Matching the Weak Mixing Angle at Low Energies

TL;DR

This paper proposes a new method for matching the weak mixing angle at the W-boson threshold by comparing the full Standard Model with an effective low-energy theory, improving the connection between different energy scale measurements.

Contribution

It introduces a novel matching condition at the W-boson threshold by comparing the full Standard Model to a low-energy effective theory for better precision in electroweak calculations.

Findings

Derived a new matching relation at the W-boson threshold.

Improved the consistency between high and low energy measurements of the weak mixing angle.

Enhanced the theoretical framework for electroweak precision tests.

Abstract

The running weak mixing angle is used as a convenient tool to keep control of dominating logarithmic corrections in the Standard Model of the electroweak interactions connecting measurements at largely differing energy scales. To relate the solutions of the renormalization group equation for the weak mixing angle above and below particle thresholds one needs matching conditions. We suggest to define the matching at the W-boson threshold by comparing the full Standard Model with a low-energy effective theory where the weak neutral current, in particular for parity-violating fermion scattering, is described by 4-fermion operators and calculate the corresponding matching relation.