Smooth Threshold Effects from Dimensional Regularization

TL;DR

This paper introduces a non-minimal dimensional regularization scheme that naturally incorporates heavy particle threshold effects, providing a smooth transition across energy scales while maintaining gauge independence.

Contribution

It proposes a mass-dependent renormalization scheme based on dimensional regularization that improves threshold behavior over traditional schemes.

Findings

Scheme reduces to minimal subtraction at high energies.

Provides smooth threshold effects in QCD calculations.

Maintains gauge independence similar to minimal subtraction.

Abstract

We suggest a non-minimal renormalization scheme based on dimensional regularization that naturally incorporates threshold effects of heavy particles. By renormalizing couplings and masses to subtract all poles in $d \geq 4$, the resulting scheme is mass-dependent and circumvents shortcomings of mass-independent schemes like minimal subtraction. At the same time, many advantages of minimal subtraction such as gauge independence are retained. Through explicit one-loop computations in QCD, we demonstrate that this scheme reduces to minimal subtraction at high energies while providing smooth transitions at particle thresholds and implementing the Appelquist-Carazzone theorem. Potential future applications and extensions are discussed.