Search for neutrinoless quadruple-$\beta$ decay of $^{150}$Nd with the NEMO-3 detector

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We report the results of a first experimental search for lepton number violation by four units in the neutrinoless quadruple-$\beta$ decay of $^{150}$Nd using a total exposure of $0.19$ kg$\cdot$y recorded with the NEMO-3 detector at the Modane Underground Laboratory (LSM).

• We find no evidence of this decay and set lower limits on the half-life in the range $T_{1/2}>(1.1-3.2)\times10^{21}$ y at the $90\%$ CL, depending on the model used for the kinematic distributions of the emitted electrons.