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 ^ { \prime } , the Stückelberg mass M _ { Z ^ { \prime } } , and the kinetic mixing angle \chi . The new force could manifest itself at any scale , and we collect and derive bounds on g ^ { \prime } over the entire testable range M _ { Z ^ { \prime } } = 0 – 10 ^ { 13 } \mathrm { 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 \mathrm { eV } < M _ { Z ^ { \prime } } < 10 \mathrm { 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 ^ { \prime } } / g ^ { \prime } from TeV up to 10 ^ { 10 } \mathrm { GeV } .