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We recently showed that a new gauge boson $\gamma_B$ coupling only to baryonnumber is phenomenologically allowed, even if $m_B<m_Z$ and $\alpha_B \approx0.2$. In our previous work we assumed that kinetic mixing between the baryonnumber and hypercharge gauge bosons (via an $F^{\mu\nu}_B F_{\mu\nu}^Y$ 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 naturallyabsent above the electroweak scale. We show that the generation of a mixingterm through radiative corrections in the low-energy effective theory does notlead to conflict with precision electroweak measurements and may provide aleptonic signal for models of this type at an upgraded Tevatron.Comment: 21 pages, LaTeX, 4 figures in a uuencoded compressed postscript file

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