Abstract:
Inspired by the relation between the hadronic decay of the tau lepton and the electron-positron annihilation into hadrons, we derive new tests of perturbative QCD. We design a set of commensurate scale relations to test the self-consistency of leading-twist QCD predictions for any observable which defines an effective charge. This method provides renormalization scheme and scale invariant probes of QCD which can be applied over wide data ranges.

Abstract:
We construct new tests of perturbative QCD by considering a hypothetical tau lepton of arbitrary mass, which decays hadronically through the electromagnetic current. We can explicitly compute its hadronic width ratio directly as an integral over the e^+ e^- annihilation cross section ratio, R_{e^+e^-}. Furthermore, we can design a set of commensurate scale relations and perturbative QCD tests by varying the weight function away from the form associated with the V-A decay of the physical tau. This method allows the wide range of the R_{e^+e^-} data to be used as a probe of perturbative QCD.

Abstract:
The article describes the identification of hadronically decaying tau leptons in ppbar collisions at 1.96 TeV collected by the DZero detector at the Fermilab Tevatron. After a brief description of the motivations and the challenges of considering tau leptons in high energy hadronic collisions, details of the tau reconstruction and identification will be discussed. The challenges associated for tau energy measurements in an hadronic environment will be presented including approaches to deal with such measurements.

Abstract:
Sufficiently inclusive observables in the decay of the tau lepton can be calculated using the methods of perturbative QCD. These include the asymmetry parameter $A_\tau$ that determines that angular distribution of the total hadron momentum in the decay of a polarized tau. It should be possible to measure $A_\tau$ accurately using existing data from LEP. Reliable estimates of theoretical errors are essential in order to determine whether a given observable is sufficiently inclusive to be calculated using perturbative methods. The theoretical uncertainties due to higher orders in $\alpha_s$ can be estimated using recent calculations to all orders in the large-$(33-2N_f)$ limit. These estimates indicate that tau decay data can be used to determine $\alpha_s(M_Z)$ to a precision of 2% or better.

Abstract:
Hadronically decaying tau leptons are of prime importance in numerous physics analyses in ATLAS. The spectrum of the possible applications of hadronically decaying tau leptons reaches from Standard Model measurements, including Higgs searches, to searches for physics beyond the Standard Model. The basic principles behind the sophisticated tau reconstruction and identification techniques, which are specifically designed to identify hadronically decaying taus and reject various background processes, are delineated here along with current data-driven estimates of their respective performance.

Abstract:
Analytic expressions are given for the $\tau$ decays into three charged leptons, $\tau\rta \ell\ell\overline \ell\nu_\tau\overline \nu_\ell$, where the $\ell$ are combinations of electrons and muons, and for the radiative decays $\tau\rta \gamma\ell\nu_\tau\overline \nu_\ell$. The branching ratios are sensitive functions of whether the final state $\ell$ are muons or electrons.

Abstract:
We study the effects induced by excited leptons on the leptonic tau decay at one loop level. Using a general effective lagrangian approach to describe the couplings of the excited leptons, we compute their contributions to the leptonic decays and use the current experimental values of the branching ratios to put limits on the mass of excited states and the substructure scale.

Abstract:
Analytic formulae for the one-loop order QCD corrections to the differential width of the semileptonic b decay are given with the tau polarization taken into account. Thence the polarization of tau is expressed by its energy and the invariant mass of the tau + antineutrino system. The non-perturbative corrections by Falk et al. are incorporated in the calculation.

Abstract:
Supersymmetry is perhaps most effectively probed at the Tevatron through production and decay of weak gauginos. Most of the analyses of weak gaugino observables require electrons or muons in the final state. However, it is possible that the gauginos will decay primarily to tau leptons, thus complicating the search for supersymmetry. The motivating reasons for high tau multiplicity final states are discussed in three approaches to supersymmetry model building: minimal supergravity, gauge mediated supersymmetry breaking, and more minimal supersymmetry. The concept of ``e/mu/tau candidate'' is introduced, and an observable with three e/mu/tau candidates is defined in analog to the trilepton observable. The maximum mass reach for supersymmetry is then estimated when gaugino decays to tau leptons have full branching fraction.

Abstract:
In Run II of the CDF experiment, traditional dilepton triggers are enriched by lepton (electrons or muons) plus track, di-tau and tau plus missing transverse energy triggers at Level-3 dedicated to physical processes including tau leptons. We describe these triggers, along with their physics motivations, implementation and cross-sections and report on their initial performance.