Charm-quark mass from weighted finite energy QCD sum rules

TL;DR

This paper determines the charm-quark mass using weighted finite energy QCD sum rules with optimized kernels, combining experimental data and high-order perturbative calculations to achieve a precise result.

Contribution

It introduces the use of simple pinched and Legendre-type kernels in FESR to reduce duality violations and extend analysis regions, improving charm-quark mass determination.

Findings

Charm-quark mass at 3 GeV: 1008 ± 26 MeV

Optimal kernels reduce duality violations

Method achieves stable results across various energy scales

Abstract

The running charm-quark mass in the $\bar{MS}$ scheme is determined from weighted finite energy QCD sum rules (FESR) involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of $s$, the squared energy. The optimal kernels are found to be a simple {\it pinched} kernel, and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s-plane, and the latter allows to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three different methods, fixed order perturbation theory (FOPT), contour improved perturbation theory (CIPT), and a fixed renormalization scale $\mu$ (FMUPT). The final result is $\bar{m}_c (3\, {GeV}) = 1008\,\pm\, 26\, {MeV}$, in a wide region of stability against changes in the integration radius $s_0$ in the complex s-plane.