X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Strange-quark mass from tau-lepton decays with O(alpha3s) accuracy

The first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate is presented including its real part at the four-loop level. This allows us to perform the extraction of the strange-quark mass m(s) from the decay width of the tau-lepton with full O(alpha3s) accuracy. In agreement with previous estimates, the newly computed alpha3s term proves to be rather large. This justifies inclusion of the similarly estimated alpha4s term in phenomenological analysis. Combined with an updated value of V us and an "improved" version of the renormalization group improvement of the perturbative series, this leads to an increase of the central value of m(s) by about 20% and a partial reduction of the theoretical uncertainty by about 50%.     

Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD

New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass. Implications for the value of the quark masses are briefly discussed. PACS 12.38.Bx, 12.38.-t, 11.55.Fv, 14.65.Dw, 14.65.Fy     

Operator expansions in the minimal subtraction scheme. II. Explicit formulas for coefficient functions

Institute of Nuclear Research, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 76, No. 2, pp. 207–218, August, 1988.     

Four loop massless propagators: An algebraic evaluation of all master integrals

The old “glue-and-cut” symmetry of massless propagators, first established in Ref. [1] (Chetyrkin and Tkachov, 1981), leads — after reduction to master integrals is performed   — to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (ζ_2n${\zeta }_{2n}$) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.     

Order alphas4 QCD corrections to Z and tau decays

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alphas4 for the nonsinglet part of the cross section for electron-positron annihilation into hadrons and for the decay rates of the Z boson and the tau lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alphas, as extracted from these measurements, and to a small shift of the central value, moving the two central values closer together. The agreement between two values of alphas measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alphas(MZ)=0.1198+/-0.0015 as one of the most precise and presently only result for the strong coupling constant in order alphas4.     

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs) in pQCD

We present the results of the analytical evaluation of the massless four-loop

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(α³_s) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons. In numerical form we found (in

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scheme) that Γ (H →

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b ) = (3G_F/4

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π) M_Hm²_b (M_H) [1 + 5.667α_s/π + (35.94 − 1.359n_f) (α_s/π)² + (164.139 − 25.771n_f + 0.259n²_f) (α_s/π)³] where n_f is the number of quark flavour and α_s = α_s(M_H).