Abstract:
In this thesis exact results on O(alpha^2) single bremsstrahlung corrections to low angle Bhabha scattering at LEP/SLC energies are given. The calculation represents the last outstanding theoretical second order subleading electroweak contribution for that process, needed to determine the experimental luminosity at second generation LEP detectors below the 0.1% precision threshold. The exact, fully differential result is obtained by employing analytical as well as computer-algebraic methods and includes terms up to O(0.05%) relative to the Born cross section. The initial output of over 20,000 terms could be reduced to 90, only 18 of which are shown to be numerically relevant and for which a simple logarithmic ansatz is derived, that is in remarkable agreement with the complete answer. Strong consistency checks are performed, including Ward-Takahashi identities and tests on the right infrared limit according to the Yennie, Frautschi and Suura program. Monte Carlo results for the integrated cross section are compared with existing calculations in the leading logarithmic approximation for a chosen set of experimental cuts. The size of the missing subleading terms is found to be small but non negligible in the context of setting stringent limits on Standard Model predictions and thus its realm of validity.

Abstract:
The infrared structure of spontaneously broken gauge theories is phenomenologically very important and theoretically a challenging problem. Various attempts have been made to calculate the higher order behavior of large double-logarithmic (DL) corrections originating from the exchange of electroweak gauge bosons resulting in contradictory claims. We present results from two loop electroweak corrections for the process $g \longrightarrow f_{\rm R} {\bar f}_{\rm L}$ to DL accuracy. This process is ideally suited as a theoretical model reaction to study the effect of the mass gap of the neutral electroweak gauge bosons at the two loop level. Contrary to recent claims in the literature, we find that the calculation performed with the physical Standard Model fields is in perfect agreement with the results from the infrared evolution equation method. In particular, we can confirm the exponentiation of the electroweak Sudakov logarithms through two loops.

Abstract:
The potential between infinitely heavy quarks in a color singlet state is of fundamental importance in QCD. While the confining long distance part is inherently non-perturbative, the short-distance (Coulomb-like) regime is accessible through perturbative means. In this paper we present new results of the short distance potential in coordinate space with quark masses through two loops. The results are given in explicit form based on reconstructed solutions in momentum space in the Euclidean regime. Thus, a comparison with lattice results in the overlap region between the perturbative and non-perturbative regime is now possible with massive quarks. We also discuss the definition of the strong coupling based on the force between the static sources.

Abstract:
In future collider experiments at the TeV scale, large logarithmic corrections originating from massive boson exchange can lead to significant corrections to observable cross sections. Recently double logarithms of the Sudakov-type were resummed for spontaneously broken gauge theories and found to exponentiate. In this paper we use the virtual contributions to the Altarelli-Parisi splitting functions to obtain the next to leading order kernel of the infrared evolution equation in the fixed angle scattering regime at high energies where particle masses can be neglected. In this regime the virtual corrections can be described by a generalized renormalization group equation with infrared singular anomalous dimensions. The results are valid for virtual electroweak corrections to fermions and transversely polarized vector bosons with an arbitrary number of external lines. The subleading terms are found to exponentiate as well and are related to external lines, allowing for a probabilistic interpretation in the massless limit. For $Z$-boson and $\gamma$ final states our approach leads to exponentiation with respect to each amplitude containing the fields of the unbroken theory. For longitudinal degrees of freedom it is shown that the equivalence theorem can be used to obtain the correct double logarithmic asymptotics. At the subleading level, corrections to the would be Goldstone bosons contribute which should be considered separately. Explicit comparisons with existing one loop calculations are made.

Abstract:
Recent investigations of electroweak radiative corrections have revealed the importance of higher order contributions in high energy processes, where the size of typical corrections can exceed those associated with QCD considerably. Beyond one loop, only universal (angular independent) corrections are known to all orders except for massless $e^+ e^- \longrightarrow f {\overline f}$ processes where also angular dependent corrections exist in the literature. In this paper we present general arguments for the consistent resummation of angular dependent subleading (SL) logarithmic corrections to all orders in the regime where all invariants are still large compared to the gauge boson masses. We discuss soft isospin correlations, fermion mass and gauge boson mass gap effects, the longitudinal and Higgs boson sector as well as mixing contributions including CKM effects for massive quarks. Two loop arguments are interpreted in the context of the effective high energy effective theory based on the Standard Model Lagrangian in the symmetric basis with the appropriate matching conditions to include the soft QED regime. The result is expressed in exponentiated operator form in a CKM-extended isospin space in the symmetric basis. Thus, a full electroweak SL treatment based on the infrared evolution equation method is formulated for arbitrary high energy processes at future colliders. Comparisons with known results are presented.

Abstract:
A physically defined QCD coupling parameter naturally incorporates massive quark flavor thresholds in a gauge invariant, renormalization scale independent and analytical way. In this paper we summarize recent results for the finite-mass fermionic corrections to the heavy quark potential through two loops leading to the numerical solution of the physical and mass dependent Gell-Mann Low function. The decoupling-, massless- and Abelian-limits are reproduced and an analytical fitting function is obtained in the V-scheme. Thus the gauge invariant mass dependence of $\alpha_V$ is now known through two loops. Possible applications in lattice analyses, heavy quark physics and effective charges are briefly discussed.

Abstract:
With the LEP II Higgs search approaching exclusion limits on low values of $\tan \beta \sim 2$ it becomes increasingly important to investigate physical quantities sensitive to large masses of a pseudoscalar Higgs mass. This regime is difficult and over a large range of $\tan \beta$ impossible to cover at the LHC proton proton collider. In this paper we focus on the achievable statistical precision of the Higgs decay into two photons at a future $\gamma \gamma$ collider (PLC) in the MSSM mass range below 130 GeV. The MSSM and SM predictions for $\Gamma (H \longrightarrow \gamma \gamma)$ can differ by up to 10 % even in the decoupling limit of large $m_A$. We summarize recent progress in both the theoretical understanding of the background process $\gamma \gamma \longrightarrow q \bar{q}$, $q=\{b,c\}$, and in the expected detector performance allow for a high accuracy of the lightest MSSM or SM Higgs boson decay into a $b \bar{b}$ pair. We find that for optimized but still realistic detector and accelerator assumptions, statistically a 1.4% accuracy is feasible after about four years of collecting data for a Higgs boson mass which excludes $\tan \beta <2$.

Abstract:
The partial Higgs width $\Gamma (H \longrightarrow \gamma \gamma)$ is important at the LHC for Higgs masses in the MSSM mass window up to 140 GeV as a relatively background free signal of a fundamental scalar. At the photon photon mode at the NLC it would be the Higgs production mechanism . Two loop QCD corrections exist for the fermionic contribution and in the case of the bottom loop large non-Sudakov double logarithms can be resummed to all orders and contribute up to 12 % compared to the t-quark. In more complicated Higgs sectors, such as in the MSSM, large $\tan \beta$ enhancements of bottom type Yukawa couplings can potentially dominate even the whole partial width. A main uncertainty in all existing calculations is the scale of the strong coupling as it is only renormalized at the three loop level. In this paper we include the exact two loop running coupling to all orders into the bottom contribution. We find that the effective scale is close to $\alpha_s (10 m_b^2)$.

Abstract:
In this talk \footnote{Presented at ICHEP'98, Vancouver, CA, July 1998}, we present a recently suggested way on how to analytically incorporate massive threshold effects into observables calculated in massless QCD. No matching is required since the renormalization scale is in this approach connected to the physical momentum transfer between static quarks in a color singlet state. We discuss massive fermionic corrections to the heavy quark potential through two loops. The calculation uses a mixed approach of analytical, computer-algebraic and numerical tools including Monte Carlo integration of finite terms. Strong consistency checks are performed by ensuring the proper cancellation of all non-local divergences by the appropriate counterterms and by comparing with the massless limit. The size of the effect for the (gauge invariant) fermionic part of $\alpha_V ({\bf q^2},m^2) $ relative to the massless case at the charm and bottom flavor thresholds is found to be of order 33%.

Abstract:
The loop induced coupling of an intermediate mass Higgs boson to two photons is a sensitive and unique measure for precision tests of physics beyond the Standard Model. In this work we summarize recent results on the expected precision of the partial $\Gamma (H \to \gamma \gamma)$ width at the $\gamma \gamma$ option of a future linear collider. Heavy particles do not decouple in general and differences between the SM and MSSM predictions or 2HD-models can differ in the percentile regime. Large non-Sudakov DL corrections need to be resummed and consistency requirements demand the use of the Sterman-Weinberg jet definition in order to avoid additional DL terms from three jet final states. We find that the well understood background process $\gamma \gamma \to q \bar{q}$ allows for a ${\mathcal O}$(2%) determination of $\Gamma (H \to \gamma \gamma)$ using conservative collider parameters. Recent improvements in the expected $\gamma \gamma$ luminosity suggest that the precision for the diphoton partial Higgs width can be further improved and is dominated by the error in BR($H \to b \bar{b}$) from the $e^\pm$ mode, which is presently estimated to be in the one percent regime.