Fully analytical O(\alpha_s) results for on-shell and off-shell polarized W-boson decays into massive quark pairs

We provide analytical $O(\alpha_s)$ results for the three polarized decay structure functions $H_{++},\,H_{00}$ and $H_{--}$ that describe the decay of a polarized $W$ boson into massive quark--antiquark pairs. As an application we consider the decay $t\to b+W^+$ involving the helicity fractions $\rho_{mm}$ of the $W^+$ boson followed by the polarized decay \hbox{W^+(\uparrow)}\to q_1\bar{q}_2 described by the polarized decay structure functions $H_{mm}$. We thereby determine the $O(\alpha_s)$ polar angle decay distribution of the cascade decay process $t\to b+W^+(\to q_1\bar{q}_2)$. As a second example we analyze quark mass and off-shell effects in the cascade decays $H\to W^{-}+W^{\ast +}(\to q_1\bar{q}_2)$ and $H\to Z+Z^{\ast}(\to q\bar{q})$. For the decays $H\to W^{-}+W^{\ast +}(\to c\bar b)$ and $H\to Z+Z^{\ast}(\to b\bar{b})$ we find substantial deviations from the mass-zero approximation in particular in the vicinity of the threshold region.Comment: 56 pages, 15 figures and 2 table

The Rigidly Rotating Magnetosphere of Sigma Ori E

We attempt to characterize the observed variability of the magnetic helium-strong star sigma Ori E in terms of a recently developed rigidly rotating magnetosphere model. This model predicts the accumulation of circumstellar plasma in two co-rotating clouds, situated in magnetohydrostatic equilibrium at the intersection between magnetic and rotational equators. We find that the model can reproduce well the periodic modulations observed in the star's light curve, H alpha emission-line profile, and longitudinal field strength, confirming that it furnishes an essentially correct, quantitative description of the star's magnetically controlled circumstellar environment.Comment: 4 pages, 3 figures, accepted by Ap

Non-Abelian gauge theories with composite fields in the background field method

Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green's functions for a Yang--Mills theory with composite and background fields are introduced, including the generating functional of vertex Green's functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and utilized on a systematic basis. On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov--Zwanziger theory, including the case of a local BRST-invariant horizon, and by the Volovich--Katanaev model of two-dimensional gravity with dynamical torsion.Comment: 42 pages, presentation improved, Section 5 with Loop expansion added, subsection 6.3 with Local BRST Invariant Horizon Term with composite and background fields and 7 references added, summary improve