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

Abstract

New spectral representations for f_\pi and 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 \sigma and gluon correlation length T_g without fitting parameters. As a result one obtains <\bar q q> = - N_c\sigma^2 T_g a_1, f_\pi =\sqrt{N_c} \sigma T_g a_2, with a_1=0.0823, a_2=0.30. Taking \sigma=0.18 GeV^2 and T_g=1 GeV^(-1), as known from analytic and lattice calculations, this yields <\bar q q>(\mu=2 GeV)=-(0.225 GeV)^3, f_\pi=0.094 GeV, which is close to the standard values.