Nonperturbative improvement and tree-level correction of the quark propagator

We extend an earlier study of the Landau gauge quark propagator in quenched QCD where we used two forms of the $\mathcal{O}\mathrm{}\left(a\right)\mathrm{}$-improved propagator with the Sheikholeslami-Wohlert quark action. In the present study we use the nonperturbative value for the clover coefficient $c_{\mathrm{sw}}$ and mean-field improvement coefficients in our improved quark propagators. We compare this with our earlier results which used the mean-field $c_{\mathrm{sw}}$ and tree-level improvement coefficients for the propagator. We also compare three different implementations of tree-level correction: additive, multiplicative, and hybrid. We show that the hybrid approach is the most robust and reliable and can successfully deal even with strong ultraviolet behavior and zero crossing of the lattice tree-level expression. We find good agreement between our improved quark propagators when using the appropriate nonperturbative improvement coefficients and hybrid tree-level correction. We also present a simple extrapolation of the quark mass function to the chiral limit.