Propagator of the Lattice Domain Wall Fermion and the Staggered Fermion

We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16(3) x 32 x 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling alpha (s,g1)(q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling alpha (s,g1)(q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling alpha (s) (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q (2)) with c a parts per thousand integral 2.8 GeV2 on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling alpha (s) (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling alpha (s,g1)(q) in the infrared region increases monotonically as q -> 0. Above 2 GeV, the quark-gluon coupling alpha (s,g1)(q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste.