New spectral representation and evaluation of f_πand the quark condensate <\bar q q> in the terms of string tension

Abstract

New spectral representations for f_πand chiral condensate are derived in QCD and used for calculations in the large N_c limit. Both quantities are expressed in this limit through string tension σand gluon correlation length T_g without fitting parameters. As a result one obtains <\bar q q> = - N_cσ^2 T_g a_1, f_π=\sqrt{N_c} σT_g a_2, with a_1=0.0823, a_2=0.30. Taking σ=0.18 GeV^2 and T_g=1 GeV^(-1), as known from analytic and lattice calculations, this yields <\bar q q>(μ=2 GeV)=-(0.225 GeV)^3, f_π=0.094 GeV, which is close to the standard values.