Abstract: The running charm-quark mass in the scheme is determined from weighted finite energy QCD sum rules involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of s, the squared energy. The optimal kernels are found to be a simple pinched kernel and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s plane, and the latter allows us to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e. g. inverse moments finite energy sum rules. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the finite energy sum rules, together with the latest experimental data. The integration in the complex s plane is performed using three different methods: fixed order perturbation theory, contour improved perturbation theory, and a fixed renormalization scale mu. The final result is (m) over bar (c)(3 GeV) = 1008 +/- 26 MeV, in a wide region of stability against changes in the integration radius s(0) in the complex s plane.

Abstract: The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, delta(pi), the value delta(pi) = (6.2 +/- 1.6)%. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate < 0 vertical bar(u) over baru vertical bar 0 > similar or equal to < 0 vertical bar(d) over bard vertical bar 0 > < 0 vertical bar(q) over barq vertical bar 0 >vertical bar(2GeV) = (-267 +/- 5MeV)(3). As a byproduct, the chiral perturbation theory (unphysical) low energy constant H-2(r) is predicted to be H-2(r)(nu(X) = M-p) = -(5.1 +/- 1.8) x10(-3), or H-2(r) (nu(X) = M-eta) = -(5.7 +/- 2.0) x10(-3).

Abstract: QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the (MS) over bar 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 -(s(0)/s)(2), where s(0) 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 similar or equal to 20-25 GeV2. This feature leads to a substantial reduction in the sensitivity of the results to changes in s(0), 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) over bar scheme at a scale of 3 GeV is (m) over bar (c)(3 GeV) = 987 +/- 9 MeV, where the error includes all sources of uncertainties added in quadrature.

Abstract: The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and three fermion generations as part of the framed gauge theory (FGT) structure, is here developed further to show that it gives both quarks and leptons hierarchical masses and mixing matrices akin to what is experimentally observed. Among its many distinguishing features which lead to the above results are (i) the vacuum is degenerate under a global su(3) symmetry which plays the role of fermion generations, (ii) the fermion mass matrix is “universal,” rank-one and rotates (changes its orientation in generation space) with changing scale mu, (iii) the metric in generation space is scale-dependent too, and in general nonflat, (iv) the theta-angle term in the quantum chromodynamics (QCD) action of topological origin gets transformed into the CP-violating phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix for quarks, thus offering at the same time a solution to the strong CP problem.

Abstract: It is shown that if, from the starting point of a universal rank-one mass matrix long favored by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only six real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles theta(12), theta(13), theta(23) in nu-oscillation, and the masses m(c), m(mu), m(e)) agree well with experiment, mostly to within experimental errors; four others (m(s), m(u), m(d), m(nu 2)), the experimental values for which can only be inferred, agree reasonably well; while two others (m(nu 1), delta(CP) for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass m(nu R) and (ii) the strong CP angle theta inherent in QCD. One notes in particular that the output value for sin(2) 2 theta(13) from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit two new testable constraints: (i) that theta(23) must depart from its “maximal” value: sin(2) 2 theta(23) similar to 0.935 +/- 0.021, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only vertical bar sin delta(CP)vertical bar <= 0.31 if not vanishing altogether.