Charm Quark Mass with Calibrated Uncertainty

TL;DR

This paper accurately determines the charm quark mass using QCD sum rules, combining experimental data with a self-consistent approach to estimate uncertainties, resulting in a precise value with bounded error.

Contribution

It introduces a method to calibrate and quantify uncertainties in charm quark mass determination using sum rules and experimental data, improving precision.

Findings

Charm quark mass is ${ m 1272 ext{ MeV}} imes ext{ with } ext{uncertainty } ext{8 MeV}$

Self-consistent sum rule approach bounds theoretical errors

Experimental data effectively constrains continuum contributions

Abstract

We determine the charm quark mass ${\hat m}_c({\hat m}_c)$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD. Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to bound the theoretical error. Our result is ${\hat m}_c({\hat m}_c) = 1272 \pm 8$ MeV for $\hat\alpha_s(M_Z) = 0.1182$. Special attention is given to the question how to quantify and justify the uncertainty.