The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization

We calculate the two-mass contribution to the 3-loop vacuum polarization of the gluon in Quantum Chromodynamics at virtuality $p^2 = 0$ for general masses and also present the analogous result for the photon in Quantum Electrodynamics.Comment: 5 pages Late

Hall effect in laser ablated Co_2(Mn,Fe)Si thin films

Pulsed laser deposition was employed to grow thin films of the Heusler compounds Co_2MnSi and Co_2FeSi. Epitaxial growth was realized both directly on MgO (100) and on a Cr or Fe buffer layer. Structural analysis by x-ray and electron diffraction shows for both materials the ordered L2_1 structure. Bulk magnetization was determined with a SQUID magnetometer. The values agree with the Slater-Pauling rule for half-metallic Heusler compounds. On the films grown directly on the substrate measurements of the Hall effect have been performed. The normal Hall effect is nearly temperature independent and points towards a compensated Fermi surface. The anomalous contribution is found to be dominated by skew scattering. A remarkable sign change of both normal and anomalous Hall coefficients is observed on changing the valence electron count from 29 (Mn) to 30 (Fe).Comment: 9 pages, 6 figures submitted to J Phys

Testing gravity at the Second post-Newtonian level through gravitational deflection of massive particles

Expression for second post-Newtonian level gravitational deflection angle of massive particles is obtained in a model independent framework. Several of its important implications including the possibility of testing gravitational theories at that level are discussed.Comment: 5 pages, couple of equations of the previous version are correcte

A Note on Asymptotic Freedom at High Temperatures

This short note considers, within the external field approach outlined in hep-ph/0202026, the role of the lowest lying gluon Landau mode in QCD in the high temperature limit. Its influence on a temperature- and field-dependent running coupling constant is examined. The thermal imaginary part of the mode is temperature-independent in our approach and exactly cancels the well-known zero temperature imaginary part, thus rendering the Savvidy vacuum stable. Combining the real part of the mode with the contributions from the higher lying Landau modes and the vacuum contribution, a field-independent coupling alpha_s(T) is obtained. It can be interpreted as the ordinary zero temperature running coupling constant with average thermal momenta \approx 2pi T for gluons and \approx pi T for quarks.Comment: 4 pages; minor changes, version to appear in Phys. Rev.

The two-mass contribution to the three-loop pure singlet operator matrix element

We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function $F_2(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.Comment: 28 papges Latex, 3 figure

The weakly perturbed Schwarzschild lens in the strong deflection limit

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.Comment: 12 pages, 1 figure