Renormalization Group Treatment of Nonrenormalizable Interactions

The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. Explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the na\"ive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms.Comment: LaTex, 11 page

Mass enhancement, correlations, and strong coupling superconductivity in the beta-pyrochlore KOs2O6

To assess electron correlation and electron-phonon coupling in the recently discovered beta-pyrochlores KOs2O6 and RbOs2O6, we have performed specific heat measurements in magnetic fields up to 14 T. We present data from high quality single crystalline KOs2O6, showing that KOs2O6 is a strong coupling superconductor with a coupling parameter lambda_ep \approx 1.0 to 1.6 (RbOs2O6: lambda_ep \approx 1). The estimated Sommerfeld coefficient of KOs2O6, gamma=76 to 110 mJ/(mol K^2), is twice that of RbOs2O6 [gamma=44 mJ/(mol K^2)]. Using strong-coupling corrections, we extract useful thermodynamic parameters of KOs2O6. Quantifying lambda_ep allows us to determine the mass enhancement over the calculated band electronic density of states. A significant contribution in addition to the electron-phonon term of lambda_c=1.7 to 4.3 is deduced. In an effort to understand the origin of the enhancement mechanism, we also investigate an unusual energetically low-lying phonon. There are three phonon modes per RbOs2O6, suggestive of the phonon source being the rattling motion of the alkali ion. This dynamic instability of the alkali ions causes large scattering of the charge carriers which shows up in an unusual temperature dependence of the electrical resistivity.Comment: Accepted for publication in PR

The Mellin moments of deep inelastic structure functions at two loops

We perform the analytic calculation of the Mellin moments of the structure functions F_2 and F_L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F_2 and F_L. Our results are in agreement with earlier calculations in the literature.Comment: 4 pages LaTeX, talk given at the QCD 99 Euroconference, Montpellier (France