Measurement of the ${B^0_s \to \phi \phi}$ branching fraction and angular analysis of ${B^0_{(s)} \to \phi \pi^{+}\pi^{-}}$.

Using 3~fb$^{-1}$ of $pp$ collisions collected by the LHCb detector at $\sqrt{s} = 7$ and 8~TeV, the $B_s^0 \to \phi \phi$ branching fraction is measured to be \[ \mathcal{B}(B^0_s \to \phi \phi) = \left[ 1.84 \pm 0.05 (\mathrm{stat}) \pm 0.07 (\mathrm{syst}) \pm 0.11 (f_s/f_d) \pm 0.12 (\mathrm{norm}) \right] \times 10^{-5}. \] 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 \[ \mathcal{B}(B^0 \to \phi \phi) < 2.8 \times 10^{-8}. \] The rare decays $B_s^0 \to \phi \pi^+ \pi^-$ and $B^0 \to \phi \pi^+ \pi^-$ are observed for the first time. The branching fractions in the range $400<m(\pi^+ \pi^-)<1600$~MeV/$c^{2}$ are measured to be \[ \mathcal{B}(B_s^0 \to \phi \pi^+ \pi^-) = \left[ 3.37 \pm 0.20 (\mathrm{stat}) \pm 0.16 (\mathrm{syst}) \pm 0.34 (\mathrm{norm}) \right] \times 10^{-6} \] \[\mathcal{B}(B^0 \to \phi \pi^+ \pi^-) = \left[ 1.58 \pm 0.18 (\mathrm{stat}) \pm 0.35 (\mathrm{syst}) \pm 0.13 (\mathrm{norm}) \right] \times 10^{-7}. \] An amplitude fit is performed to extract the following exclusive branching fractions: \[ \mathcal{B}(B_s^0 \to \phi f_0(980) \to \phi \pi^+ \pi^-) = \left[ 1.12 \pm 0.16 (\mathrm{stat}) ^{+0.07}_{-0.14} (\mathrm{syst}) \pm 0.11 (\mathrm{norm}) \right] \times 10^{-6} \] \[ \mathcal{B}(B_s^0 \to \phi f_2(1270) \to \phi \pi^+ \pi^-) = \left[ 0.55 \pm 0.10 (\mathrm{stat}) ^{+0.18}_{-0.05} (\mathrm{syst}) \pm 0.06 (\mathrm{norm}) \right] \times 10^{-6}. \] Evidence is found for the decay $B_s^0 \to \phi \rho^0$. An upper limit on the branching fraction is set as \[ \mathcal{B}(B_s^0 \to \phi \rho^0) < 4 \times 10^{-7}. \]