Quark-meson vertices and pion properties at finite chemical potential

Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the quark-meson vertex in the neighborhood of zero chemical potential ({mu}=0) and neglecting the {mu}-dependence of the dressed gluon propagator, we use the method of studying the dressed quark propagator at finite chemical potential given in [H. S. Zong, L. Chang, F.Y. Hou, W. M. Sun, and Y. X. Liu, Phys. Rev. C 71, 015205 (2005)] to show that the axial-vector quark-meson vertex at finite {mu} can be obtained from the corresponding one at {mu}=0 by a shift of variable: {gamma}{sub 5{nu}}{sup j}[{mu}](k, p)={gamma}{sub 5{nu}}{sup j}(k{approx}, p), where k and p are the relative and total momentum of the quark-antiquark pair, respectively, and k{approx}=(k-vector, k{sub 4}+i{mu}). Similar relations hold for any other type of quark-meson vertex. This feature would facilitate the numerical calculations of the quark-meson vertex function at finite {mu} considerably. Based on these results and using the dressed quark propagator at {mu}=0 proposed in [R. Alkofer, W. Detmold, C. S. Fischer, and P. Maris, Phys. Rev. D 70, 014014 (2004)], we calculate the pion decay constant f{sub {pi}} and the pion mass m{sub {pi}} at finite {mu} and a comparison of our results with those in the literature is made.