Charmonium Sum Rules Research Articles

Precise αs determination from charmonium sum rules

The strong coupling, αs, governs perturbative Quantum Chromodynamics (QCD) and is one of the free parameters of the Standard Model. We introduce a new method that allows a precise extraction of αs(mZ) from dimensionless ratios of roots of moments of the charm-quark vector correlator. The ratios we use in our analysis have a rather weak logarithmic quark-mass dependence, starting at O(αs2), and can be obtained from experimental data with good precision, since they benefit from positive correlations among the individual experimentally determined moments. We perform a careful and conservative error analysis with special emphasis on uncertainties related to the truncation of perturbation theory, treating the renormalization scales such as to ensure order-by-order convergence. Our final result, with expressions at O(αs3), is αs(mZ)=0.1168±0.0019.

Charm mass determination from QCD charmonium sum rules at order $ \alpha_s^3 $

We determine the $ \overline{\mathrm{MS}} $ charm quark mass from a charmonium QCD sum rules analysis. On the theoretical side we use input from perturbation theory at $ \mathcal{O}\left( {\alpha_s^3} \right) $ . Improvements with respect to previous $ \mathcal{O}\left( {\alpha_s^3} \right) $ analyses include (1) an account of all available e + e − hadronic cross section data and (2) a thorough analysis of perturbative uncertainties. Using a data clustering method to combine hadronic cross section data sets from different measurements we demonstrate that using all available experimental data up to c.m. energies of 10.538 GeV allows for determinations of experimental moments and their correlations with small errors and that there is no need to rely on theoretical input above the charmonium resonances. We also show that good convergence properties of the perturbative series for the theoretical sum rule moments need to be considered with some care when extracting the charm mass and demonstrate how to set up a suitable set of scale variations to obtain a proper estimate of the perturbative uncertainty. As the final outcome of our analysis we obtain $ {{\overline{m}}_c}\left( {{{\overline{m}}_c}} \right)=1.282\pm {{\left( {0.006} \right)}_{\mathrm{stat}}}\pm {{\left( {0.009} \right)}_{\mathrm{syst}}}\pm {{\left( {0.019} \right)}_{\mathrm{pert}}}\pm {{\left( {0.010} \right)}_{{{\alpha_s}}}}\pm {{\left( {0.002} \right)}_{{\left\langle {GG} \right\rangle }}}\mathrm{GeV} $ . The perturbative error is an order of magnitude larger than the one obtained in previous $ \mathcal{O}\left( {\alpha_s^3} \right) $ sum rule analyses.

Charmonium sum rules applied to a holographic model

The heavy-quark QCD sum rules are applied to a model of charmonium based upon the gauge/gravity duality. We find that there is strong agreement between the moments of the polarization function calculated from the holographic model and the experimental data suggesting that the model is consistent with the heavy-quark QCD sum rules at zero temperature.

Formula omitted] charm mass from charmonium sum rules with contour improvement

A detailed error analysis is carried out for the determination of the MS charm quark mass m̄c(m̄c) from moments at order αs2 of the charm cross section in e+e− annihilation. To estimate the theoretical uncertainties the renormalization scale is implemented in various ways including energy-dependent functions, which lead to “contour-improved” predictions. We obtain m̄c(m̄c)=1.29±0.07 GeV which contains a substantial theoretical uncertainty.

Gluon condensate andc-quark mass in pseudoscalar sum rules at 3-loop order

Charmonium sum rules for pseudoscalar 0^{-+} state eta_c(1S) are analyzed within perturbative QCD and Operator Product Expansion. The perturbative part of the pseudoscalar correlator is considered at alpha_s^2 order and the contribution of the gluon condensate <G^2> is taken into account with alpha_s correction. The OPE series includes the operators of dimension D=6,8 computed both in the instanton and factorization model. The method of moments in MS-bar scheme allows to establish acceptable values of the charm quark mass and gluon condensate, using the experimental mass of eta_c. In result of the analisys the charm quark mass is found to be m_c(m_c)=1.26+-0.02 GeV independently of the condensate value. The sensitivity of the results to various approximations for the massive 3-loop pseudoscalar correlator is discussed.

Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of dimension 4 gluon condensate. The moments M_n(Q^2) of the polarization operator of vector charm currents are calculated and compared with experimental data. The 3-loop (alpha_s^2) perturbative corrections, the gluon condensate contribution with alpha_s corrections and dimension 6 operator G^3 contribution are accounted. It is shown that the sum rules for the moments do not work at Q^2=0, where the perturbation series diverges and G^3 contribution is large. The domain in the plane (n, Q^2), where the sum rules are legitimate, is found. Strong correlation of the values of gluon condensate and MS-bar charm quark mass quark is determined. The absolute limits are found to be for gluon condensate <(alpha_s/pi)G^2>=0.009+-0.007 GeV^4 and for charm quark mass m(m)=1.275+-0.015 GeV in MS-bar scheme.

QCD charmonium sum rules up to O( G4) order

The results are presented for the O( G 4) power correction to QCD charmonium sum rules in the vector channel. It is shown that, under the standard assumptions concerning QCD vacuum structure, the inclusion of the O( G 4) terms radically changes the theoretical curve for the ratio r r , normally used to analyse the lowest charmonium states within the QCD sum rule approach.

Vacuum corrections to QCD charmonium sum rules: Basic formalism and O( G3) results

We present a detailed description of a new method for computing higher gluonic power corrections to QCD charmonium sum rules. The method is equivalent to using the Schwinger gauge ( x μ − z 0 μ ) A μ ( x)=0 for vacuum gluons. Results for O( G 2) and O( G 3) corrections are presented.

Charmonium sum rules andη c production in two-photon reactions

Charmonium sum rules andη c production in two-photon reactions

A method for computing higher gluonic power corrections to QCD charmonium sum rules

We propose a new method of calculating gluonic power corrections in QCD based on the Schwinger gauge x μ A μ ( x) = 0. Results of the calculation of the O( m c −6)-correction to the QCD charmonium sum rules are presented and discussed.

Analysis of the QCD sum rules for the heavy quarkonium

We study phenomenologically the QCD sum rules given by Shifman et al. for the heavy quarkonium. In the charmonium sum rules, we find that the contribution of the physical continuum to the moment ℳn is consistent with that of the effective one. As for the bottonium, the sum rules corrected by the Coulomb-like interaction are saturated very well by the four resonances observed at CESR. It is predicted that the3S1 ground state of the toponium must exist in the range of\(M_{t\bar t} \)=30–44GeV, if the sum rules for the top quark are assumed.

Quarkonium sum rules: A critical reappraisal

We reanalyze the ITEP charmonium sum rules incorporating experimental errors and allowing for variations in input parameters. The necessity of a gluon condensate term is apparent for the ratio sum rules, but the presence or absence of this term cannot be established using the moment sum rules. Plausibility arguments are given for trusting the results of the ratio sum rules and the advantages of mass-independent double ratio sum rules are stressed. Sum rules for the bottomonium system are also analyzed and the results are shown to be consistent with what is obtained in the charmonium sector.