We study a doubly-bottomed tetra-quark state (bbuΛdΛ) with
quantum number I(JP)=0(1+), denoted by Tbbβ, in lattice QCD with the
Non-Relativistic QCD (NRQCD) quark action for b quarks. Employing
(2+1)-flavor gauge configurations at aβ0.09 {fm} on 323Γ64
lattices, we have extracted the coupled channel potential between
BΛBΛβ and BΛβBΛβ in the HAL QCD method, which
predicts an existence of a bound Tbbβ below the BΛBΛβ
threshold. By extrapolating results at mΟββ410,570,700 {MeV}
to the physical pion mass mΟββ140 {MeV}, we obtain a biding energy
with its statistical error as Ebinding(single)β=155(17) MeV
and Ebinding(coupled)β=83(10) MeV, where ``coupled" means that
effects due to virtual BΛβBΛβ states are included through the
coupled channel potential, while only a potential for a single
BΛBΛβ channel is used in the analysis for ``single". A comparison
shows that the effect from virtual BΛβBΛβ states is quite
sizable to the binding energy of Tbbβ. We estimate systematic errors to be
Β±20 MeV at most, which are mainly caused by the NRQCD approximation for
b quarks.Comment: 27 pages, 8 figure