Two-loop renormalisation in UED models

TL;DR

This paper derives two-loop renormalisation group equations for gauge and Yukawa couplings in a five-dimensional Standard Model compactified on an orbifold, focusing on brane-localized matter fields, and compares these results to one-loop calculations.

Contribution

It provides the first detailed derivation of two-loop RGEs in UED models with brane-localized matter fields, extending previous one-loop analyses.

Findings

Two-loop corrections significantly affect coupling evolution.

The evolution of       is analyzed.

Comparison shows notable differences from one-loop results.

Abstract

The evolution equations of the gauge and Yukawa couplings are derived for the two-loop renormalisation group equations in a five-dimensional SM compactified on a $S^1/Z_2$ to yield standard four space-time dimensions. Different possibilities can be discussed, however, we shall consider the limiting case in which all matter fields are localised on the brane. We will compare our two-loop results to the results found at one-loop level, and investigate the evolution of $\sin^2 \theta_W$ in this scenario also.