arXiv subjects
Publications and source records attributed to Tobias Hurth.
The Stueckelberg model for massive vector fields is cast into a BRS invariant, polynomial form. Its symmetry algebra simplifies to an abelian gauge symmetry which is sufficient to decouple the negative norm states. The propagators fall off like $1/k^2$ and the Lagrangean is polynomial but it is not powercounting renormalizable due to derivative couplings.
We consider a new MacDowell-Mansouri R^2-type of supergravity theory, an extension of conformal supergravity, based on the superalgebra Osp(1|8). Invariance under local symmetries with negative Weyl weight is achieved by imposing chirality-duality and double-duality constraints on curvatures, along with the usual constraint of vanishing supertorsion. An analysis of the remaining gauge symmetries shows that those with vanishing Weyl weight are invariances of the action at the linearized level. For the symmetries with positive Weyl weight we find that invariance of the action would require further modifications of the transformation rules. This conclusion is supported by a kinematical analysis of the closure of the gauge algebra.
We analyze nonabelian massive Higgs-free theories in the causal Epstein-Glaser approach. Recently, there has been renewed interest in these models. In particular we consider the well-known Curci-Ferrari model and the nonabelian Stückelberg models. We explicitly show the reason why the considered models fail to be unitary. In our approach only the asymptotic (linear) BRS-symmetry has to be considered.
The calculation of the $O(\a_s)$ virtual corrections to the matrix element of the inclusive decay $b \to s γ$ is reported. These contributions drastically reduce the large renormalization scale dependence of the leading logarithmic calculation. Combining these results with the preliminary result for the Wilson coefficient $C_7(m_b)$ calculated recently by Chetyrkin, Misiak, and Münz, we estimate the branching ratio to be $BR(B \to X_s γ)=(3.25 \pm 0.50) \times 10^{-4}$.
We present the causal construction of perturbative Yang-Mills theories in four(3+1)-dimensional space-time. We work with free quantum fields throughout. The inductive causal method by Epstein and Glaser leads directly to a finite perturbation series and does not rely on an intermediary regularization of the theory. The causal method naturally separates the physical infrared problem of massless theories from ultraviolet-sensitive features like normalizability by regarding the distributional character of the S-matrix. We prove the normalizability of the Yang-Mills theory with fermionic matter fields and study the discrete symmetry transformations in the causal formalism. We introduce a definition of nonabelian gauge invariance which only involves the free asymptotic field operators and give mathematically rigorous and conceptually simple proofs of nonabelian gauge invariance and of the physical unitarity of the S-matrix in all orders of perturbation theory.
We present in detail the calculation of the $O(\a_s)$ virtual corrections to the matrix element for $b \to s \g$. Besides the one-loop virtual corrections of the electromagnetic and color dipole operators $O_7$ and $O_8$, we include the important two-loop contribution of the four-Fermi operator $O_2$. By applying the Mellin-Barnes representation to certain internal propagators, the result of the two-loop diagrams is obtained analytically as an expansion in $m_c/m_b$. These results are then combined with existing $O(\a_s)$ Bremsstrahlung corrections in order to obtain the inclusive rate for $B \to X_s \g$. The new contributions drastically reduce the large renormalization scale dependence of the leading logarithmic result. Thus a very precise Standard Model prediction for this inclusive process will become possible once also the corrections to the Wilson coefficients are available.
We present some generalizations of a recently proposed alternative approach to nonabelian gauge theories based on the causal Epstein-Glaser method in perturbative quantum field theory. Nonabelian gauge invariance is defined by a simple commutator relation in every order of perturbation theory separately using only the linear (abelian) BRS-transformations of the asymptotic fields. This condition is sufficient for the unitarity of the S-matrix in the physical subspace. We derive the most general specific coupling compatible with the conditions of nonabelian gauge invariance and normalizability. We explicitly show that the quadrilinear terms, the four-gluon-coupling and the four-ghost-coupling, are generated by our linear condition of nonabelian gauge invariance. Moreover, we work out the required generalizations for linear gauges.
A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.