Large $t\to cZ$ as a Sign of Vector-Like Quarks in Light of the $W$ Mass

TL;DR

This paper explores how vector-like quarks can simultaneously produce a sizable $t\to cZ$ decay rate and explain the recent $W$ mass measurement anomaly, providing specific predictions for branching ratios.

Contribution

It identifies three vector-like quark representations capable of enhancing $t\to cZ$ decay and shifting the $W$ mass, consistent with experimental bounds, using one-loop effective field theory calculations.

Findings

$Br(t\to cZ)$ can reach up to $10^{-4}$ for certain vector-like quarks.

All three quark representations can account for the $W$ mass anomaly.

The models remain consistent with $B$ physics constraints.

Abstract

The rare flavour changing top quark decay $t\to cZ$ is a clear sign of new physics and experimentally very interesting due to the huge number of top quarks produced at the LHC. However, there are few (viable) models which can generate a sizable branching ratio for $t\to cZ$ -- in fact vector-like quarks seem to be the only realistic option. In this paper, we investigate all three representations (under the Standard Model gauge group) of vector-like quarks ($U$, $Q_1$ and $Q_7$) that can generate a sizable branching ratio for $t\to cZ$ without violating bounds from $B$ physics. Importantly, these are exactly the three vector-like quarks which can lead to a sizable positive shift in the prediction for $W$ mass, via the couplings to the top quark also needed for a sizable Br($t\to cZ$). Calculating and using the one-loop matching of vector-like quarks on the Standard Model Effective Field Theory, we find that Br($t\to cZ$) can be of the order of $10^{-6}$, $10^{-5}$ and $10^{-4}$ for $U$, $Q_1$ and $Q_7$, respectively and that in all three cases the large $W$ mass measurement can be accommodated.