Probing the Boundary of the Non-Perturbative QCD by Small Size Instantons

The lattice data on the instanton size distribution suggest an additional O($\rho^2)$ action. The small-$\rho$ effect O($\rho^4)$ predicted by the Operator Product Expansion (OPE) is not observed. Similar deviations are also found for non-perturbative response to a small static color dipoles: it is O(r) not O(r$^2$). We suggest that small instanton radii in the QCD vacuum and small radii of the QCD strings (to which this observation relates) are consequences of the same phenomenon: a very robust dual superconductivity in the QCD vacuum, with relatively large Higgs VEV and surprisingly large Higgs mass.