Journal of High Energy Physics

, 2010:83 | Cite as

Operator product expansion and the short distance behavior of 3-flavor baryon potentials



The short distance behavior of baryon-baryon potentials defined through Nambu-Bethe-Salpeter wave functions is investigated using the operator product expansion. In a previous analysis of the nucleon-nucleon case, corresponding to the SU(3) channels 27s and \( {\overline {10}_a} \), we argued that the potentials have a repulsive core. A new feature occurs for the case of baryons made up of three flavors: manifestly asymptotically attractive potentials appear in the singlet and octet channels. Attraction in the singlet channel was first indicated by quark model considerations, and recently been found in numerical lattice simulations. The latter have however not yet revealed asymptotic attraction in the octet channels; we give a speculative explanation for this apparent discrepancy.


Asymptotic Freedom Renormalization Group QCD Lattice QCD 


  1. [1]
    N. Ishii, S. Aoki and T. Hatsuda, The nuclear force from lattice QCD, Phys. Rev. Lett. 99 (2007) 022001 [nucl-th/0611096] [SPIRES].ADSCrossRefGoogle Scholar
  2. [2]
    S. Aoki, T. Hatsuda and N. Ishii, Nuclear force from Monte Carlo simulations of lattice quantum chromodynamics, Comput. Sci. Dis. 1 (2008) 015009 [arXiv:0805.2462] [SPIRES].CrossRefGoogle Scholar
  3. [3]
    S. Aoki, T. Hatsuda and N. Ishii, Theoretical foundation of the nuclear force in QCD and its applications to central and tensor forces in quenched lattice QCD simulations, Prog. Theor. Phys. 123 (2010) 89 [arXiv:0909.5585] [SPIRES].ADSMATHCrossRefGoogle Scholar
  4. [4]
    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 [arXiv:0903.5497] [SPIRES].
  5. [5]
    S. Aoki, J . Balog and P. Weisz, A pplication of the operator product expansion to the short distance behavior of nuclear potentials, JHEP 05 (2010) 008 [arXiv:1002.0977] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    M. Oka, K. Shimizu and K. Yazaki, The dihyperon state in the quark cluster model, Phys. Lett. B 130 (1983) 365 [SPIRES]. ADSGoogle Scholar
  7. [7]
    M. Oka, K. Shimizu and K. Yazaki, Hyperon-nucleon and hyperon-hyperon interaction in a quark model, Nucl. Phys. A 464 (1987) 700 [SPIRES].ADSGoogle Scholar
  8. [8]
    M. Oka, K. Shimizu and K. Yazaki, Quark cluster model of baryon baryon interaction, Prog. Theor. Phys. Suppl. 137 (2000) 1 [SPIRES].ADSCrossRefGoogle Scholar
  9. [9]
    C. Itzykson and M. Nauenberg, Unitary groups: representation and decompositions, Rev. Mod. Phys. 38 (1966) 95 [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    HAL QCD collaboration, T. Inoue, Baryon-baryon potentials in the flavor SU(3) limit from lattice QCD, PoS(LAT2009)133.
  11. [11]
    HAL QCD collaboration, T. Inoue et al., Baryon-baryon interactions in the flavor SU(3) limit from full QCD simulations on the lattice, arXiv:1007.3559 [SPIRES].

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

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

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