Abstract
We determine the charm quark mass hat{m}_c from QCD sum rules of the moments of the vector current correlator calculated in perturbative QCD at mathcal{O} (hat{alpha }_s^3). 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 theoretic uncertainty. Our result is hat{m}_c(hat{m}_c) = 1272 pm 8 MeV for hat{alpha }_s(M_Z) = 0.1182, where the central value is in very good agreement with other recent determinations based on the relativistic sum rule approach. On the other hand, there is considerably less agreement regarding the theory dominated uncertainty and we pay special attention to the question how to quantify and justify it.
Highlights
As a fundamental parameter of the standard model (SM) of particle physics that enters the calculation of many physical observables, it is important to determine the charm quark mass as accurately as possible and by using several different methods
In order to determine an error for the continuum contributions we proceed in the following way: we compare experimental data with the zeroth moment in the r√estricted energy range of s ≤ 4.8 GeV, to obtain denoted λ3c,exp
We presented a determination of the charm quark mass from QCD sum rules with a careful determination of the uncer
Summary
As a fundamental parameter of the standard model (SM) of particle physics that enters the calculation of many physical observables, it is important to determine the charm quark mass as accurately as possible and by using several different methods. Consistency between different QCD sum rules will be seen to suffice to constrain the continuum of charm pair production with good precision For this procedure to work it is crucial to include alongside the first and higher moment sum rules the zeroth moment, as the latter exhibits enhanced sensitivity to the continuum. Comparison with existing data on the R-ratio for hadronic relative to leptonic final states in e+e− annihilation will serve as a control, providing an independent error estimate which we interpret as the error on the method and add it as an additional error contribution In this way, we can show that the overall precision in mc from relativistic sum rules is at the sub-percent level.
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