Measurement of the resonant and $CP$ components in ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays

The resonant structure of the reaction ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ is studied using data from $3{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the LHCb experiment, one third at 7 TeV center-of-mass energy and the remainder at 8 TeV. The invariant mass of the ${\pi }^{+}{\pi }^{-}$ pair and three decay angular distributions are used to determine the fractions of the resonant and nonresonant components. Six interfering ${\pi }^{+}{\pi }^{-}$ states, $\rho (770)$, $f_0(500)$, $f_2(1270)$, $\rho (1450)$, $\omega (782)$ and $\rho (1700)$, are required to give a good description of invariant mass spectra and decay angular distributions. The positive and negative charge parity fractions of each of the resonant final states are determined. The $f_0(980)$ meson is not seen and the upper limit on its presence, compared with the observed $f_0(500)$ rate, is inconsistent with a model where these scalar mesons are formed from two quarks and two antiquarks (tetraquarks) at the eight standard deviation level. In the $q\overline{q}$ model, the absolute value of the mixing angle between the $f_0(980)$ and the $f_0(500)$ scalar mesons is limited to be less than 17° at 90% confidence level.

Figure 1

(a) Tree level and (b) penguin diagram for ${\overline{B}}^0$ decays into $J/\psi {\pi }^{+}{\pi }^{-}$.

Figure 2

Illustration of the three angles used in this analysis.

Figure 3

Invariant mass of $J/\psi {\pi }^{+}{\pi }^{-}$ combinations together with the data fit. The (red) solid curve shows the ${\overline{B}}^0$ signal, the (brown) dotted line shows the combinatorial background, the (green) short-dashed line shows the $B^{-}$ background, the (purple) dot-dashed curve is ${\overline{B}}_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$, the (light blue) long-dashed line is the sum of ${\overline{B}}_s^0\to J/\psi {\eta }^{(\prime )}$, ${\overline{B}}_s^0\to J/\psi \varphi$ with $\varphi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ backgrounds and the ${\mathrm{\Lambda }}_b^0\to J/\psi K^{-}p$ reflection, the (black) dot-long dashed curve is the ${\overline{B}}^0\to J/\psi K^{-}{\pi }^{+}$ reflection and the (blue) solid curve is the total. The points at the bottom show the difference between the data points and the total fit divided by the statistical uncertainty on the data.

Figure 4

Distribution of $m^2({\pi }^{+}{\pi }^{-})$ versus $m^2(J/\psi {\pi }^{+})$ for all events within $\pm 20\mathrm{MeV}$ of the ${\overline{B}}^0$ mass.

Figure 5

Distributions of (a) $m(J/\psi {\pi }^{+})$ and (b) $m({\pi }^{+}{\pi }^{-})$ for ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ candidates within $\pm 20\mathrm{MeV}$ of the ${\overline{B}}^0$ mass. The red points with error bars show the background contributions obtained by fitting the $m(J/\psi {\pi }^{+}{\pi }^{-})$ distribution in bins of the plotted variables.

Figure 6

Projections of invariant mass squared (a) $s_{12}\equiv m^2(J/\psi {\pi }^{+})$ and (b) $s_{23}\equiv m^2({\pi }^{+}{\pi }^{-})$ of the simulated Dalitz plot used to measure the efficiency parameters. The points represent the simulated event distributions and the curves the polynomial fit.

Figure 7

The variation of ${ϵ}_1$ is shown as a function of $m({\pi }^{+}{\pi }^{-})$ and $\cos {\theta }_{{\pi }^{+}{\pi }^{-}}$.

Figure 8

Distributions of $m({\pi }^{+}{\pi }^{-})$ of background components. The (blue) histogram shows the like-sign combinations added with additional backgrounds using simulations. The (black) points with error bars show the background obtained from the fits to the $m(J/\psi {\pi }^{+}{\pi }^{-})$ mass spectrum in each bin of ${\pi }^{+}{\pi }^{-}$ mass.

Figure 9

Projections of (a) $\cos {\theta }_{\pi \pi }$ and (b) $m({\pi }^{+}{\pi }^{-})$ of the background. The points with error bars show the like-sign data combinations added with the ${\mathrm{\Lambda }}_b^0$ background and additional simulated backgrounds. The (magenta) dot-dashed line shows the ${\eta }^{(\prime )}\to \rho \gamma$ background, the (dark-blue) dashed line the ${\overline{K}}^{*}$ reflection background, and the (blue) solid line the total. The points at the bottom show the difference between the data points and the total fit divided by the statistical uncertainty on the data.

Figure 10

The $\cos {\theta }_{J/\psi }$ distribution of the data-simulated hybrid background sample. The points with error bars show the like-sign data combinations added with the ${\mathrm{\Lambda }}_b^0$ background and additional simulated backgrounds. The (magenta) dot-dashed line shows the $\rho$ background, the (dark-blue) dashed the ${\overline{K}}^{*}$ reflection background and the (blue) solid line the total.

Figure 11

The $\chi$ distribution of the data-simulated hybrid background sample including the ${\mathrm{\Lambda }}_b^0$ background and the fitted function $1+p_{b1}\cos \chi +p_{b2}\cos 2\chi$. The $p$-value of this fit is 40%.

Figure 12

Dalitz fit projections of (a) $m({\pi }^{+}{\pi }^{-})$, (b) $\cos ({\theta }_{{\pi }^{+}{\pi }^{-}})$, (c) $\cos {\theta }_{J/\psi }$ and (d) $\chi$ for the 5R model + $\rho (1700)$ (best model). The points with error bars are data compared with the overall fit, shown by the (blue) solid line. The individual fit components are signal, shown with a (red) dashed line, background, shown with a (black) dotted line and $K_{\mathrm{s}}^0$, shown with a (green) dashed line.

Figure 13

Fit projection of $m({\pi }^{+}{\pi }^{-})$ showing the different resonant contributions in the best model.

Figure 14

The ${\pi }^{+}{\pi }^{-}$ mass dependence of the spherical harmonic moments of $\cos {\theta }_{\pi \pi }$ after efficiency corrections and background subtraction: (a) $⟨Y_0^0⟩$, (b) $⟨Y_1^0⟩$, (c) $⟨Y_2^0⟩$, (d) $⟨Y_3^0⟩$, (e) $⟨Y_4^0⟩$, (f) $⟨Y_5^0⟩$. The errors on the black data points are statistical. The (blue) curves show the fit projections.