Observation of the decay $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ and evidence for $B^0\to \varphi {\pi }^{+}{\pi }^{-}$

The first observation of the rare decay$B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ and evidence for $B^0\to \varphi {\pi }^{+}{\pi }^{-}$ are reported, using $pp$ collision data recorded by the LHCb detector at centre-of-mass energies $\sqrt{s}=7$ and 8~TeV, corresponding to an integrated luminosity of $3f{b}^{-1}$. The branching fractions in the ${\pi }^{+}{\pi }^{-}$ invariant mass range $400<m({\pi }^{+}{\pi }^{-})<1600\mathrm{M}\mathrm{e}\mathrm{V}\text{\hspace{0.17em}⁣}\mathrm{/}{c}^2$ are $[3.48\pm 0.23\pm 0.17\pm 0.35]\times 10^{-6}$and$[1.82\pm 0.25\pm 0.41\pm 0.14]\times 10^{-7}$for$B^0_s \to \phi\pi^+\pi^-$and$B^0 \to \phi\pi^+\pi^-$ respectively, where the uncertainties are statistical, systematic and from the normalisation mode $B_s^0\to \varphi \varphi$. A combined analysis of the ${\pi }^{+}{\pi }^{-}$ mass spectrum and the decay angles of the final-state particles identifies the exclusive decays $B_s^0\to \varphi f_0(980)$, $B_s^0 \to \phi f_2(1270) $,and$B^0_s \to \phi\rho^0$withbranchingfractionsof$[1.12\pm 0.16^{+0.09}{-0.08}\pm 0.11]\times 10^{-6}$,$[0.61\pm 0.13^{+0.12}{-0.05}\pm 0.06]\times 10^{-6}$and$[2.7\pm 0.7\pm 0.2\pm 0.2]\times 10^{-7}$, respectively.