Λ* = Λ(1405) plays an essential role in the formation of kaonic nuclear clusters (KNC). The simplest KNC, K-pp, has the structure Λ*p = (K-p)I=0p, in which a real kaon migrates between two nucleons, mediating super-strong Λ*p attraction. Production data of K-pp have been accumulated by DISTO, J-PARC E27 and J-PARC E15 experiments. For K-K-pp the attractive covalent bond of Λ*Λ* is doubly enhanced compared to the Λ*p one. Consequently, Λ* multiplet, (Λ*)m, with m(m-1)/2 bonds becomes more stable than its corresponding neutron aggregate, (n)m, at m = 8-12, suggesting the possible existence of stable Λ* matter. A long-lived strangelet of (Λ*)m=6 is presumed as a precursor. The production of K-K-pp by high-energy pp or heavy-ion collisions is awaited as a doorway to so-far unknown Λ* matter.
Keywords: anti-quarks in nuclei; kaonic nuclei; super-strong nuclear force; Λ* matter; Λ* strangelet.