Study of the $K^-pp$ bound state in the FINUDA experiment

The possible existence of antikaon-nuclear bound states has been suggested by many theoretical studies in this decade, after the first quantitative calculations on few-body systems by Akaishi and Yamazaki [Phys. Rev. C 65, 044005 (2002)]. Experimental searches, including reanalyses of old experiments, on such a bound state has been carried out in several institutes up to now. The FINUDA experiment also investigated the existence of light kaonic nuclei, produced by stopped $K^-$ absorption. It was carried at a $\phi$-factory DA$\Phi$NE at INFN-LNF (Italy), which supplies very slow kaons ($\sim 16\,\mathrm{MeV}$) as decay particles of $\phi$ mesons produced by the electron-positron collision. In 2005, we reported the first result on the invariant mass spectrum of back-to-back $\Lambda$-p pairs, emitted from light nuclear targets [Phys. Rev. Lett. 94, 212303 (2005)]. Their invariant mass distributes far below the $K^-+p+p$ threshold around $2.37\,\mathrm{GeV}/c^2$, and we proposed a possibility that a $K^-pp$ bound state with its binding energy $\sim 115\,\mathrm{MeV}$ and width $\sim 67\,\mathrm{MeV}$ was produced by kaon absorption, and decayed into a $\Lambda$ and a proton. However, there are alternative interpretations on the $\Lambda$-$p$ invariant-mass spectrum, such as the effect of final state interaction, pointed out by Magas \textit{et al.} [Phys. Rev. C 74, 025206 (2006)] In order to distinguish them experimentally, we analyzed three kinds of back-to-back hyperon-nucleon pairs ($\Lambda$-$p$, $\Lambda$-$n$, $\Sigma^-$-$p$) with about one order of magnitude more statistics taken in 2006--2007. We observed a large difference, especially between the $\Lambda$-$p$ and $\Lambda$-$n$ pairs, with regard to the distribution near the threshold. It may originate from a strong isospin dependence of $\overline{K}N$ interaction, and reinforce the assumption of the $K^-pp$ production in kaon absorption. In this talk, the current status of the analysis on hyperon-nucleon pairs will be presented.