Techniques for the calculation of electroweak radiative corrections at the one-loop level and results for W-physics at LEP200 (0709.1075v1)

Abstract: We review the techniques necessary for the calculation of virtual electroweak and soft photonic corrections at the one-loop level. In particular we describe renormalization, calculation of one-loop integrals and evaluation of one-loop Feynman amplitudes. We summarize many explicit results of general relevance. We give the Feynman rules and the explicit form of the counter terms of the electroweak standard model, we list analytical expressions for scalar one-loop integrals and reduction of tensor integrals, we present the decomposition of the invariant matrix element for processes with two external fermions and we give the analytic form of soft photonic corrections. These techniques are applied to physical processes with external W-bosons. We present the full set of analytical formulae and the corresponding numerical results for the decay width of the W-boson and the top quark. We discuss the cross section for the production of W-bosons in e^{+}e^{-}-annihilaton including all O(alpha) radiative corrections and finite width effects. Improved Born approximations for these processes are given.

• The paper develops one-loop radiative correction techniques by detailing renormalization and tensor reduction to enhance precision in electroweak calculations.
• It reports robust numerical results for W decay widths and pair production cross sections, emphasizing the influence of top and Higgs masses.
• The study establishes a standardized approach for collider experiments, supporting the validation and refinement of the electroweak Standard Model.

Overview of Electroweak Radiative Corrections and W-Physics Techniques

The paper, authored by A. Denner, presents a comprehensive examination of the methodologies required to calculate electroweak radiative corrections at the one-loop level and demonstrates their implications in W-physics at LEP200. It offers an intricate exploration of renormalization, loop integral calculations, and the assessment of Feynman amplitudes, integral to understanding processes with external W bosons. The discourse includes detailed representation of the counterterms in the electroweak standard model and provides Feynman rules, alongside an analytical foundation of the loop integrals and reduction of tensor integrals essential for these computations.

Key Techniques and Methodologies

The paper delineates several crucial techniques:

• Renormalization: This process ensures that divergences in the computed quantities, particularly in the electroweak theory, are managed by redefining the theory's parameters. The paper explicates the renormalization constants and conditions, specifically detailing the on-shell scheme.
• One-Loop Integrals: The paper outlines definitions and reduction strategies for one-loop integrals. It expresses these integrals in terms of scalar functions and elaborates on the dimensional regularization used to manage divergences. Explicit results for scalar integrals like the one-point, two-point, three-point, and four-point functions are offered.
• Calculation of Amplitudes: The examination covers the algebraic reduction of Feynman diagrams to standard matrix elements coupled with form factors, facilitating systematic calculation of loop corrections.

Core Results and Analysis

The application of these techniques to W decay and pair production is particularly emphasized. The paper provides robust numerical results for W boson decay widths, integrating electroweak and QCD corrections. It discusses the corrections in the context of various fermion masses, underscoring the importance of considering higher-order effects for precision.

• W Decay and Widths: Detailed numerical evaluations within the SM are presented, taking into account the strong interaction effects, with specific focus given to the influence of top and Higgs boson masses on the decay widths.
• W-Pair Production Cross Section: Attention is given to the precision required in predicting the cross section at LEP200 energies, which is vital for understanding gauge boson interactions. The inclusion of finite width effects and photonic corrections is critical to accurately capture the experimental scenarios.

Theoretical and Practical Implications

The research suggests substantial implications:

• Precision in Electroweak Theory: The methodology establishes a standardized approach for precision calculations of electroweak processes, which are fundamental to testing the SM against experimental data.
• Impacts on Collider Physics: This work is pivotal in refining predictions for experiments at colliders such as LEP200, endorsing the validity of the electroweak theory under diverse energy scales and contributing to the exploration of phenomena like gauge boson self-interactions.
• Prospective Developments: Looking forward, the methodologies can be adapted to investigate complex processes anticipated at future colliders, potentially unveiling new physics beyond the current SM framework.

Concluding Remarks

The paper stands as a comprehensive guide on the one-loop electroweak radiative corrections, with practical applications in high-energy physics experiments. The analytical frameworks and numerical insights presented are indispensable tools for researchers exploring the precision physics of the electroweak sector and exploring its limits through current and future experimental endeavors. The detailed examination of renormalization, along with systematic calculation strategies, exhibits potential utility for further validation and enhancement of the SM or probing uncharted theoretical territories.