We present results on the search for two-neutrino double-electron capture ($2\nu \text{ECEC}$) of ${}^{124}\mathrm{Xe}$ and neutrinoless double-$\beta$ decay ($0\nu \beta \beta$) of ${}^{136}\mathrm{Xe}$ in XENON1T. We consider captures from the $K$ shell up to the $N$ shell in the $2\nu \text{ECEC}$ signal model and measure a total half-life of $T_{1/2}^{2\nu \text{ECEC}}=(1.1\pm 0.2_{\text{stat}}\pm 0.1_{\text{sys}})\times {10}^{22}\text{yr}$ with a $0.87\text{kg}\text{yr}$ isotope exposure. The statistical significance of the signal is $7.0\sigma$. We use XENON1T data with $36.16\text{kg}\text{yr}$ of ${}^{136}\mathrm{Xe}$ exposure to search for $0\nu \beta \beta$. We find no evidence of a signal and set a lower limit on the half-life of $T_{1/2}^{0\nu \beta \beta }>1.2\times {10}^{24}\text{yr}\text{at}90\%\text{CL}$. This is the best result from a dark matter detector without an enriched target to date. We also report projections on the sensitivity of XENONnT to $0\nu \beta \beta$. Assuming a $275\text{kg}\text{yr} {}^{136}\mathrm{Xe}$ exposure, the expected sensitivity is $T_{1/2}^{0\nu \beta \beta }>2.1\times {10}^{25}\text{yr}\text{at}90\%\text{CL}$, corresponding to an effective Majorana mass range of $\langle m_{\beta \beta }\rangle <(0.19–0.59)\mathrm{eV}/c^2$.

• Received 10 May 2022
• Accepted 20 July 2022

DOI:https://doi.org/10.1103/PhysRevC.106.024328

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Published by the American Physical Society