A New Precision Charm Quark Mass Estimate

We determine the charm quark mass m̂ c from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at Order (α̂_s³). 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. Existing data from the continuum region can then be used to bound the theoretic uncertainty. Our result is m̂ c(m̂ c)=1272±8~MeV for α̂_s(M_Z)=0.1182.

Jens Erler, Pere Masjuan, and Hubert Spiesberger, "Charm Quark Mass with Calibrated Uncertainty" (26 Oct 2016).

This almost as precise as you can get (or at least that it is worth trying to get) under greater precision in measurements of α̂_s (i.e. the strong force coupling constant) is available. The paper correctly cites the PDG value for that constant, but omits the margin of error in that measurement which is α̂_s(M_Z)=0.1182(12). Any greater precision in the charm quark mass would provide only spurious accuracy.

How does this compare to existing global averages?

The c-quark mass corresponds to the ``running'' mass mc (μ = mc) in the MS¯ scheme. We have converted masses in other schemes to the MS¯ scheme using two-loop QCD perturbation theory with αs(μ=mc) = 0.380.38±0.03±0.03. The value 1.27±0.03 GeV for the MS¯ mass corresponds to 1.67±0.07 GeV for the pole mass.

Thus, the precision of this estimate is about four times the global average.