  We reinvestigate the QCD sum rule for the pi NN coupling constant, g,
starting from the vacuum-to-pion matrix element of the correlation function of
the interpolating fields of two nucleons. We study in detail the physical
content of the correlation function without referring to the effective theory.
We consider the invariant correlation functions by splitting the correlation
function into different Dirac structures. We show that the coefficients of the
double-pole terms are proportional to g but that the coefficients of the
single-pole terms are not determined by g. In the chiral limit the single-pole
terms as well as the continuum terms are ill defined in the dispersion
integral. Therefore, the use of naive QCD sum rules obtained from the invariant
correlation functions is not justified. A possible procedure to avoid this
difficulty is discussed.
