Application of the operator product expansion to the short distance behavior of nuclear potentials
- 210 Downloads
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.
KeywordsAsymptotic Freedom Renormalization Group QCD Lattice QCD
- N. Ishii, S. Aoki and T. Hatsuda, Nuclear forces from quenched and NF=2+1 full lattice QCD using the PACS-CS gauge configurations, PoS(Lattice 2008)155.
- S. Aoki, J. Balog and P. Weisz, Repulsive core of the NN potential and operator product expansion, PoS(LAT2009)132.
- C. Itzykson and J.B. Zuber, Quantum Field Theory, International Series In Pure and Applied Physics, McGraw-Hill, New York U.S.A. (1980).Google Scholar
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.