Loop integration results using numerical extrapolation for a non-scalar integral

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar four-point diagram. Extensions to accommodate loop integration by existing integration packages are also discussed. These include: using previously generated partitions of the domain and roundoff error guards.Comment: 4 pages, 3 figures, revised, contribution to ACAT03 (Dec. 2003

GRACE at ONE-LOOP: Automatic calculation of 1-loop diagrams in the electroweak theory with gauge parameter independence checks

We describe the main building blocks of a generic automated package for the calculation of Feynman diagrams. These blocks include the generation and creation of a model file, the graph generation, the symbolic calculation at an intermediate level of the Dirac and tensor algebra, implementation of the loop integrals, the generation of the matrix elements or helicity amplitudes, methods for the phase space integrations and eventually the event generation. The report focuses on the fully automated systems for the calculation of physical processes based on the experience in developing GRACE-loop. As such, a detailed description of the renormalisation procedure in the Standard Model is given emphasizing the central role played by the non-linear gauge fixing conditions for the construction of such automated codes. The need for such gauges is better appreciated when it comes to devising efficient and powerful algorithms for the reduction of the tensorial structures of the loop integrals. A new technique for these reduction algorithms is described. Explicit formulae for all two-point functions in a generalised non-linear gauge are given, together with the complete set of counterterms. We also show how infrared divergences are dealt with in the system. We give a comprehensive presentation of some systematic test-runs which have been performed at the one-loop level for a wide variety of two-to-two processes to show the validity of the gauge check. These cover fermion-fermion scattering, gauge boson scattering into fermions, gauge bosons and Higgs bosons scattering processes. Comparisons with existing results on some one-loop computation in the Standard Model show excellent agreement. We also briefly recount some recent development concerning the calculation of mutli-leg one-loop corrections.Comment: 131 pages. Manuscript expanded quite substantially with the inclusion of an overview of automatic systems for the calculation of Feynman diagrams both at tree-level and one-loop. Other additions include issues of regularisation, width effects and renormalisation with unstable particles and reduction of 5- and 6-point functions. This is a preprint version, final version to appear as a Phys. Re

Spectroscopic Constraints on the Surface Magnetic Field of the Accreting Neutron Star EXO 0748-676

Gravitationally redshifted absorption lines of Fe XXVI, Fe XXV, and O VIII were inferred recently in the X-ray spectrum of the bursting neutron star EXO 0748-676. We place an upper limit on the stellar magnetic field based on the iron lines. The oxygen absorption feature shows a multiple component profile that is consistent with Zeeman splitting in a magnetic field of ~(1-2)x10^9 gauss, and for which the corresponding Zeeman components of the iron lines are expected to be blended together. In other systems, a field strength >5x10^{10} gauss could induce a blueshift of the line centroids that would counteract gravitational redshift and complicate the derivation of constraints on the equation of state of the neutron star.Comment: 5 pages, submitted to Phys. Rev. Let

Cohomologically hyperbolic endomorphisms of complex manifolds

We show that if a compact Kahler manifold X admits a cohomologically hyperbolic surjective endomorphism then its Kodaira dimension is non-positive. This gives an affirmative answer to a conjecture of Guedj in the holomorphic case. The main part of the paper is to determine the geometric structure and the fundamental groups (up to finite index) for those X of dimension 3.Comment: International Journal of Mathematics (to appear

Kondo Problem and Related One-Dimensional Quantum Systems: Bethe Ansatz Solution and Boundary Conformal Field Theory

We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.Comment: 6 pages, no figure

Full one-loop electroweak radiative corrections to single Higgs production in e+ e-

We present the full ${{\cal O}}(\alpha)$ electroweak radiative corrections to single Higgs production in \epemt. This takes into account the full one-loop corrections as well as the effects of hard photon radiation. We include both the fusion and Higgs-strahlung processes. The computation is performed with the help of {\tt GRACE-loop} where we have implemented a generalised non-linear gauge fixing condition. The latter includes 5 gauge parameters that can be used for checks on our results. Besides the UV, IR finiteness and gauge parameter independence checks it proves also powerful to test our implementation of the 5-point function. We find that for a 500GeV machine and a light Higgs of mass 150GeV, the total ${{\cal O}}(\alpha)$ correction is small when the results are expressed in terms of $\alpha_{{\rm QED}}$. The total correction decreases slightly for higher energies. For moderate centre of mass energies the total ${{\cal O}}(\alpha)$ decreases as the Higgs mass increases, reaching -10% for $M_H=350$GeV and $\sqrt{s}=500$GeV. In order to quantify the genuine weak corrections we have subtracted the universal virtual and bremsstrahlung correction from the full ${{\cal O}}(\alpha)$. We find, for $M_H=150$GeV, a weak correction slowly decreasing from -2% to -4% as the energy increases from $\sqrt{s}=300$GeV to $\sqrt{s}=1$TeV after expressing the tree-level results in terms of $G_\mu$Comment: 16 pages, 3 figures. Only correction is a reference to a web-pag