  We study the lifetime and weak decays of the full-heavy S-wave $0^+$
tetraquark $T^{\{bb\}}_{\{\bar c\bar c\}}$. Using the operator product
expansion rooted in heavy quark expansion, we find a rather short lifetime, at
the order $(0.1-0.3)\times 10^{-12}s$ depending on the inputs. With the flavor
SU(3) symmetry, we then construct the effective Hamiltonian at the hadron
level, and derive relations between decay widths of different channels.
According to the electro-weak effective operators, we classify different decay
modes, and make a collection of the golden channels, such as $T_{\{\bar c \bar
c\}}^{\{bb\}}\to B^- K^0 B_c^-$ for the charm quark decay and $T_{\{\bar c \bar
c\}}^{\{bb\}}\to B^-D^-$ for the bottom quark decay. Our results for the
lifetime and golden channels are helpful to search for the fully-heavy
tetraquark in future experiments.
