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We measured a set of $\pi^\pm\Sigma^\mp$, $\pi^0\Sigma^0$, and$\pi^-\Sigma^0$ invariant mass spectra below and above the $\bar{K}N$ massthreshold in $K^-$-induced reactions on deuteron. We deduced the $S$-wave$\bar{K}N\rightarrow\pi\Sigma$ and $\bar{K}N\rightarrow\bar{K}N$ scatteringamplitudes in the isospin 0 channel in the framework of a $\bar{K}N$ and$\pi\Sigma$ coupled channel. We find that a resonance pole corresponding to$\Lambda(1405)$ is located at 1417.7$^{+6.0}_{-7.4}$(fittingerrors)$^{+1.1}_{-1.0}$(systematic errors) + $[-26.1^{+6.0}_{-7.9}$(fittingerrors)$^{+1.7}_{-2.0}$(systematic errors)]$i$ MeV/$c^2$, closer to the$\bar{K}N$ mass threshold than the value determined by the Particle Data Group.

Pole position of $\Lambda(1405)$ measured in $d(K^-,n)\pi\Sigma$ reactions