows long-range propagation, and infrared Abelian dominance is found for the gluon propagator. In the MA gauge, the off-diagonal gluon component A Ϯ behaves as a massive vector boson with the effective mass M off Ӎ1.2 GeV in the region of rտ0.2 fm, and its propagation is limited within a short range. We conjecture that infrared Abelian dominance can be interpreted as infrared inactivity of the offdiagonal gluon due to its large mass generation induced by the MA gauge fixing. ͓S0556-2821͑99͒05223-6͔

Abelian dominance and gluon propagators in the maximally Abelian gauge of SU(2) lattice gauge theory

“…The Maximally Abelian (MA) gauge is the most convenient for demonstration of the dual superconductor nature of the gluodynamics vacuum (see, e.g., [13] for a review). The first study of the MA gauge gluon propagator in the coordinate space was made in [14]. It was found that the propagator of the off-diagonal gluons is exponentially suppressed at large distances by the effective mass about 1.2 GeV.…”

The infrared behavior of the gluon and ghost propagators in SU(2) Yang-Mills theory in the maximal abelian gauge

“…In the case of small gauge transformations, this is easily obtained by requiring that the gauge transformed fields (12), fulfill the same gauge conditions obeyed by A µ , A a µ , i.e. (13) and (15). Thus, to the first order in the gauge parameters (ω, ω a ), one gets…”

“…Moreover, as it is apparent from the presence of the covariant derivative D ab µ , (13) allows for a residual local U(1) invariance corresponding to the diagonal subgroup of SU (2). This additional invariance has to be fixed by means of a suitable gauge condition on the diagonal component A µ , which will be chosen to be of the Landau type, also adopted in lattice simulations [15,16], namely…”

“…The first study of the gluon propagator on the lattice in the maximal Abelian gauge was made in [15] in the case of SU (2). The gluon propagator was analyzed in coordinate space.…”

“…The interested reader can find the details for the MAG in [28]. We define the Gribov region C 0 as the set of fields fulfilling the gauge conditions (13), (15) and for which the Faddeev-Popov operator M ab is positive definite, namely…”