QCD Sum Rules for Nucleon-Nucleon Interactions

The QCD sum rules for spin-dependent nucleon-nucleon interactions areformulated and their physical implications are studied. The basic object of thestudy is the correlation function of the nucleon interpolating field, where thematrix element is taken with respect to the one-nucleon state. The dispersionintegral of the correlation function around the nucleon threshold isinvestigated in detail. It turns out that the integral can be identified as ameasure of the nucleon-nucleon interaction strength, which is proportional tothe scattering length in the small scattering length limit and to one half ofthe effective range in the large scattering length limit. New operators must betaken into account in the OPE of the correlation function. There behavioroperators do not vanish when the matrix element is taken with respect to thespin-nonaveraged one-nucleon state. The Wilson coefficients of such operatorsare calculated. The sum rules obtained in this manner relate the spin-dependentnucleon-nucleon interaction strengths with the spin-dependent nucleon matrixelements of the quark-gluon composite operators. The sum rules imply that theinteraction is stronger in the spin-triplet channel than in the spin-singletchannel, but that the spin-dependence of the nucleon-nucleon interactions israther small. In the spin-singlet channel the calculated strength is inqualitative agreement with the empirical strength, which is estimated by theempirical low energy scattering observables.Comment: 27 pages, 2 figure