QCD duality and the mass of the Charm Quark

The mass of the charm quark is analyzed in the context of QCD finite energy sum rules using recent BESII e+e- annihilation data and a large momentum expansion of the QCD correlator which incorporates terms to order (alpha_s)^2 (m_c^2/q^2)^6. Using various versions of duality, we obtain the consistent result m_c(m_c)=(1.37 +- 0.09)GeV. Our result is quite independent of the ones based on the inverse moment analysis

Bottom quark mass and QCD duality

The mass of the bottom quark is analyzed in the context of QCD finite energy sum rules. In contrast to the conventional approach, we use a large momentum expansion of the QCD correlator including terms to order alpha(S)(2)(m(b)(2)/q(2))(6) with the upsilon resonances from e(+)c(-) annihilation data as main input. A stable result m(b)(m(b)) = (4.19 +/- 0.05) GeV for the bottom quark mass is obtained. This result agrees with the independent calculations based on the inverse moment analysis

QCD sum rule determination of the charm-quark mass

QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the MS¯ scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form p(s)=1−(s0/s)2, where s0 is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range s≃20−25GeV2. This feature leads to a substantial reduction in the sensitivity of the results to changes in s0, as well as to a much reduced impact of the experimental uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the MS¯ scheme at a scale of 3 GeV is m¯c(3GeV)=987±9MeV, where the error includes all sources of uncertainties added in quadrature

Analytic O(alpha(s)) results for bottom and top quark production in e(+)e(-) collisions

We present a new derivation of the O(alpha_s) differential cross section for the production of massive quarks in e+ e- collisions. In our calculation we express the three-particle phase-space integration of the bremsstrahlung process in terms of a general set of analytic integral solutions. A consistent treatment of the QCD one-loop corrections to the axial-vector current deserves special attention. This is relevant in the derivation of the forward-backward asymmetry predicted by the standard model. Finally, we provide the full analytical solutions for the differential rates in closed form and conclude with numerical estimates for bottom and top quark production