  The difference between baryon number B and lepton number L is the only
anomaly-free global symmetry of the Standard Model, easily promoted to a local
symmetry by introducing three right-handed neutrinos, which automatically make
neutrinos massive. The non-observation of any (B-L)-violating processes leads
us to scrutinize the case of unbroken gauged B-L; besides Dirac neutrinos, the
model contains only three parameters, the gauge coupling strength g', the
Stueckelberg mass $M_{Z'}$, and the kinetic mixing angle $\chi$. The new force
could manifest itself at any scale, and we collect and derive bounds on g' over
the entire testable range $M_{Z'}$ = 0 - $10^{13}$ eV, also of interest for the
more popular case of spontaneously broken B-L or other new light forces. We
show in particular that successful Big Bang nucleosynthesis provides strong
bounds for masses 10 eV < $M_{Z'}$ < 10 GeV due to resonant enhancement of the
rate $\bar{f} f \leftrightarrow \bar{\nu}_R \nu_R$. The strongest limits
typically arise from astrophysics and colliders, probing scales $M_{Z'}/g'$
from TeV up to $10^{10}$ GeV.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Experiment