A possible origin of the Casimir scaling of the nonperturbative force

The Casimir scaling phenomena of the nonperturbative force is viewed in terms of the hadronic flux tube as described by the dual Ginzburg-Landau (DGL) theory, the dual superconducting scenario of confinement. The ratios of the string tension of flux tube between higher and fundamental SU(3) representations, dD ≡ σD/σD=3, are systematically studied in a Weyl symmetric formulation of the DGL theory as a function of the Ginzburg-Landau (GL) parameter, κ ≡ mχ/mB , the mass ratio between monopoles mχ and dual gauge bosons mB . While the ratios dD satisfy a simple flux counting rule in the case of Bogomol’nyi limit (κ = 1), systematic deviation from this appears as increasing κ, which can be understood as a result of self interaction between fundamental flux inside a higher dimensional flux tube. In spite of the Abelian nature of the DGL theory, the ratio of string tension is not only far from the Abelian scaling, but even consistent with the Casimir scaling. This result suggests that not only the group theoretical factor but also dynamical mechanism, such as the flux-tube formation can become a possible origin of the “Casimir scaling” phenomena suggested by lattice QCD simulations.