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

It is possible, and for several reasons attractive, to explain a collection of recent anomalies involving $b\to s\mu \mu$ processes with a $Z^{\mathrm{\prime }}$ 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 $Z^{\mathrm{\prime }}$ 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 $Z^{\mathrm{\prime }}$ 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.