High precision in CKM unitarity tests in $b$ and $c$ decays

TL;DR

This paper reviews the current status and future prospects of high-precision tests of CKM matrix unitarity in $b$ and $c$ decays, emphasizing experimental and theoretical challenges and potential for discovering New Physics.

Contribution

It provides a comprehensive survey of CKM unitarity tests, discusses current anomalies, and evaluates future experimental upgrades and collider prospects for improved precision.

Findings

Current CKM anomalies identified

Projected precision improvements at LHCb and Belle II

Future collider opportunities for CKM tests

Abstract

This article surveys the important questions attached to unitarity tests of the Cabibbo-Kobayashi-Maskawa matrix, with a focus on the direct determinations of the magnitude of CKM matrix elements. The current CKM anomalies are discussed and the clear-cut prospects at LHCb and Belle II envisaged. The anticipated precision on $C\!P$-conserving and $C\!P$-violating observables at the projected upgrades of the LHCb and Belle~II experiments is examined from the point of view of the search for New Physics in $B$-meson mixing, addressing the bottlenecks in precision for the interpretation of the measurements for future experiments and highlighting the related theoretical and experimental challenges. The vibrant prospects at future $e^+e^-$ colliders running at the $Z^0$ pole and $W^+W^-$ are eventually discussed.