Analysis of the resonant components in ${\overline{B}}^0\to J/\psi {\pi }^{\mathbf{+}}{\pi }^{\mathbf{-}}$

Interpretation of $CP$ violation measurements using charmonium decays, in both the ${\overline{B}}^0$ and ${\overline{B}}_s^0$ systems, can be subject to changes due to “penguin” type diagrams. These effects can be investigated using measurements of the Cabibbo-suppressed ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays. The final state composition of this channel is investigated using a $1.0{\mathrm{fb}}^{-1}$ sample of data produced in 7 TeV $pp$ collisions at the LHC and collected by the LHCb experiment. A modified Dalitz-plot analysis is performed using both the invariant mass spectra and the decay angular distributions. An improved measurement of the ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ branching fraction of $(3.97\pm 0.09\pm 0.11\pm 0.16)\times {10}^{-5}$ is reported where the first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty of the branching fraction of the decay $B^{-}\to J/\psi K^{-}$ used as a normalization channel. Significant production of $f_0(500)$ and $\rho (770)$ resonances is found in the substructure of the $J/\psi {\pi }^{+}{\pi }^{-}$ final state, and this indicates that they are viable final states for $CP$ violation studies. In contrast evidence for the $f_0(980)$ resonance is not found. This allows us to establish the first upper limit on the branching fraction product $\mathcal{B}({\overline{B}}^0\to J/\psi f_0(980))\times \mathcal{B}(f_0(980)\to {\pi }^{+}{\pi }^{-})<1.1\times {10}^{-6}$, leading to an upper limit on the absolute value of the mixing angle of the $f_0(980)$ with the $f_0(500)$ of less than 31°, both at 90% confidence level.

Figure 1

(a) Tree level and (b) penguin diagram examples for ${\overline{B}}^0$ decays into $J/\psi K_{\mathrm{S}}^0$.

Figure 2

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

Figure 3

Distributions of the BDT classifier for both training and test samples of $J/\psi {\pi }^{+}{\pi }^{-}$ signal and background events. The signal samples are from simulation and the background samples are from data.

Figure 4

Invariant mass of $J/\psi {\pi }^{+}{\pi }^{-}$ combinations. The data are fitted with a double-Gaussian signal and several background functions. The (red) solid double-Gaussian function centered at 5280 MeV is the ${\overline{B}}^0$ signal, the (brown) dotted line shows the combinatorial background, the (green) short-dashed shows the $B^{-}$ background, the (purple) short-dash-dotted line shows the contribution of ${\overline{B}}_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays, the (black) long-dash-dotted is the sum of ${\overline{B}}_s^0\to J/\psi {\eta }^{\prime }(\to \rho \gamma )$ and ${\overline{B}}_s^0\to J/\psi \varphi (\to {\pi }^{+}{\pi }^{-}{\pi }^0)$ backgrounds, the (light blue) long-dashed is the ${\overline{B}}^0\to J/\psi K^{-}{\pi }^{+}$ reflection, and the (blue) solid line is the total.

Figure 5

Invariant mass of $J/\psi K^{-}$ combinations. The data points are fitted with a double-Gaussian function for signal and a linear function for background. The dotted line shows the background, and the (blue) solid line is the total.

Figure 6

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

Figure 7

Distribution of (a) $m(J/\psi {\pi }^{+})$ and (b) $m({\pi }^{+}{\pi }^{-})$ for ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ candidate decays within $\pm 20\mathrm{MeV}$ of ${\overline{B}}^0$ mass shown with the solid line. The (red) points with error bars show the background contribution determined from $m(J/\psi {\pi }^{+}{\pi }^{-})$ fits performed in each bin.

Figure 8

Distributions of $\cos {\theta }_{J/\psi }$ for the $J/\psi {\pi }^{+}{\pi }^{-}$ simulated sample in (a) the entire dipion mass region and (b) $\rho (770)$ region.

Figure 9

Exponential fit to the acceptance parameter $a(s_{12})$ used in Eq. (18).

Figure 10

Parametrized detection efficiency as a function of $m^2({\pi }^{+}{\pi }^{-})$ versus $m^2(J/\psi {\pi }^{+})$ determined from simulation. The $z$-axis scale is arbitrary.

Figure 11

Projections onto (a) $m^2(J/\psi {\pi }^{+})$ and (b) $m^2({\pi }^{+}{\pi }^{-})$ of the simulated Dalitz plot used to determine the efficiency parameters. The points represent the simulated event distributions and the curves the projections of the polynomial fits.

Figure 12

The $m^2(\pi \pi )$ distribution of background. The (black) histogram with error bars shows the same-sign data combinations with additional background from simulation, the (blue) points with error bars show the background obtained from the mass fits, the (black) dashed line is the partially reconstructed ${\overline{B}}_s^0$ background, and the (red) dotted is the misidentified ${\overline{B}}^0\to J/\psi K^{-}{\pi }^{+}$ contribution.

Figure 13

Projections of invariant mass squared of (a) $m^2(J/\psi {\pi }^{+})$ and (b) $m^2({\pi }^{+}{\pi }^{-})$ of the background Dalitz plot. The points with error bars show the same-sign combinations with additional background from simulation.

Figure 14

Distribution of the background in $\cos {\theta }_{J/\psi }$ resulting from $J/\psi {\pi }^{+}{\pi }^{-}$ candidate mass fits in each bin of $\cos {\theta }_{J/\psi }$. The curve represents the fitted function $1+\alpha {cos}^2{\theta }_{J/\psi }$.

Figure 15

Dalitz fit projections of (a) $m^2({\pi }^{+}{\pi }^{-})$, (b) $m^2(J/\psi {\pi }^{+})$, (c) $\cos {\theta }_{J/\psi }$, and (d) $m({\pi }^{+}{\pi }^{-})$ for the best model. The points with error bars are data, the signal fit is shown with a (red) dashed line, the background with a (black) dotted line, and the (blue) solid line represents the total. In (a) and (d), the shape variations near the $\rho (770)$ mass are due to $\rho (770)-\omega (782)$ interference, and the dip at the $K_{\mathrm{S}}^0$ mass [15] is due to the $K_{\mathrm{S}}^0$ veto.

Figure 16

Helicity angle distributions of (a) $\cos {\theta }_{J/\psi }$ (${\chi }^2/\mathrm{ndf}=15/20$) and (b) $\cos {\theta }_{\pi \pi }$ (${\chi }^2/\mathrm{ndf}=14/20$) in the $\rho (770)$ mass region defined within one full width of the $\rho (770)$ mass. The points with error bars are data, the signal fit to the best model is shown with a (red) dashed line, the background with a (black) dotted line, and the (blue) solid line represents the total.

Figure 17

Background subtracted and efficiency corrected helicity distributions of (a) $\cos {\theta }_{J/\psi }$ (${\chi }^2/\mathrm{ndf}=20/20$) and (b) $\cos {\theta }_{\pi \pi }$ (${\chi }^2/\mathrm{ndf}=13/20$) in the $\rho (770)$ mass region defined within one full width of the $\rho (770)$ mass. The points with error bars are data and the solid blue lines show the fit to the best model.