In the 2D large-N O(N) quartic model, the large-momentum OPE of the scalar two-point function is divergent: coefficient functions and operator condensates carry n! factorial growths that cancel only off-diagonally, never within a fixed power.
Infrared Renormalons and Power Corrections in Deep-Inelastic Sum Rules
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abstract
Infrared renormalons and $1/Q^2$ power corrections in deep-inelastic sum rules are studied. The renormalization of operators with power divergence are discussed. The higher-twist terms in the operator product expansion are shown to account for the residual soft contributions survived from the Kinoshita-Lee-Nauenberg type of cancellation in Feynman diagrams. The presence of some degree of arbitrariness in the twist separation allows one to define the most convenient higher-twist operators suitable for a particular non-perturbative method. The discussion is focused on the Bjorken sum rule, for which the $1/Q^2$ corrections are considered on a lattice.
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Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model
In the 2D large-N O(N) quartic model, the large-momentum OPE of the scalar two-point function is divergent: coefficient functions and operator condensates carry n! factorial growths that cancel only off-diagonally, never within a fixed power.