Search for the decay $B^0\to\phi\mu^+\mu^-$

A search for the decay $B^0\to\phi\mu^+\mu^-$ is performed using proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV collected by the LHCb experiment and corresponding to an integrated luminosity of 9 fb$^{-1}$. No evidence for the $B^0\to \phi \mu^+ \mu^-$ decay is found and an upper limit on the branching fraction, excluding the $\phi$ and charmonium regions in the dimuon spectrum, of $4.4 \times 10^{-3}$ at a 90$\%$ credibility level, relative to that of the $B^0_s \to \phi \mu^+ \mu^-$ decay, is established. Using the measured $B^0_s\to\phi\mu^+\mu^-$ branching fraction and assuming a phase-space model, the absolute branching fraction of the decay $B^0\to \phi \mu^+ \mu^-$ in the full $q^2$ range is determined to be less than $3.2 \times 10^{-9}$ at a 90$\%$ credibility level.