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We investigate a speculative short-distance force, proposed to explaindiscrepancies observed between measurements of certain neutral current decaysof $B$ hadrons and their Standard Model predictions. The force derives from aspontaneously 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 thirdfamily baryon number minus second family lepton number. The only fields beyondthose of the Standard Model are three right-handed neutrinos, a gauge fieldassociated with $U(1)_{B_3-L_2}$ and a Standard Model singlet complex scalarwhich breaks $U(1)_{B_3-L_2}$, a `flavon'. This simple model, via interactionsinvolving a TeV scale force-carrying $Z^\prime$ vector boson, can successfullyexplain the neutral current $B-$anomalies whilst accommodating other empiricalconstraints. 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 outthe 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, whichsubsequently decays into two Higgs bosons.

$U(1)_{B_3-L_2}$ Explanation of the Neutral Current $B-$Anomalies