Practical Algebraic Renormalization

TL;DR

This paper introduces a practical algebraic renormalization method that simplifies quantum correction calculations in quantum field theory, ensuring scheme-independent counterterms and demonstrating its effectiveness with Standard Model processes.

Contribution

It presents a new optimized algebraic renormalization approach that reduces computational effort and handles non-invariant regularization schemes effectively.

Findings

Reduces calculation complexity for quantum corrections.

Counterterms are universal and scheme-independent.

Successfully applied to Higgs decay and B-meson decay processes.

Abstract

A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process $B \to X_s \gamma$.