On the Stability of $\mathrm{\Lambda }(1405)$ Matter

A hypothesis of absolutely stable strange hadronic matter composed of $\mathrm{\Lambda }(1405)$ baryons, here denoted ${\mathrm{\Lambda }}^{\ast }$, is tested within many-body calculations performed using the Relativistic Mean-Field approach. In our calculations, we employed the ${\mathrm{\Lambda }}^{\ast }{\mathrm{\Lambda }}^{\ast }$ interaction compatible with the ${\mathrm{\Lambda }}^{\ast }{\mathrm{\Lambda }}^{\ast }$ binding energy $B_{{\mathrm{\Lambda }}^{\ast }{\mathrm{\Lambda }}^{\ast }}=40$~MeV given by the phenomenological energy-independent $\bar{K}N$ interaction model by Yamazaki and Akaishi (YA). We found that the binding energy per ${\mathrm{\Lambda }}^{\ast }$, as well as the central density in ${\mathrm{\Lambda }}^{\ast }$ many-body systems saturates for mass number $A\ge 120$, leaving ${\mathrm{\Lambda }}^{\ast }$ aggregates highly unstable against strong interaction decay. Moreover, we confronted the YA interaction model with kaonic atom data and found that it fails to reproduce the $K^{-}$ single-nucleon absorption fractions at rest from bubble chamber experiments.