  Using a dataset corresponding to an integrated luminosity of 3.0 fb$^{-1}$
collected in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV, the
$B_s^0 \to \phi \phi$ branching fraction is measured to be \[ \mathcal{B}(B_s^0
\to \phi \phi) = ( 1.84 \pm 0.05 (\text{stat}) \pm 0.07 (\text{syst}) \pm 0.11
(f_s/f_d) \pm 0.12 (\text{norm}) ) \times 10^{-5}, \] where $f_s/f_d$
represents the ratio of the $B_s^0$ to $B^0$ production cross-sections, and the
$B^0 \to \phi K^*(892)^0$ decay mode is used for normalization. This is the
most precise measurement of this branching fraction to date, representing a
factor five reduction in the statistical uncertainty compared with the previous
best measurement. A search for the decay $B^0 \to \phi \phi$ is also made. No
signal is observed, and an upper limit on the branching fraction is set as \[
\mathcal{B}(B^0 \to \phi \phi) < 2.8 \times 10^{-8} \] at 90% confidence level.
This is a factor of seven improvement compared to the previous best limit.
