Realistic models with a light U(1) gauge boson coupled to baryon number

We recently showed that a new gauge boson ${\gamma }_{\mathit{B}}$ coupling only to baryon number is phenomenologically allowed, even if ${\mathit{m}}_{\mathit{B}}$${\mathit{m}}_{\mathit{Z}}$ and ${\mathrm{\alpha }}_{\mathit{B}}$≊0.2. In our previous work we assumed that kinetic mixing between the baryon number and hypercharge gauge bosons (via an ${\mathit{F}}_{\mathit{B}}^{\mathrm{\mu }\nu }$ ${\mathit{F}}_{\mathrm{\mu }\nu }^{\mathit{Y}}$ term) was small enough to evade constraints from precision electroweak measurements. In this paper we propose a class of models in which this term is naturally absent above the electroweak scale. We show that the generation of a mixing term through radiative corrections in the low-energy effective theory does not lead to a conflict with precision electroweak measurements and may provide a leptonic signal for models of this type at an upgraded Fermilab Tevatron.