Radiative Corrections to the CKM Unitarity Triangles

TL;DR

This paper investigates how radiative corrections affect the angles and sides of CKM unitarity triangles across energy scales, finding that the angles, especially lpha, are remarkably stable.

Contribution

It provides a detailed calculation of the running effects on CKM triangle parameters using one-loop renormalization-group equations, highlighting their stability.

Findings

All nine angles are stable against radiative corrections.

The CP-violating angle lpha is particularly insensitive to energy scale changes.

The study covers effects from electroweak to very high-energy scales.

Abstract

The 3 X 3 CKM matrix defines six unitarity triangles in the complex plane, which will be carefully explored in the LHCb experiment and at the Super-B factory. We calculate the running effects of nine different inner angles and eighteen different sides of the six triangles from the electroweak scale to a superhigh-energy scale by using the one-loop renormalization-group equations, and demonstrate that all the nine angles are stable against radiative corrections. In particular, we find that the CP-violating angle \alpha is most insensitive to the changes of energy scales.