Improved search for two-neutrino double electron capture on $^{124}$Xe and $^{126}$Xe using particle identification in XMASS-I

We conducted an improved search for the simultaneous capture of two $K$-shell electrons on the $^{124}$Xe and $^{126}$Xe nuclei with emission of two neutrinos using 800.0 days of data from the XMASS-I detector. A novel method to discriminate $\gamma$-ray/$X$-ray or double electron capture signals from $\beta$-ray background using scintillation time profiles was developed for this search. No significant signal was found when fitting the observed energy spectra with the expected signal and background. Therefore, we set the most stringent lower limits on the half-lives at $2.1 \times 10^{22}$ and $1.9 \times 10^{22}$ years for $^{124}$Xe and $^{126}$Xe, respectively, with 90% confidence level. These limits improve upon previously reported values by a factor of 4.5.