A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature.Comment: 11 pages, no figures, published versio

Local and global duality and the determination of \alpha(M_Z)

This talk presents work concepts and results for the determination of the fine structure constant $\alpha$ at the $Z_0$ mass resonance. The problem consisting of the break-down of global duality for singular integral weights is circumvented by using a polynomial fit which mimics this weight function. This method is conservative in the sense that it is mostly independent of special assumptions. In this context the difference between local and global duality is explained.Comment: 8 pages in LaTeX using aipproc.cls (appended), 2 PostScript figures, talk given at the conference High Energy Physics at the Millennium (MRST'99), Ottawa, Canada, May 10-12, 1999, to appear in the proceeding

On the rigidity of back-to-back top quark pairs in e^+e^- annihilation

We consider the effect of gluon radiation on the energy of top/antitop quarks and on the anticollinearity of top-antitop quark pairs produced in $e^+e^-$ annihilation. Our results are presented in terms of the $E_q$-dependence of the $t\bar tg$ cross section and the dependence on the cosine of the opening angle $\theta_{12}$ between top and antitop for a center of mass energy of $\sqrt{q^2}=500 GeV$. We then go on to determine mean values for the top quark's energy as well as its longitudinal and transverse projections, and for the deviation of $\sin\theta_{12}$ and $\cos\theta_{12}$ from the anticollinearity limits $\sin\theta_{12}=0$ and $\cos\theta_{12}=-1$. For a center of mass energy of $500 GeV$ we obtain $=248.22 GeV$, $=247.24 GeV$ and $=4.70 GeV$. Thus, at this energy gluon radiation causes a total average energy loss of 0.71% of the top quark's energy. The average energy loss in the longitudinal direction is 1.06% and the average energy gain in the transverse direction is 1.88%. These percentage figures go up to 3.77%, 5.19% and 6.06%, respectively, at 1000\GeV. For the mean of the acollinearity angle $\bar\theta_{12}=180^0-\theta_{12}$ we obtain $=1.25^0$ at $500 GeV$, the value of which goes up to $4.62^0$ at $1000 GeV$. From an analysis of the transverse momentum of the top we find that the mean transverse momentum of the top stays close to the mean total momentum of the gluon in the energy range from threshold to $1000 GeV$ showing that the gluon momentum has a large mean transverse component in this energy range.Comment: 17 pages, 7 postscript figures, to appear in Nucl. Phys.

Variations of the high-level Balmer line spectrum of the helium-strong star Sigma Orionis E

Using the high-level Balmer lines and continuum, we trace the density structure of two magnetospheric disk segments of the prototypical Bp star sigma Ori E (B2p) as these segments occult portions of the star during the rotational cycle. High-resolution spectra of the Balmer lines >H9 and Balmer edge were obtained on seven nights in January-February 2007 at an average sampling of 0.01 cycles. We measured equivalent width variations due to the star occultations by two disk segments 0.4 cycles apart and constructed differential spectra of the migrations of the corresponding absorptions across the Balmer line profiles. We first estimated the rotational and magnetic obliquity angles. We then simulated the observed Balmer jump variation using the model atmosphere codes synspec/circus and evaluated the disk geometry and gas thermodynamics. We find that the two occultations are caused by two disk segments. The first of these transits quickly, indicating that the segment resides in a range of distances, perhaps 2.5-6R_star, from the star. The second consists of a more slowly moving segment situated closer to the surface and causing two semi-resolved absorbing maxima. During its transit this segment brushes across the star's "lower" limb. Judging from the line visibility up to H23-H24 during the occultations, both disk segments have mean densities near 10^{12} cm^{-3} and are opaque in the lines and continuum. They have semiheights less than 1/2 of a stellar radius, and their temperatures are near 10500K and 12000K, respectively. In all, the disks of Bp stars have a much more complicated geometry than has been anticipated, as evidenced by their (sometimes) non-coplanarity, de-centerness, and from star to star, differences in disk height.Comment: Accepted by Astron. Astrophys, 13 pages, 4 embedded figure