Result of the search for neutrinoless double-$β$ decay in ¹⁰⁰Mo with the NEMO-3 experiment

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The NEMO-3 detector, which had been operating in the Modane Underground Laboratory from 2003 to 2010, was designed to search for neutrinoless double $β$ ($0νββ$) decay. We report final results of a search for $0νββ$ decays with $6.914$ kg of ¹⁰⁰Mo using the entire NEMO-3 data set with a detector live time of $4.96$ yr, which corresponds to an exposure of 34.3 kg·yr. We perform a detailed study of the expected background in the $0νββ$ signal region and find no evidence of $0νββ$ decays in the data. The level of observed background in the $0νββ$ signal region $[2.8-3.2]$ MeV is 0.44 ± 0.13 counts/yr/kg, and no events are observed in the interval $[3.2-10]$ MeV. We therefore derive a lower limit on the half-life of $0νββ$ decays in ¹⁰⁰Mo of T1/2(0νββ)> 1.1 × 10²⁴ yr at the $90%$ Confidence Level, under the hypothesis of light Majorana neutrino exchange. Depending on the model used for calculating nuclear matrix elements, the limit for the effective Majorana neutrino mass lies in the range m_ν < 0.33--$0.62$ eV. We also report constraints on other lepton-number violating mechanisms for $0νββ$ decays.