Measurement of the mesonic decay branch of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:math> quasibound state

We conducted measurements of ${K}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}\ensuremath{\pi}YN+{N}^{\ensuremath{'}}$ reactions using a $1\phantom{\rule{4pt}{0ex}}\mathrm{GeV}/c\phantom{\rule{4pt}{0ex}}{K}^{\ensuremath{-}}$-beam, with the objective of understanding the broad decay width of $\overline{K}NN$ (approximately twice as broad as that of $\mathrm{\ensuremath{\Lambda}}(1405)$ considered to be the $\overline{K}N$ quasibound state). We successfully reproduced distributions of the $\ensuremath{\pi}YN$ invariant mass and momentum transfer for $\ensuremath{\pi}YN$ using model-fitting functions for $\overline{K}NN$ formation and quasifree $\overline{K}$ absorption (${\mathrm{QF}}_{\overline{K}\ensuremath{-}\mathrm{abs}}$) processes. The model can describe the experimental data quite well, and four $\overline{K}NN\ensuremath{\rightarrow}\ensuremath{\pi}YN$ cross sections were obtained. The results indicate that mesonic decay is the dominant decay branch of $\overline{K}NN$. The results also suggest that ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\pi}\mathrm{\ensuremath{\Lambda}}N}\ensuremath{\approx}{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\pi}\mathrm{\ensuremath{\Sigma}}N}$, which indicates that the ${I}_{\overline{K}N}=1$ absorption channel, in addition to the ${I}_{\overline{K}N}=0$ absorption channel, substantially contributes to the $\overline{K}NN$ decay, making the $\overline{K}NN$ state approximately twice as unstable as $\mathrm{\ensuremath{\Lambda}}$(1405).

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