  We present a method to extract the low energy behavior of physical
observables from their high energy expansions, systematically calculable via
the operator product expansion (OPE), in asymptotically free and mass-gapped
theories. By applying the inverse Laplace transform to correlation functions,
their analytic structure is modified such that low-energy information connects
with high energy expansions. Furthermore, this transformation alleviates the
renormalon problem, enabling a more straightforward application of the OPE
compared to the OPE before the transformation. We demonstrate that the low
energy limit of correlation functions can be accurately extracted using the OPE
in the two dimensional $O(N)$ nonlinear $\sigma$ model, serving as a first
testing ground.
