Correlators Of Pseudoscalar Currents Research Articles

New Charm and Bottom Quark Mass Determinations from QCD Sum Rules

In this talk we discuss results of a new extraction of the MS‾ charm quark mass using relativistic QCD sum rules at O(αs3) based on moments of the vector and the pseudoscalar current correlators, and using the available experimental measurements from e+e− collisions and lattice results, respectively. The analysis of the perturbative uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling, following a work we carried out earlier. Accounting for the perturbative series that result from this double scale variation is crucial, since some of the series can exhibit extraordinarily small scale dependence, if the two scales are set equal. The new aspect of the work reported here addresses the problem that double scale variation might also lead to an overestimate of the perturbative uncertainties. We supplement the analysis by a convergence test that allows to quantify the overall convergence of QCD perturbation theory for each moment, and to discard series that are artificially spoiled by specific choices of the renormalization scales. We also apply the new method to an extraction of the MS‾ bottom quark mass using experimental moments that account for a modeling uncertainty associated to the continuum region where no experimental data is available. We obtain mc(m‾c)=1.288±0.020 GeV and m‾b(m‾b)=4.176±0.023 GeV.

Bottom and charm mass determinations with a convergence test

We present new determinations of the MS charm quark mass using relativistic QCD sum rules at O( 3 ) from the moments of the vector and the pseudoscalar current correlators. We use available experimental measurements from e + e collisions and lattice simulation results, respectively. Our analysis of the theoretical uncertainties is based on dierent implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling. Taking into account the resulting set of series to estimate perturbative uncertainties is crucial, since some ways to treat the perturbative expansion can exhibit extraordinarily small scale dependence when the two scales are set equal. As an additional refinement, we address the issue that double scale variation could overestimate the perturbative uncertainties. We supplement the analysis with a test that quantifies the convergence rate of each perturbative series by a single number. We find that this convergence test allows to determine an overall and average convergence rate that is characteristic for the series expansions of each moment, and to discard those series for which the convergence rate is significantly worse. We obtain mc(mc) = 1:288 0:020GeV from the vector correlator. The method is also applied to the extraction of the MS bottom quark mass from the vector correlator. We compute the experimental moments including a modeling uncertainty associated to the continuum region where no data is available. We obtain mb(mb) = 4:176 0:023GeV.

Corrections to the SU(3) × SU(3) Gell-Mann-Oakes-Renner relation and chiral couplings $ L_8^r $ and $ H_2^r $

Next to leading order corrections to the SU(3) × SU(3) Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is ψ 5(0) = (2.8 ± 0.3) ×10-3 GeV4, leading to the chiral corrections to GMOR: δ K = (55 ± 5)%. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral SU(2) × SU(2). Combining these results with our previous determination of the corrections to GMOR in chiral SU(2) × SU(2), δ π , we are able to determine two low energy constants of chiral perturbation theory, i.e. $ L_8^r=\left( {1.0\pm 0.3} \right)\times {10^{-3 }} $ , and $ H_2^r=-\left( {4.7\pm 0.6} \right)\times {10^{-3 }} $ , both atthe scaleof the ρ-meson mass.

Moments of heavy–light current correlators up to three loops

We consider moments of the non-diagonal vector, axial-vector, scalar and pseudo-scalar current correlators involving two different massive quark flavours up to three-loop accuracy. Expansions around the limits where one mass is zero and the equal-mass case are computed. These results are used to construct approximations valid for arbitrary mass values.

Axial and pseudoscalar current correlators and their couplings toηandη′mesons

Correlators of singlet and octet axial currents, as well as anomaly and pseudoscalar densities have been studied using QCD sum rules. Several of these sum rules are used to determine the couplings ${f}_{\ensuremath{\eta}}^{8}$, ${f}_{\ensuremath{\eta}}^{0}$, ${f}_{{\ensuremath{\eta}}^{\ensuremath{'}}}^{8}$ and ${f}_{{\ensuremath{\eta}}^{\ensuremath{'}}}^{0}$. We find mutually consistent values which are also in agreement with phenomenological values obtained from data on various decay and production rates. While most of the sum rules studied by us are independent of the contributions of direct instantons and screening correction, the singlet-singlet current correlator and the anomaly-anomaly correlator improve by their inclusion.

Pseudoscalar mesons and instantons

We discuss the QCD sum rules for the correlators of pseudoscalar currents with quantum numbers of π, K, η, η′ mesons. In the framework of the instanton model of the QCD vacuum suggested earlier by the author, we calculate SU(3) breaking effects such as K, η masses and ηη′ mixing, as well as the U(1) breaking effect, the η′ mass. We conclude that all these phenomena are very well reproduced by this model.