  We investigate a speculative short-distance force, proposed to explain
discrepancies observed between measurements of certain neutral current decays
of $B$ hadrons and their Standard Model predictions. The force derives from a
spontaneously broken, gauged $U(1)_{B_3-L_2}$ extension to the Standard Model,
where the extra quantum numbers of Standard Model fields are given by third
family baryon number minus second family lepton number. The only fields beyond
those of the Standard Model are three right-handed neutrinos, a gauge field
associated with $U(1)_{B_3-L_2}$ and a Standard Model singlet complex scalar
which breaks $U(1)_{B_3-L_2}$, a `flavon'. This simple model, via interactions
involving a TeV scale force-carrying $Z^\prime$ vector boson, can successfully
explain the neutral current $B-$anomalies whilst accommodating other empirical
constraints. In an ansatz for fermion mixing, a combination of up-to-date
$B-$anomaly fits, LHC direct $Z^\prime$ search limits and other bounds rule out
the domain 0.15 TeV$< M_{Z^\prime} <$ 1.9 TeV at the 95$\%$ confidence level.
For more massive $Z^\prime$s, the model possesses a {\em flavonstrahlung}\
signal, where $pp$ collisions produce a $Z^\prime$ and a flavon, which
subsequently decays into two Higgs bosons.
