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

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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.


Asymptotic Freedom Renormalization Group QCD Lattice QCD 


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© The Author(s) 2010

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Authors and Affiliations

  1. 1.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukuba, IbarakiJapan
  2. 2.Research Institute for Particle and Nuclear PhysicsBudapestHungary
  3. 3.Max-Planck-Institut für PhysikMünchenGermany

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