QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the M S 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 − 25 GeV 2 . 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 M S scheme at a scale of 3 GeV is mc(3 GeV) = 987 ± 9 MeV, where the error includes all sources of uncertainties added in quadrature. is based on inverse (Hilbert) moment QCD sum rules, requiring QCD knowledge of the vector correlator in the low energy, as well as in the high energy region. In [18] an alternative approach was used which involves only QCD information at short distances, together with (a) a simple integration kernel p(s) = 1 − s/s 0 (local constraint), and (b) Legendre-type polynomial kernels (global constraint). In this paper we describe an improved analysis based on the use of direct as well as inverse moment kernels of the form p(s) = 1 − (s 0 /s) n , with n ≥ 1.These kernels enhance considerably the impact of the well known narrow resonances, as compared with e.g. a simple kernel p(s) = 1/s 2 , or p(s) = 1 − s/s 0 . They also provide a welcome stronger suppression of the contribution of data in the range s ≃ 20 − 25 GeV 2 . In comparison with simple inverse moments without pinching, this means that results are less sensitive to assumptions about the onset of perturbative QCD (PQCD), as well as to the treatment of the higher resonance data. For instance, changes in s 0 in the range s 0 ≃ 15 − 23 GeV 2 lead to a variation in m c (3 GeV) of only 4 MeV (for n = 2) as opposed to a variation of 14 MeV for p(s) = 1/s 2 , as used in [17] We consider the vector current correlator Π µν (q 2 ) = i d 4 x e iqx 0|T (V µ (x) V ν (0))|0

Finite energy QCD sum rules involving both inverse and positive moment integration kernels are employed to determine the bottom quark mass. The result obtained in the MS scheme at a reference scale of 10 GeV is m b (10 GeV) = 3623(9) MeV. This value translates into a scale invariant mass m b (m b ) = 4171(9) MeV. This result has the lowest total uncertainty of any method, and is less sensitive to a number of systematic uncertainties that affect other QCD sum rule determinations.

Experimental data on the total cross section of e + e − annihilation into hadrons are confronted with QCD and the operator product expansion using finite energy sum rules. Specifically, the power corrections in the operator product expansion, i.e. the vacuum condensates, of dimension d = 2, 4 and 6 are determined using recent isospin I = 0 + 1 data sets. Reasonably stable results are obtained which are compatible within errors with values from τ -decay. However, the rather large data uncertainties, together with the current value of the strong coupling constant, lead to very large errors in the condensates. It also appears that the separation into isovector and isoscalar pieces introduces additional uncertainties and errors. In contrast, the high precision τ -decay data of the ALEPH collaboration in the vector channel allows for a more precise determination of the condensates. This is in spite of QCD asymptotics not quite been reached at the end of the τ spectrum. We point out that isospin violation is negligible in the integrated cross sections, unlike the case of individual channels.

The leading order hadronic contribution to the muon g-2, a HAD µ , is determined entirely from theory using an approach based on Cauchy's theorem in the complex squared energy s-plane. This is possible after fitting the integration kernel in a HAD µ with a simpler function of s. The integral determining a HAD µ in the light-quark region is then split into a low energy and a high energy part, the latter given by perturbative QCD (PQCD). The low energy integral involving the fit function to the integration kernel is determined by derivatives of the vector correlator at the origin, plus a contour integral around a circle calculable in PQCD. These derivatives are calculated using hadronic models in the light-quark sector. A similar procedure is used in the heavy-quark sector, except that now everything is calculable in PQCD, thus becoming the first entirely theoretical calculation of this contribution. Using the dual resonance model realization of Large Nc QCD to compute the derivatives of the correlator leads to agreement with the experimental value of aµ. Accuracy, though, is currently limited by the model dependent calculation of derivatives of the vector correlator at the origin. Future improvements should come from more accurate chiral perturbation theory and/or lattice QCD information on these derivatives, allowing for this method to be used to determine a HAD µ accurately entirely from theory, independently of any hadronic model.The value of the muon g-2 is well known as a test of the standard model (SM) of particle physics.[1]. The SM result for the anomalous magnetic moment of the muon is conveniently separated into the contributions due to QED, the hadronic sector, and the electroweak sector. A sizable theoretical uncertainty arises from the (leading order) hadronic vacuum polarization term, the second largest contribution after that of QED. A substantial effort has been made to determine this contribution from experimental data on e + e − → hadrons and τ → hadrons [2]- [3]. Currently, there is some yet unresolved discrepancy between both results. Writing the muon anomaly in the SM asthe leading contribution is that from QED, followed by the hadronic and the electroweak terms. In this paper we concentrate on the leading order hadronic contribution and discuss a new approach to its calculation entirely from theory. The method relies on Cauchy's theorem in the complex squared energy s-plane, after fitting the integration kernel entering a HAD µwith a simple function of s . In the region of the light-quark sector the method requires knowledge of some of the derivatives of the (electromagnetic) vector correlator at zero momentum, as well as its perturbative QCD (PQCD) behavior. Currently, these derivatives will be obtained here from hadronic models, thus being affected by systematic uncertainties. Hence, at this stage the method cannot rival in accuracy with the standard approach of using experimental data on the vector correlator at low/intermediate energies. However, future precision determinations of these ...

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