On the quark-hadron duality for orbital excitations

Duality between the physical and ''bare'' quark cross sections for the current annihilation into states with high orbital momenta is investigated. A simple nature of the duality is shown that must take place at sufficiently high energies in any theory with an interaction switched off at small distances. However the duality is not guaranteed for lower levels (in a channel with given spin); moreover, it is absent for high orbital excitations. In quantum chromodynamics the averaged cross section for production of a resonance with spin n deviates sharply from the quark cross section at s approximately μ2n2, where μ is a characteristic hadronic mass, while for low-lying levels the mass squared is approximately μ2n (the lieanear Regge trajectories). There is wide energy range, from s approximately μ2n up to s approximately μ2n2, where the physical spectral density in non-zero, but not dual to the quark density. A similar phenomenon takes place also in the non-relativistic problem of harmonical oscillator where the renormalization of the spectral density becomes of the order of unity at E approximately #betta#lsup(3/2), wiriwhile the energy of lower levels is approximately #betta#l (l is the angular momentum)