Numerically Computing QCD Laplace Sum-Rules Using pySecDec

TL;DR

This paper demonstrates that pySecDec can accurately compute QCD Laplace sum-rules numerically, matching analytic results and enabling calculations of various sum-rules with negligible numerical errors.

Contribution

The work introduces the use of pySecDec for numerical computation of QCD sum-rules, expanding the toolkit beyond analytic methods and validating its accuracy.

Findings

Numerical errors are negligible compared to QCD parameter uncertainties.

pySecDec accurately reproduces analytic sum-rule results.

Numerical methods can compute finite-energy and Gaussian sum-rules.

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.