EFT Approach of Inelastic Dark Matter for Xenon Electron Recoil
  Detection
  Measuring dark matter (DM) signals via electron recoil provides an important
means for direct detection of light DM particles. The recent XENON1T anomaly
with electron recoil energy around $\,E_R^{}\!=\!(2-3)$keV can be naturally
explained by DM inelastic scattering which injects energy to the recoiled
electrons and gives a narrow peak structure in the recoil spectrum. We present
an effective field theory (EFT) approach to exothermic inelastic DM signals for
the Xenon electron recoil detection. For relatively heavy mediator, we fairly
formulate the DM-lepton interactions by effective contact operators with two DM
fields $(X,\,X')$ and two leptons. Using the XENON1T data, we fit the electron
recoil spectrum and constrain the allowed scalar DM mass-splitting as
$\,2.1\,\text{keV}\!<\!\Delta m\!<\!3.3\,\text{keV}$ (95%C.L.), with the best
fit $\,\Delta m \!=\! 2.8$keV. We analyze the relic abundance produced by such
effective DM-electron contact interaction. To provide both the DM relic
abundance and the XENON1T excess, we derive new constraints on the DM mass and
the UV cutoff scale of DM effective interactions. Finally, we study possible UV
completions for the effective DM-lepton contact interactions.
