Systematics in the XENON1T data: The 15-keV anti-axion

The XENON1T collaboration Aprile et al. [2020] has found an excess of electron recoil events in their Science Run 1 data below $\sim$7 keV with a spectral shape consistent with that expected from a solar-axion-induced signal. The claimed statistical significance of the solar-axion model over the null hypothesis is 3.5$\sigma$. In this work we provide suggestive evidence for mismodeling in the electron recoil data that may decrease the local significance of the axion model. To reach this conclusion, we search for a signal with the spectral template of the solar axion model, but shifted to higher (unphysical) energies above $\sim$7 keV. We find that the distribution of significances found from this side-band analysis does not follow the expected chi-square distribution. For example, we find a high-significance feature in the data, with a global $p$-value $p\approx 0.026$, when the solar axion model is shifted upwards in energy by $\sim$15 keV and allowed to have a negative normalization. We argue that such statistical tests, if performed a priori, provide a data-driven way to test and potentially account for systematic uncertainties on the background model in low-threshold dark matter experiments.