Numerically Computing QCD Laplace Sum-Rules Using pySecDec

Abstract

pySecDec is a program that numerically calculates dimensionally regularized integrals. We use pySecDec to compute QCD Laplace sum-rules for pseudoscalar (i.e., $J^{PC}=0^{-+}$) charmonium hybrids, and compare the results to sum-rules computed using analytic results for dimensionally regularized integrals. We find that the errors due to the use of numerical integration methods is negligible compared to the uncertainties in the sum-rules stemming from the uncertainties in the parameters of QCD, e.g., the coupling constant, quark masses, and condensate values. Also, we demonstrate that numerical integration methods can be used to calculate finite-energy and Gaussian sum-rules in addition to Laplace sum-rules.