QCD Sum Rules for Nucleon-Nucleon Interactions

The QCD sum rules for spin-dependent nucleon-nucleon interactions are formulated and their physical implications are studied. The basic object of the study is the correlation function of the nucleon interpolating field, where the matrix element is taken with respect to the one-nucleon state. By means of the dispersion relation, the correlation function in the deep Euclidean region, where it is expressed in terms of the nucleon matrix elements of the quark-gluon composite operators by using the operator product expansion (OPE), is related with its integral over the physical region. The dispersion integral of the correlation function around the nucleon threshold is investigated in detail. It turns out that the integral can be identified as a measure of the nucleon-nucleon interaction strength, which is proportional to the scattering length in the small scattering length limit and to one half of the effective range in the large scattering length limit. New operators, such as , must be taken into account in the OPE of the correlation function. These operators do not vanish when the matrix element is taken with respect to the spin-nonaveraged one-nucleon state. The Wilson coefficients of such operators are calculated. The sum rules obtained in this manner relate the spin-dependent nucleon-nucleon interaction strengths with the spin-dependent nucleon matrix elements of the quark-gluon composite operators. The sum rules imply that the interaction is stronger in the spin-triplet channel than in the spin-singlet channel, but that the spin-dependence of the nucleon-nucleon interactions is rather small. In the spin-singlet channel the calculated strength is in qualitative agreement with the empirical strength, which is estimated by the empirical low-energy scattering observables.