The analytic approach in quantum chromodynamics

In a new “renormalization invariant analytic formulation” of calculations in quantum chromodynamics, the renormalization group summation is correlated with the analyticity with respect to the square of the transferred momentum $Q^2$. The expressions for the invariant charge and matrix elements are then modified such that the nonphysical singularities of the ghost pole type do not appear at all: additional nonperturbative contributions compensate them by construction. With the new scheme, the calculation results for several physical processes are stable with respect to higher-loop effects and the choice of the renormalization prescription. Having applications of the new formulation to inelastic lepton–nucleon scattering processes in mind, we analyze the corresponding structure functions starting from general principles of the theory in the Jost–Lehmann–Dyson integral representation. A nonstandard scaling variable leads to modified moments of the structure functions possessing Källén–Lehmann analytic properties with respect to $Q^2$. We find the relation between these “modified analytic moments” and the operator product expansion.