Application of the operator product expansion to the short distance behavior of nuclear potentials

Abstract

We investigate the short distance behavior of nucleon-nucleon (NN) potentials defined through Bethe-Salpeter wave functions, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, 1-loop computations give certain exact results for the potentials in the zero distance limit. In particular the functional form of the S-state central NN potential at short distance $r$ is predicted to be a little weaker than $r^{-2}$. On the other hand, due to the intriguing character of the anomalous dimension spectrum, perturbative considerations alone can not determine whether this potential is repulsive or attractive at short distances. A crude estimation suggests that the force at short distance is repulsive, as found numerically in lattice QCD. A similar behavior is found for the tensor potential.

40 pages, no figures

References in corpus (4)

• Nuclear Force from Lattice QCD
• Theoretical Foundation of the Nuclear Force in QCD and its applications to Central and Tensor Forces in Quenched Lattice QCD Simulations
• Nuclear Force from Monte Carlo Simulations of Lattice Quantum Chromodynamics
• Bethe--Salpeter wave functions in integrable models

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• Neutron-proton scattering and singular potentials
• Marchenko method with incomplete data and singular nucleon scattering