Complete Corrections of O(\alpha\alpha_s) to the Decay of the Z Boson into Bottom Quarks

For the vertex corrections to the partial decay rate $\Gamma(Z \to b\bar{b})$ involving the top quark only the leading terms of order $\alpha\alpha_s$ in the $1/M_t$ expansion are known. In this work we compute the missing next-to-leading corrections. Thus at $O(\alpha\alpha_s)$ the complete corrections to the decay of the Z boson into bottom quarks are at hand.Comment: Latex, 11 pages, 1 figure included as ps-file. Two references changed. The complete paper is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp97/ttp97-52/ or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

Nest Site Characteristics and Breeding Biology of Flammmulated Owls in Missoula Valley

Seidensticker, Mathew, M.S., Spring 2011 Environmental Studies Nest Sites and Breeding Biology of Flammulated Owls in Missoula Valley Chairperson: Len Broberg The Flammulated Owl is listed as a sensitive or species of concern with United States Forest Service, Bureau of Land Management, and Montana Fish, Wildlife and Parks. Despite these listings the Flammulated Owl is little studied in Montana. Although region-wide surveys have greatly increased our understanding of distribution and landscape level habitat associations of Flammulated Owls, information about breeding is lacking. In order to address this need for breeding information I searched for and quantified nest site characteristics and breeding biology of Flammulated Owls in Missoula Valley from 2008-2010. I located 17 Flammulated Owl territories, four nests, and banded 12 individuals. I also utilized radio telemetry to help gather information about roosting and foraging habitat. Although our sample size is limited, nest site characteristics and breeding parameters in my study were within the range of information published by other authors for Flammulated Owl nests. Much more information about Flammulated Owl breeding biology is needed to comprehensively assess the status of this owl species and build scientifically responsible models for managing habitat in Montana

Dimensional Reduction applied to QCD at three loops

Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the $\beta$ function and the anomalous dimension of the quark masses are derived to three-loop order. Special emphasis is put on the proper treatment of the so-called $\epsilon$-scalars and the additional couplings which have to be considered.Comment: 13 pages, minor changes, references adde

The four-loop DRED gauge beta-function and fermion mass anomalous dimension for general gauge groups

We present four-loop results for the gauge beta-function and the fermion mass anomalous dimension for a gauge theory with a general gauge group and a multiplet of fermions transforming according to an arbitrary representation, calculated using the dimensional reduction scheme. In the special case of a supersymmetric theory we confirm previous calculations of both the gauge beta-function and the gaugino mass beta-function.Comment: 44 pages, added references (v2) minor changes (v3

Two-loop parameter relations between dimensional regularization and dimensional reduction applied to SUSY-QCD

The two-loop relations between the running gluino-quark-squark coupling, the gluino and the quark mass defined in dimensional regularization (DREG) and dimensional reduction (DRED) in the framework of SUSY-QCD are presented. Furthermore, we verify with the help of these relations that the three-loop beta-functions derived in the minimal subtraction scheme combined with DREG or DRED transform into each other. This result confirms the equivalence of the two schemes through three-loops, if applied to SUSY-QCD.Comment: 14 pages, Latex; v2 matches published versio

Strong-Coupling Constant at Three Loops in Momentum Subtraction Scheme

In this paper we compute the three-loop corrections to the $\beta$ function in a momentum subtraction (MOM) scheme with a massive quark. The calculation is performed in the background field formalism applying asymptotic expansions for small and large momenta. Special emphasis is devoted to the relation between the coupling constant in the MOM and $\overline{\rm{MS}}$ schemes as well as their ability to describe the phenomenon of decoupling. It is demonstrated by an explicit comparison that the $\overline{\rm{MS}}$ scheme can be consistently used to relate the values of the MOM-scheme strong-coupling constant in the energy regions higher and lower than the massive-quark production threshold. This procedure obviates the necessity to know the full mass dependence of the MOM $\beta$ function and clearly demonstrates the equivalence of both schemes for the description of physics outside the threshold region.Comment: 17 pages, 5 figure

Four-Loop Decoupling Relations for the Strong Coupling

We compute the matching relation for the strong coupling constant within the framework of QCD up to four-loop order. This allows a consistent five-loop running (once the $\beta$ function is available to this order) taking into account threshold effects. As a side product we obtain the effective coupling of a Higgs boson to gluons with five-loop accuracy.Comment: 11 page