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Search for neutrinoless quadruple beta decay of $^{136}$Xe in XMASS-I

A search for the neutrinoless quadruple beta decay of $^{136}$Xe was conducted with the liquid-xenon detector XMASS-I using $\rm 327\; kg \times 800.0 \; days$ of the exposure. The pulse shape discrimination based on the scintillation decay time constant which distinguishes $γ$-rays including the signal and $β$-rays was used to enhance the search sensitivity. No significant signal excess was observed from the energy spectrum fitting with precise background evaluation, and we set a lower limit of the half life of 3.7 $\times$ 10$^{24}$ years at 90$\%$ confidence level. This is the first experimental constraint of the neutrinoless quadruple beta decay of $^{136}$Xe.