  The baryon-baryon interactions with strangeness S = -2 with the flavor SU(3)
breaking are calculated for the first time by using the HAL QCD method extended
to coupled channel system in lattice QCD. The potential matrices are extracted
from the Nambu-Bethe-Salpeter wave functions obtained by the 2+1 flavor gauge
configurations of CP-PACS/JLQCD Collaborations with a physical volume of 1.93
fm cubed and with m_pi/m_K = 0.96, 0.90, 0.86. The spatial structure and the
quark mass dependence of the potential matrix in the baryon basis and in the
SU(3) basis are investigated.
