Connecting neutral current $B$ anomalies with the heaviness of the third family

TL;DR

This paper proposes a model where a $Z'$ gauge boson coupled only to the third family explains $B$ anomalies and the heaviness of the third family, with anomaly cancellation fixing the charge assignment and phenomenological constraints shaping the model.

Contribution

It introduces a Third Family Hypercharge Model with anomaly cancellation conditions that uniquely determine fermion charges, linking $B$ anomalies to third family mass hierarchy.

Findings

The model explains $b ightarrow s\mu\mu$ anomalies with a $Z'$ boson.

Anomaly cancellation fixes fermion charge assignments proportional to hypercharge.

Phenomenological constraints restrict the model's parameter space.

Abstract

It is possible, and for several reasons attractive, to explain a collection of recent anomalies involving $b\rightarrow s\mu\mu$ processes with a $Z^{\prime}$ gauge boson coupled only to the third family in the weak eigenbasis. From this premise, requiring cancellation of all gauge anomalies (including mixed and gravitational anomalies) fixes a unique charge assignment for the third family Standard Model fermions, which is simply proportional to hypercharge. After a brief discussion of some general features of anomaly cancellation in $Z^\prime$ theories, we discuss the phenomenology of such a `Third Family Hypercharge Model', which is subject to a trio of important constraints: (i) $B_s-\bar{B}_s$ mixing, (ii) lepton universality of the $Z$ boson couplings, and (iii) constraints from direct searches for the $Z^\prime$ boson at the LHC. Finally, in gauging third family hypercharge, this model forbids all Yukawa couplings (at the renormalisable level) save those of the third family, leading to a possible explanation of the heaviness of the third family.