Two-dimensional gluon propagators in maximally Abelian gauge in SU(2) Lattice QCD

الأصل · EN

Using SU(2) lattice QCD in two dimensions, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge (MAG) with U(1)₃ Landau gauge fixing. These propagators are investigated both in momentum space and coordinate space. The Monte Carlo simulation is performed at β=7.99, 30.5, and 120 on 62², 128², and 256² at the quenched level. In the momentum space, the transverse component of the diagonal gluon propagator shows suppression with increasing β in the infrared region and the dressing function at β=120 has a maximum at p² ≃ 4GeV, while the transverse component of the off-diagonal gluon propagator does not show the β-dependence and the dressing function does not have a maximum. This behavior indicates that the effect of the Gribov copies is found for the diagonal gluon, consistent with the result obtained by the Gribov-Zwanziger action in the MAG. In addition, this behavior supports that the Abelian dominance is not found in two dimensions. In the coordinate space, the diagonal gluon propagator decreases as β increases at long distance. In particular, at β=120 the diagonal propagator decreases more rapidly with increasing distance than the off-diagonal propagator. These behaviors also indicate the presence of Gribov copies and no Abelian dominance in two dimensions. Furthermore, we also study these propagators at zero-spatial-momentum. The result suggests that all of the spectral functions of diagonal and off-diagonal gluons would have negative regions and thus they show the violation of the Kallen-Lehmann representation.