Laplacian gauge gluon propagator in SU „

Lattice QCD provides a well suited theoretical framework for the study of nonperturbative quantities as a function of the number of colors. Although experimentally inaccessible, QCD for Nc52 and Nc54 is interesting from the theoretical point of view. Recently SU(Nc) Yang-Mills theories were investigated for various Nc by two groups @1,2# with emphasis on the evaluation of string tensions and glueball masses and their large Nc limit. It is the purpose of the present work to examine the gluon propagator for different numbers of colors. Like in our previous work in SU(3), we evaluate the gluon propagator in the Laplacian gauge which, unlike the more usual Landau gauge, is free of spurious Gribov copies on the lattice. Therefore no doubt can be cast on our results due to the lattice gauge fixing procedure. Furthermore, theoretical arguments have been presented supporting gauge invariance of the pole mass of the transverse gluon propagator @3# and it is therefore an interesting quantity to investigate as a function of Nc even in a particular gauge. Studying the dependence of the gluon mass on Nc has theoretical implications for confinement and chiral symmetry breaking. It has been argued that a nonzero gluon mass is connected to vortex condensation and to the glueball mass @4#. Since the Nc dependence of the glueballs has been investigated, a study of the gluon mass can shed light on their relation. In DysonSchwinger studies the form of the gluon propagator affects that of the quark propagator, which in turn provides a determination of the quark mass and therefore is connected to chiral symmetry breaking. In previous studies @5,6# we considered the gluon propagator in SU(3), and presented evidence for a pole which survives the continuum limit. In this work we present results in SU(2),SU(3) and SU(4) at similar couplings. We refer the reader to Ref. @5# for our notation and the details of our approach.