Improved method for extracting low-energy expansion from OPE in mass-gapped theories

Abstract

Recently, Takaura proposed a new method for extracting the first nonzero coefficient of the low-energy expansion of an observable from its operator product expansion (OPE) in asymptotically free theories with a mass gap and a single threshold. The method uses a weight function to suppress the contribution of the ``duality-violation'' (DV) term that arises when relating the OPE to the low-energy expansion. We extend this method to low-energy expansion coefficients at arbitrary orders. We present two approaches: Method I uses weight functions that isolate the coefficients of low-energy expansion from the OPE. Method II subtracts the DV contribution from the OPE before the extraction. Applying these methods to the two-dimensional large-$N$ $O(N)$ nonlinear sigma model, we find that both methods successfully reconstruct higher-order low-energy expansion coefficients.