Superasymptotic and hyperasymptotic approximation to the operator product expansion

Given an observable and its operator product expansion, we present expressions that carefully disentangle truncated sums of the perturbative series in powers of α from the nonperturbative (NP) corrections. This splitting is done with NP power accuracy. Analytic control of the splitting is achieved and the organization of the different terms is done along an super/hyperasymptotic expansion. As a test we apply the methods to the static potential in the large β0 approximation. We see the superasymptotic and hyperasymptotic structure of the observable in full glory.