Constraints on the $U(1)_L$ gauge boson in a wide mass range

There is a growing interest for the search of new light gauge bosons. The small mass of a new boson can turn various kinds of low-energy experiments to a new discovery machine, depending on their couplings to the standard model particles. It is important to understand the properties of each type of gauge boson and their current constraints for a given mass. While the dark photon (which couples to the electric charges) and the $U(1)_{B-L}$ gauge boson have been well studied in an extensive mass range, the $U(1)_L$ gauge boson has not been fully investigated yet. We consider the gauge boson of the $U(1)_L$ in a wide mass range $m_{Z'} \approx 0 - 10^{12} ~\ev$ and investigate the constraints on its coupling from various experiments, discussing the similarities and differences from the dark photon and the $U(1)_{B-L}$ gauge boson.