The difference between baryon number B and lepton number L is the only
anomalyfree global symmetry of the Standard Model, easily promoted to a local
symmetry by introducing three righthanded neutrinos, which automatically make
neutrinos massive. The nonobservation of any (BL)violating processes leads
us to scrutinize the case of unbroken gauged BL; 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 BL 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 $overline{f} f leftrightarrow overline{nu}_R nu_R$. The strongest
limits typically arise from astrophysics and colliders, probing scales
$M_{Z'}/g'$ from TeV up to $10^{10}$ GeV.
