Search for the $Z_1(4050{)}^{+}$ and $Z_2(4250{)}^{+}$ states in ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$

We search for the $Z_1(4050{)}^{+}$ and $Z_2(4250{)}^{+}$ states, reported by the Belle Collaboration, decaying to ${\chi }_{c1}{\pi }^{+}$ in the decays ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$ where ${\chi }_{c1}\to J/\psi \gamma$. The data were collected with the BABAR detector at the SLAC PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider operating at center-of-mass energy 10.58 GeV, and correspond to an integrated luminosity of $429{\mathrm{fb}}^{-1}$. In this analysis, we model the background-subtracted, efficiency-corrected ${\chi }_{c1}{\pi }^{+}$ mass distribution using the $K\pi$ mass distribution and the corresponding normalized $K\pi$ Legendre-polynomial moments, and then test the need for the inclusion of resonant structures in the description of the ${\chi }_{c1}{\pi }^{+}$ mass distribution. No evidence is found for the $Z_1(4050{)}^{+}$ and $Z_2(4250{)}^{+}$ resonances, and 90% confidence level upper limits on the branching fractions are reported for the corresponding $B$-meson decay modes.

Figure 1

Distributions of $\Delta E$ for (a) ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and (b) $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$ summed over the $J/\psi$ decay modes; the ${\chi }_{c1}$ and $m_{\mathrm{ES}}$ selection criteria have been applied. The shaded areas indicate the signal regions.

Figure 2

The $J/\psi \gamma$ mass distribution for (a) ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and (b) $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$ candidates, summed over the $J/\psi$ decay modes. The $m_{\mathrm{ES}}$ and $\Delta E$ selection criteria have been applied. The shaded areas indicate the signal regions.

Figure 3

Dalitz plot for ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ in (a) the signal region and (b) the $\Delta E$ sidebands. The shaded area defines the Dalitz plot boundary.

Figure 4

Dalitz plot for $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$ in (a) the signal region and (b) the $\Delta E$ sidebands. The shaded area defines the Dalitz plot boundary.

Figure 5

Fitted efficiency on the $\cos \theta \mathrm{\text{vs}}.m(K\pi )$ plane for (a) ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and (b) $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$ summed over the $J/\psi$ decay modes.

Figure 6

Efficiency as a function of $m({\chi }_{c1}{\pi }^{+})$ for (a) ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and (b) $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$ summed over the $J/\psi$ decay modes.

Figure 7

Fits to the background-subtracted and efficiency-corrected $K\pi$ mass spectra for (a) ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and (b) $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$. The $K^{*}(1680)$ contribution is shown in each figure by the dashed curve.

Figure 8

Legendre-polynomial moments $⟨Y_L^0⟩$ for $L=1,\dots ,6$ as functions of $K\pi$ mass for $B\to {\chi }_{c1}K\pi$ after background subtraction and efficiency correction.

Figure 9

Background-subtracted and efficiency-corrected $J/\psi \pi$ mass distribution for the $B\to J/\psi K\pi$ control sample with the superimposed curves resulting from the MC simulation described in the text. The solid curve is obtained using the total weight $w$ obtained with $L_{\max }=5$, and the dotted curve by omitting the angular-dependence factor $w_L$.

Figure 10

Background-subtracted and efficiency-corrected ${\chi }_{c1}\pi$ mass distribution from $B\to {\chi }_{c1}K\pi$. The solid curve results from the MC simulation described in the text, which uses the moments from the same channels. The dotted curve shows the result of the simulation when the $w_L$ weight is removed.

Figure 11

Background-subtracted and efficiency-corrected ${\chi }_{c1}\pi$ mass distribution from $B\to {\chi }_{c1}K\pi$, which includes a simulated $Z_2(4250{)}^{+}$ (vertical crosses). In (a) the distribution with solid dots represents the ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ data component. The continuous curve is the result from the mixed simulation described in the text and obtained from the MC simulation. The dashed curve shows a simulation with $L_{\max }=15$. (b) Result from the fit described in the text, which incorporates a Breit-Wigner line shape describing the $Z_2(4250{)}^{+}$. The dashed curve represents the background model from the mixed simulation.

Figure 12

(a), (b) Background-subtracted and efficiency-corrected ${\chi }_{c1}\pi$ mass distribution for $B\to {\chi }_{c1}K\pi$. (a) Fit with $Z_1(4050{)}^{+}$ and $Z_2(4250{)}^{+}$ resonances. (b) Fit with only the $Z(4150{)}^{+}$ resonance. (c), (d) Efficiency-corrected and background-subtracted ${\chi }_{c1}\pi$ mass distribution for $B\to {\chi }_{c1}K\pi$ in the $K\pi$ mass region $1.0<m^2(K\pi )<1.75{\mathrm{GeV}}^2/c^4$. (c) Fit with $Z_1(4050{)}^{+}$ and $Z_2(4250{)}^{+}$ resonances. (d) Fit with only the $Z(4150{)}^{+}$ resonance. In each fit the dashed curve shows the prediction from the mixed $B\to {\chi }_{c1}K\pi$ simulation explained in the text. The dot-dashed curves indicate the fitted resonant contributions.