### Abstract

We investigate the short distance behavior of the nucleon-nucleon (NN) potential defined through the Bethe-Salpeter wave function, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, the 1-loop estimations give exact results for the potential in the zero distance limit. We show that the chiral symmetry of the gauge interaction implies the existence of an operator whose anomalous dimension is zero for a given quantum number. Furthermore we find that non-zero anomalous dimensions of other operators are all negative. These results predict the functional form of the NN potential at short distance, which is a little weaker than r-2. On the other hand, the computation of the anomalous dimension spectrum alone can not determine whether the potential is repulsive or attractive at short distance. An additional analytic non-perturbative analysis suggests that the force at short distance is indeed repulsive at low energy as found numerically. Some extensions of the method are briefly discussed.

Original language | English |
---|---|

Journal | Proceedings of Science |

Volume | 91 |

Publication status | Published - Jan 1 2009 |

Event | 27th International Symposium on Lattice Field Theory, LAT 2009 - Beijing, China Duration: Jul 26 2009 → Jul 31 2009 |

### Fingerprint

### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of Science*,

*91*.

**The repulsive core of the NN potential and the operator product expansion.** / Aoki, Sinya; Balog, J.; Weisz, Peter.

Research output: Contribution to journal › Conference article

*Proceedings of Science*, vol. 91.

}

TY - JOUR

T1 - The repulsive core of the NN potential and the operator product expansion

AU - Aoki, Sinya

AU - Balog, J.

AU - Weisz, Peter

PY - 2009/1/1

Y1 - 2009/1/1

N2 - We investigate the short distance behavior of the nucleon-nucleon (NN) potential defined through the Bethe-Salpeter wave function, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, the 1-loop estimations give exact results for the potential in the zero distance limit. We show that the chiral symmetry of the gauge interaction implies the existence of an operator whose anomalous dimension is zero for a given quantum number. Furthermore we find that non-zero anomalous dimensions of other operators are all negative. These results predict the functional form of the NN potential at short distance, which is a little weaker than r-2. On the other hand, the computation of the anomalous dimension spectrum alone can not determine whether the potential is repulsive or attractive at short distance. An additional analytic non-perturbative analysis suggests that the force at short distance is indeed repulsive at low energy as found numerically. Some extensions of the method are briefly discussed.

AB - We investigate the short distance behavior of the nucleon-nucleon (NN) potential defined through the Bethe-Salpeter wave function, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, the 1-loop estimations give exact results for the potential in the zero distance limit. We show that the chiral symmetry of the gauge interaction implies the existence of an operator whose anomalous dimension is zero for a given quantum number. Furthermore we find that non-zero anomalous dimensions of other operators are all negative. These results predict the functional form of the NN potential at short distance, which is a little weaker than r-2. On the other hand, the computation of the anomalous dimension spectrum alone can not determine whether the potential is repulsive or attractive at short distance. An additional analytic non-perturbative analysis suggests that the force at short distance is indeed repulsive at low energy as found numerically. Some extensions of the method are briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=85055250737&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055250737&partnerID=8YFLogxK

M3 - Conference article

VL - 91

JO - Proceedings of Science

JF - Proceedings of Science

SN - 1824-8039

ER -