Energy resolution and linearity in the keV to MeV range measured in XENON1T

Xenon dual-phase time projection chambers designed to search for Weakly Interacting Massive Particles have so far shown a relative energy resolution which degrades with energy above $\sim$200 keV. This has limited their sensitivity in the search for rare events like the neutrinoless double-beta decay of $^{136}$Xe at its $Q$-value, $Q_{\beta\beta}\simeq$ 2.46 MeV. For the XENON1T dual-phase time projection chamber, we demonstrate that the relative energy resolution at 1 $\sigma/\mu$ is as low as (0.79$\pm$0.02) % in its one-ton fiducial mass, and for single-site interactions at $Q_{\beta\beta}$. We achieve this by using a signal correction method to rectify the saturation effects of the signal readout system. The very good energy resolution from keV to MeV energies demonstrated in XENON1T opens up new windows for the xenon dual-phase dark matter detectors to simultaneously search for other rare events.