A projected correlation function approach to the pi NN coupling constant in QCD sum rules

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%.