Feebly Interacting $U(1)_{\rm B-L}$ Gauge Boson Warm Dark Matter and
  XENON1T Anomaly
  The recent observation of an excess in the electronic recoil data by the
XENON1T detector has drawn many attentions as a potential hint for an extension
of the Standard Model (SM). Absorption of a vector boson with the mass of
$m_{A'}\!\in\!(2\,{\rm keV},\!3\,{\rm keV})$ is one of the feasible
explanations to the excess. In the case where the vector boson explains the
dark matter (DM) population today, it is highly probable that the vector boson
belongs to a class of the warm dark matter (WDM) due to its suspected mass
regime. In such a scenario, providing a good fit for the excess, the kinetic
mixing $\kappa\!\sim\!10^{-15}$ asks for a non-thermal origin of the vector DM.
In this letter, we consider a scenario where the gauge boson is nothing but the
$U(1)_{\rm B-L}$ gauge boson and its non-thermal origin is attributed to the
decay of the coherently oscillating scalar of which condensation induces the
spontaneous breaking of $U(1)_{\rm B-L}$. We discuss implications for the early
universe physics when the warm nature of the vector DM serves as a resolution
to both the small scale problems that $\Lambda$CDM model encounters and the
XENON1T anomaly.
