πNN coupling from the two-point correlation function with a pion

Abstract

We construct three different sum rules from the two-point correlation function with a pion, i∫d4xeiq⋅x〈0|TJN(x)J̄N(0)|π(p)〉, beyond the soft-pion limit or beyond the chiral limit. In constructing the sum rules beyond the soft-pion limit, we consider the Dirac structures, iγ5 p/ and γ5σμνqμpν. The iγ5 Dirac structure is used to construct a sum rule beyond the chiral limit. Our results suggest that the sum rule beyond the chiral limit provides the πNN coupling consistent with its empirical value.