arXiv subjects
Publications and source records attributed to Karl Schilcher.
A method used previously to calculate the masses of the vector mesons is extended to the calculation of the nucleon resonances. The method is based on the choice of integration kernels which eliminate the unknown parts of the spectrum. We obtain remarkably stable results in a wide range of R, the radius of the integration contour in the complex plane. Agreement with experiment is good.
We present a calculation of the masses of the isovector mesons ( vector, scalar and pseudoscalar including the established recurrences) using a new method of finite energy QCD sum rules. The method is based on the idea of choosing a suitable integration kernel which minimizes the occurring integral over the cut in the complex energy (squared) plane. We obtain remarkably stable results in a wide range R, where R is the radius of the integration contour. The sum rule predictions agree with the experimental values within the expected accuracy showing that QCD describes single resonances.
A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown 1=2+ and 1=2- continuum. This approach avoids the arbitrariness and instability attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling. For standard values of the condensates, the prediction of the nucleon mass in the chiral limit is mN = (830+/-50)MeV. With the pion-nucleon sigma-term given by chiral perturbation theory and the strange sigma-term estimated by the Zweig rule we get mN = (990+/-50)MeV.
The strange quark mass is determined from a QCD Finite Energy Sum Rule (FESR) optimized to reduce considerably the systematic uncertainties arising from the hadronic resonance sector, as well as from the poor convergence of the pseudoscalar correlator in perturbative QCD. The former is achieved by introducing a suitable integration kernel in the Cauchy integral in the complex squared energy plane. The latter is obtained by optimizing the perturbative expansion to accelerate its convergence. The result for the strange quark mass in the $\bar{MS}$ scheme at a scale of 2 GeV is m_s(2 GeV) = (94 \pm 9)MeV.
The strange quark mass is determined from a new QCD Finite Energy Sum Rule (FESR) optimized to reduce considerably the systematic uncertainties arising from the hadronic resonance sector. As a result, the main uncertainty in this determination is due to the value of $Λ_{QCD}$. The correlator of axial-vector divergences is used in perturbative QCD to five-loop order, including quark and gluon condensate contributions, in the framework of both Fixed Order (FOPT), and Contour Improved Perturbation Theory (CIPT). The latter exhibits very good convergence, leading to a remarkably stable result in the very wide range $s_0 = 1.0 - 4.0 {GeV}^2$, where $s_0$ is the radius of the integration contour in the complex energy (squared) plane. The value of the strange quark mass in this framework at a scale of 2 GeV is $m_s(2 {GeV}) = 95 \pm 5 (111 \pm 6) {MeV}$ for $Λ_{QCD} = 420 (330) {MeV}$, respectively.
The saturation of QCD chiral sum rules is reanalyzed in view of the new and complete analysis of the ALEPH experimental data on the difference between vector and axial-vector correlators (V-A). Ordinary finite energy sum rules (FESR) exhibit poor saturation up to energies below the tau-lepton mass. A remarkable improvement is achieved by introducing pinched, as well as minimizing polynomial integral kernels. Both methods are used to determine the dimension d=6 and d=8 vacuum condensates in the Operator Product Expansion, with the results: {O}_{6}=-(0.00226 \pm 0.00055) GeV^6, and O_8=-(0.0053 \pm 0.0033) GeV^8 from pinched FESR, and compatible values from the minimizing polynomial FESR. Some higher dimensional condensates are also determined, although we argue against extending the analysis beyond dimension d = 8. The value of the finite remainder of the (V-A) correlator at zero momentum is also redetermined: Π(0)= -4 \bar{L}_{10}=0.02579 \pm 0.00023. The stability and precision of the predictions are significantly improved compared to earlier calculations using the old ALEPH data. Finally, the role and limits of applicability of the Operator Product Expansion in this channel are clarified.
We use both old and new theoretical developments in QCD dispersion relation constraints on the scalar form factor in the decay K --> πl ν_l to obtain constraints on the strange quark mass. The perturbative QCD side of the calculation incorporates up to four-loop corrections, while the hadronic side uses a recently developed parameterization constructed explicitly to satisfy the dispersive constraints. Using chiral perturbation theory (\chiPT) as a model for soon-to-be measured data, we find a series of lower bounds on m_s increasing with the accuracy to which one believes \chiPT to represent the full QCD result.
The lepton-flavour-violating decay K_L --> e μis studied in detail within the context of SU(2)_R x SU(2)_L x U(1)_(B-L) models, which include heavy Majorana neutrinos. Particular attention is paid to the gauge independence of this decay process to one loop. In analogy with earlier studies on the K^0\bar{K}^0 mixing, it is explicitly shown how restoration of gauge invariance occurs in the decay amplitude containing the box diagrams, when the relevant Higgs-dependent self-energy and vertex graphs are taken into account in the on-shell skeleton renormalization scheme. Based on the analytic expressions so derived, we find that the branching ratio B(K_L --> e μ) can be considerably enhanced due to the presence of left- and right-handed currents in the loop, and can reach values close to or even larger than the present experimental limit 3.3 x 10^{-11} in the manifest left-right symmetric model. Constraints on the parameter space of typical left-right models are derived from the possible decay K_L --> e μand a global analysis of other low-energy data.