Determination of the gluon condensate from data in the charm-quark region

The gluon condensate, $langle frac{alpha_s}{pi} G^2 rangle$, i.e. the leading order power correction in the operator product expansion of current correlators in QCD at short distances, is determined from $e^+ e^-$ annihilation data in the charm-quark region. This determination is based on finite energy QCD sum rules, weighted by a suitable integration kernel to (i) account for potential quark-hadron duality violations, (ii) enhance the contribution of the well known first two narrow resonances, the $J/psi$ and the $psi(2S)$, while quenching substantially the data region beyond, and (iii) reinforce the role of the gluon condensate in the sum rules. By using a kernel exhibiting a singularity at the origin, the gluon condensate enters the Cauchy residue at the pole through the low energy QCD expansion of the vector current correlator. These features allow for a reasonably precise determination of the condensate, i.e. $langle frac{alpha_s}{pi} G^2 rangle =0.037 ,pm, 0.015 ;{mbox{GeV}}^4$.

Light quark masses from QCD sum rules with minimal hadronic bias

The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are $m_u(Q= 2 {GeV}) = 2.9 pm 0.2 {MeV}$, $m_d(Q= 2 {GeV}) = 5.3 pm 0.4 {MeV}$, and $m_s(Q= 2 {GeV}) = 102 pm 8 {MeV}$, for $Lambda = 381 pm 16 {MeV}$, corresponding to $alpha_s(M_tau^2) = 0.344 pm0.009$. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2 - 3 %. The remaining uncertainties above arise from those in $Lambda$, the unknown six-loop PQCD contribution, and the gluon condensate, which are all potentially subject to improvement.

Strange quark condensate from QCD sum rules to five loops

It is argued that it is valid to use QCD sum rules to determine the scalar and pseudoscalar two-point functions at zero momentum, which in turn determine the ratio of the strange to non-strange quark condensates $R_{su} = frac{<bar{s} s>}{<bar{q} q>}$ with ($q=u,d$). This is done in the framework of a new set of QCD Finite Energy Sum Rules (FESR) that involve as integration kernel a second degree polynomial, tuned to reduce considerably the systematic uncertainties in the hadronic spectral functions. As a result, the parameters limiting the precision of this determination are $Lambda_{QCD}$, and to a major extent the strange quark mass. From the positivity of $R_{su}$ there follows an upper bound on the latter: $bar{m_{s}} (2 {GeV}) leq 121 (105) {MeV}$, for $Lambda_{QCD} = 330 (420) {MeV} .$

Determination of QCD condensates from tau-decay data

We have used the latest data from the ALEPH Collaboration to extract values for QCD condensates up to dimension d=12 in the V-A channel and up to dimension d=8 in the V, A and V+A channels. Performing 2- and 3-parameter fits, we obtain new results for the correlations of condensates. The results are consistent among themselves and agree with most of the previous results found in the literature.