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Search results for nucleon decays $p \rightarrow e^+X$, $p \rightarrow\mu^+X$, $n \rightarrow \nu\gamma$ (where $X$ is an invisible, masslessparticle) as well as dinucleon decays $np \rightarrow e^+\nu$, $np \rightarrow\mu^+\nu$ and $np \rightarrow \tau^+\nu$ in the Super-Kamiokande experiment arepresented. Using single-ring data from an exposure of 273.4 kton $\cdot$ years,a search for these decays yields a result consistent with no signal.Accordingly, lower limits on the partial lifetimes of $\tau_{p \rightarrowe^+X} > 7.9 \times 10^{32}$ years, $\tau_{p \rightarrow \mu^+X} > 4.1 \times10^{32}$ years, $\tau_{n \rightarrow \nu\gamma} > 5.5 \times 10^{32}$ years,$\tau_{np \rightarrow e^+\nu} > 2.6 \times 10^{32}$ years, $\tau_{np\rightarrow \mu^+\nu} > 2.2 \times 10^{32}$ years and $\tau_{np \rightarrow\tau^+\nu} > 2.9 \times 10^{31}$ years at a $90 \% $ confidence level areobtained. Some of these searches are novel.

Search for Nucleon and Dinucleon Decays with an Invisible Particle and a Charged Lepton in the Final State at the Super-Kamiokande Experiment