Short distance repulsion in 3 nucleon forces from perturbative QCD

We investigate the short distance behavior of 3 nucleon forces (3NF) defined through Nambu–Bethe–Salpeter wave functions, using the operator product expansion(OPE) and calculating anomalous dimensions of 9–quark operators in perturbative QCD. As is the case of NN forces previously considered, we show that 3NF have repulsions at short distance at 1–loop, which becomes exact in the short distance limit thanks to the asymptotic freedom of QCD. Moreover these behaviors are universal in the sense that they do not depend on the energy of the NBS wave function for 3 nucleons.