Calculation of fπ and mπ at finite chemical potential

Based on the previous work in Y. Jiang, Y. M. Shi, H. T. Feng, W. M. Sun, and H. S. Zong, Phys. Rev. C 78, 025214 (2008) on the quark-meson vertex and pion properties at finite quark chemical potential, we provide an analytical analysis of the weak decay constant of the pion (fπ[μ]) and the pion mass (mπ[μ]) at finite quark chemical potential using the model quark propagator proposed in R. Alkofer, W. Detmold, C. S. Fischer, and P. Maris, Phys. Rev. D 70, 014014 (2004). It is found that when μ is below a threshold value μ0 (which equals 0.350, 0.377, and 0.341 GeV, for the 2CC, 1R1CC, and 3R parametrizations of the model quark propagator, respectively), fπ[μ] and mπ[μ] are kept unchanged from their vacuum values. The value of μ0 is intimately connected with the pole distribution of the model quark propagator and is found to coincide with the threshold value below which the quark-number density vanishes identically. Numerical calculations show that when μ becomes larger than μ0, fπ[μ] exhibits a sharp decrease whereas mπ[μ] exhibits a sharp increase. A comparison is given between the results obtained in this paper and those obtained in previous literature.