Precocious scaling in field theories

Abstract

We investigate precocious scaling in the sense of the Wilson operator-product expansion (OPE). We derive expressions for the coefficient functions appearing in such an expansion in terms of moments of the appropriate deep-inelastic structure functions. In these sum rules target-mass terms are treated exactly. Ratios of certain moments of structure functions have a computable deviation from naive scaling results which depends only on the magnitude of the effective charge $g({Q}^{2})$. An analysis of existing electroproduction data indicates that scaling in the OPE sense sets in for ${Q}^{2}$ as low as 2-3 Ge${\mathrm{V}}^{2}$. The charge $g({Q}^{2})$ appears to be small and may have ${Q}^{2}$ dependence only within experimental errors. We consider these results as evidence that the underlying theory of strong interactions is an asymptotically free field theory or a field theory with a small ultraviolet-stable fixed point.