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 center-of-mass energies $\sqrt{s}=7$ and 8 TeV, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$. The branching fractions in the ${\pi }^{+}{\pi }^{-}$ invariant mass range $400<m({\pi }^{+}{\pi }^{-})<1600\mathrm{MeV}/c^2$ 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 $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ and $B^0\to \varphi {\pi }^{+}{\pi }^{-}$ respectively, where the uncertainties are statistical, systematic and from the normalization 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 $B_s^0\to \varphi f_0(980)$, $B_s^0\to \varphi f_2(1270)$, and $B_s^0\to \varphi {\rho }^0$ with branching fractions of $[1.12\pm 0.16_{-0.08}^{+0.09}\pm 0.11]\times {10}^{-6}$, $[0.61\pm 0.13_{-0.05}^{+0.12}\pm 0.06]\times {10}^{-6}$ and $[2.7\pm 0.7\pm 0.2\pm 0.2]\times {10}^{-7}$, respectively.

Figure 1

Feynman diagrams for the exclusive decays (a) $B_s^0\to \varphi f_0(980)$ and (b) $B_s^0\to \varphi {\rho }^0$.

Figure 2

The $K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ invariant mass distribution for candidates in the mass range $0.4<m_{\pi \pi }<1.6\mathrm{GeV}/c^2$. The fit described in the text is overlaid. The solid (red) line is the total fitted function, the dotted (green) line the combinatorial background, the dashed (blue) line the $B_s^0$ and the dot-dashed (black) line the $B^0$ signal component.

Figure 3

The $K^{+}{K}^{-}{K}^{+}{K}^{-}$ invariant mass distribution after all selection criteria. The solid (red) line is the total fitted function including the $B_s^0\to \varphi \varphi$ signal, and the dashed (green) line is the combinatorial background.

Figure 4

The $K^{+}{K}^{-}$ invariant mass distribution for background-subtracted $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ signal events with a fit to the dominant P-wave $\varphi$ meson shown as a solid (red) line, and a small S-wave $K^{+}{K}^{-}$ contribution shown as a hatched (blue) area.

Figure 5

The definition of the decay angles ${\theta }_1$, ${\theta }_2$, and $\mathrm{\Phi }$ for the decay $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ with $\varphi \to K^{+}{K}^{-}$ and taking $f_0(980)\to {\pi }^{+}{\pi }^{-}$ for illustration.

Figure 6

One-dimensional projections of the detection efficiency parametrized using Legendre polynomials (solid red lines) as a function of (a) $\cos {\theta }_1$, (b) $\cos {\theta }_2$, (c) $\mathrm{\Phi }$ and (d) $m({\pi }^{+}{\pi }^{-})$, superimposed on the efficiency determined from the ratio of the accepted/generated $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ events.

Figure 7

Projections of (a) $\cos {\theta }_1$, (b) $\cos {\theta }_2$, (c) $\mathrm{\Phi }$, and (d) $m({\pi }^{+}{\pi }^{-})$ for the preferred fit. The ${\rho }^0$ contribution is shown by the dotted (black) line, the $f_0(980)$ by the dot-dashed (blue) line, the $f_2(1270)$ by the double-dot-dashed (magenta) line and the $f_0(1500)$ by the dashed (cyan) line. Note that the expected distributions from each resonance include the effect of the experimental efficiency. The solid (red) line shows the total fit. The points with error bars are the data, where the background has been subtracted using the $B_s^0$ signal weights from the $K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ invariant mass fit.