  We propose a new approach to construct QCD sum rules for the pi NN coupling
constant, g, starting from the vacuum-to-pion correlation function of the
interpolating fields of two nucleons and taking its matrix element with respect
to nucleon spinors. The new approach with the projected correlation function is
advantageous because even in the chiral limit the dispersion integral can be
parametrized with well-defined physical parameters. Another advantage of the
new approach is that unwanted pole contribution is projected out. Calculating
the Wilson coefficients of the operator product expansion of the correlation
function up to O(M_B^{-4}) and O(m_pi) where M_B and m_pi are the Borel mass
and the pion mass, respectively, we construct new QCD sum rules for the pi NN
coupling constant from the projected correlation function with consistently
including O(m_pi) corrections. By numerically analyzing the obtained four sum
rules we identified the most prominent one. After roughly estimating errors we
obtaind, g=10 +/- 3, as a result of this sum rule, which is in reasonable
agreement with the empirical value. It is also found that the O(m_pi)
correction is about 5%.
