A Precision Charm Quark Mass Measurement Revisited

The latest charm quark mass measurement compares to a Particle Data Group evaluation of 1.28 ± 0.03 GeV, which is provided in lieu of the weighted average of 1,274 ± 5 MeV, presumably because the wide scatter of the experimental determinations is too widely scattered to justify such a low margin of error. Both of those values are consistent with this result.

We determine the charm quark mass m̂ c(m̂ 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 m̂ c(m̂ c)=1272±8 MeV for α̂ s(MZ)=0.1182. Special attention is given to the question how to quantify and justify the uncertainty.

Jens Erler, Pere Masjuan, Hubert Spiesberger, "Charm Quark Mass with Calibrated Uncertainty" (July 28, 2017).

This paper is substantially identical to a paper blogged on October 28, 2016 at this blog by the same authors reporting the same result, although the PDG comparisons have changed in the meantime.

The result is robust because it agrees with results obtained using six other methodologies. The authors state that a determination of the bottom quark mass using the same methods is in the works and that they anticipate a margin of error of about 15 MeV for that determination (again, holding the strong force coupling constant fixed at the world average value).

The PDG values and the results from this paper are for the mass of the charm quark as defined in the MS charm quark mass (a bar appears above the "MS" if properly typeset). The value 1.28 ± 0.03 GeV for the MS¯mass corresponds to 1.67 ± 0.07 GeV for the pole mass. These definitional issues are discussed in this prior post at this blog. Definitions are critical because, unlike the top quark, charm quarks are never observed outside a confining hadron.

The current PDG value for the strong force coupling constant at the Z boson mass is 0.1181(11), which is slightly different than the old PDG value of 0.1182(16) value used in this paper, although this illustrates that the error bar for the value at the strong force coupling constant value greatly understates the true uncertainty in this measurement given the combined uncertainty in the charm quark mass measurement and the strong force coupling constant measurement.