Search for the $Z(4430{)}^{-}$ at BABAR

We report the results of a search for $Z(4430{)}^{-}$ decay to $J/\psi {\pi }^{-}$ or $\psi (2S){\pi }^{-}$ in $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$ and $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$ decays. 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 the sample corresponds to an integrated luminosity of $413{\mathrm{fb}}^{-1}$. Each $K{\pi }^{-}$ mass distribution exhibits clear $K^{*}(892)$ and $K_2^{*}(1430)$ signals, and the efficiency-corrected spectrum is well described by a superposition of the associated Breit-Wigner intensity distributions, together with an $S$-wave contribution obtained from the LASS $I=1/2$ $K{\pi }^{-}$ scattering amplitude measurements. Each $K{\pi }^{-}$ angular distribution varies significantly in structure with $K{\pi }^{-}$ mass, and is represented in terms of low-order Legendre polynomial moments. We find that each $J/\psi {\pi }^{-}$ or $\psi (2S){\pi }^{-}$ mass distribution is well described by the reflection of the measured $K{\pi }^{-}$ mass and angular distribution structures. We see no significant evidence for a $Z(4430{)}^{-}$ signal for any of the processes investigated, neither in the total $J/\psi {\pi }^{-}$ or $\psi (2S){\pi }^{-}$ mass distribution, nor in the corresponding distributions for the regions of $K{\pi }^{-}$ mass for which observation of the $Z(4430{)}^{-}$ signal was reported. We obtain branching-fraction upper limits $\mathcal{B}(B^{-}\to Z^{-}{\overline{K}}^0,Z^{-}\to J/\psi {\pi }^{-})<1.5\times {10}^{-5}$, $\mathcal{B}(B^0\to Z^{-}{K}^{+},Z^{-}\to J/\psi {\pi }^{-})<0.4\times {10}^{-5}$, $\mathcal{B}(B^{-}\to Z^{-}{\overline{K}}^0,Z^{-}\to \psi (2S){\pi }^{-})<4.7\times {10}^{-5}$, and $\mathcal{B}(B^0\to Z^{-}{K}^{+},Z^{-}\to \psi (2S){\pi }^{-})<3.1\times {10}^{-5}$ at 95% confidence level, where the $Z(4430{)}^{-}$ mass and width have been fixed to the reported central values.

Figure 1

The $m_{\mathrm{ES}}$ distributions, (a)–(d), and $\Delta E$ distributions, (e)–(h), for the decay modes $B^{-}\to J/\psi {\pi }^{-}{K}_S^0$, $B^0\to J/\psi {\pi }^{-}{K}^{+}$, $B^{-}\to \psi (2S){\pi }^{-}{K}_S^0$, and $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The points show the data, and the solid curves represent the fit functions. The dashed curves indicate the background contributions, and the filled histograms show the corresponding distributions for the sideband regions.

Figure 2

The $m_{\psi {\pi }^{-}}^2$ versus $m_{K{\pi }^{-}}^2$ Dalitz plot distributions for the signal regions for the decay modes (a) $B^{-}\to J/\psi {\pi }^{-}{K}_S^0$, (b) $B^0\to J/\psi {\pi }^{-}{K}^{+}$, (c) $B^{-}\to \psi (2S){\pi }^{-}{K}_S^0$, (d) $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The intensity scale is logarithmic.

Figure 3

The $m_{K{\pi }^{-}}$ mass projections for the Dalitz plots of Fig. 2. The data points are for the $m_{\mathrm{ES}}\mathrm{\text{−}}\Delta E$ signal regions, and the filled histograms are for the $\Delta E$ sideband regions.

Figure 4

The $m_{\psi {\pi }^{-}}$ mass projections for the Dalitz plots of Fig. 2. The data points are for the $m_{\mathrm{ES}}\mathrm{\text{−}}\Delta E$ signal regions, and the filled histograms are for the $\Delta E$ sideband regions. The dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 5

The $m_{\psi K}$ mass projections for the Dalitz plots of Fig. 2. The data points are for the $m_{\mathrm{ES}}\mathrm{\text{−}}\Delta E$ signal regions, and the filled histograms are for the $\Delta E$ sideband regions.

Figure 6

The $\psi {\pi }^{-}$ mass resolution in $50\mathrm{MeV}/c^2$ intervals as a function of $\psi {\pi }^{-}$ mass for the decay modes (a) $B^{-}\to J/\psi {\pi }^{-}{K}_S^0$, (b) $B^0\to J/\psi {\pi }^{-}{K}^{+}$, (c) $B^{-}\to \psi (2S){\pi }^{-}{K}_S^0$, and (d) $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 7

The $m_{K{\pi }^{-}}$ dependence of the average efficiency, $E_0$, for the $B$ meson decay processes (a) $B^{-}\to J/\psi {\pi }^{-}{K}_S^0$, (b) $B^0\to J/\psi {\pi }^{-}{K}^{+}$, (c) $B^{-}\to \psi (2S){\pi }^{-}{K}_S^0$, and (d) $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The key in (a) applies to all four figures, and, as indicated, the individual $J/\psi$ and $\psi (2S)$ decay modes are treated separately. The curves result from fifth-order polynomial fits to the data points.

Figure 8

The $K{\pi }^{-}$ mass distributions, after sideband subtraction and efficiency correction, for the decay modes (a) $B^{-}\to J/\psi {\pi }^{-}{K}_S^0$, (b) $B^0\to J/\psi {\pi }^{-}{K}^{+}$, (c) $B^{-}\to \psi (2S){\pi }^{-}{K}_S^0$, and (d) $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The contributions from the individual $\psi$ decay modes are obtained separately, as described in the text, and are accumulated as indicated by the keys in (a) and (c), to form the final histograms.

Figure 9

(a)–(d): The dependence of efficiency on pion momentum in the laboratory frame for the $B$ meson decay modes of Eqs. (1, 2, 3, 4). (e)–(h): The corresponding efficiency dependence on kaon laboratory-frame momentum.

Figure 10

The efficiency-corrected and sideband-subtracted $K{\pi }^{-}$ mass distributions of Fig. 8 for the decay modes (a) $B^{-}\to J/\psi {\pi }^{-}{K}_S^0$, (b) $B^0\to J/\psi {\pi }^{-}{K}^{+}$, (c) $B^{-}\to \psi (2S){\pi }^{-}{K}_S^0$, and (d) $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The data are shown as open dots, and the curves correspond to the fits described in the text.

Figure 11

The results of the fits to the $K{\pi }^{-}$ mass distributions for the combined $K{\pi }^{-}$ charge configurations (a) $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$ and (b) $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$. The data are shown as open dots, and the individual fit contributions are as indicated.

Figure 12

Illustration of the definition of the angles (a) ${\theta }_K$ and (b) ${\theta }_{\psi }$, as described in the text.

Figure 13

The $\cos {\theta }_K$ versus $m_{K{\pi }^{-}}$ rectangular Dalitz plots for the combined decay modes (a) $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$, (b) $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$. The plots are obtained after efficiency weighting, but without $\Delta E$ sideband subtraction. The intensity scale is logarithmic, and is the same for both plots.

Figure 14

The $m_{K{\pi }^{-}}$ dependence of (a) $⟨P_1^U⟩$ and (b) $⟨P_2^U⟩$ for $B^{0,-}\to J/\psi {\pi }^{-}{K}^{+,0}$; the $m_{K{\pi }^{-}}$ dependence of (c) $⟨P_1^U⟩$ and (d) $⟨P_2^U⟩$ for $B^{0,-}\to \psi (2S){\pi }^{-}{K}^{+,0}$.

Figure 15

The $m_{K{\pi }^{-}}$ dependence (for $m_{K{\pi }^{-}}>1.2\mathrm{GeV}/c^2$) of (a) $⟨P_3^U⟩$ and (b) $⟨P_4^U⟩$ for $B^{0,-}\to J/\psi {\pi }^{-}{K}^{+,0}$; the $m_{K{\pi }^{-}}$ dependence of (c) $⟨P_3^U⟩$ and (d) $⟨P_4^U⟩$ for $B^{0,-}\to \psi (2S){\pi }^{-}{K}^{+,0}$.

Figure 16

(a) The $m_{K{\pi }^{-}}$ dependence of $⟨P_5^U⟩$ for $m_{K{\pi }^{-}}>1.2\mathrm{GeV}/c^2$ for $B^{0,-}\to J/\psi {\pi }^{-}{K}^{+,0}$; (b) the $m_{K{\pi }^{-}}$ dependence of $⟨P_6^U⟩$ for $m_{K{\pi }^{-}}>1.5\mathrm{GeV}/c^2$ for $B^{0,-}\to J/\psi {\pi }^{-}{K}^{+,0}$.

Figure 17

The $K{\pi }^{-}$ mass distributions generated according to the $K{\pi }^{-}$ fit functions of Fig. 11 for (a) $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$ and (b) $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$. Each distribution contains ${10}^7$ events, normalized to the total number of events observed in the corrected data sample (Fig. 11).

Figure 18

The normalized moments corresponding to Fig. 14 obtained by using Eq. (34). Mass intervals have been combined in order to reduce statistical fluctuations. The lines indicate the linear interpolations used in weighting the MC events. The shaded regions indicate the $\pm 1\sigma$ variations used to account for statistical uncertainties.

Figure 19

The normalized moments corresponding to Fig. 15 obtained by using Eq. (34). Mass intervals have been combined in order to reduce statistical fluctuations. The lines indicate the linear interpolations used in weighting the MC events. The shaded regions indicate the $\pm 1\sigma$ variations used to account for statistical uncertainties.

Figure 20

The normalized moments corresponding to Fig. 16 obtained by using Eq. (34). Mass intervals have been combined in order to reduce statistical fluctuations. The lines indicate the linear interpolations used in weighting the MC events. The shaded regions indicate the $\pm 1\sigma$ variations used to account for statistical uncertainties.

Figure 21

The $\psi {\pi }^{-}$ mass distributions for the combined decay modes (a) $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$ and (b) $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$. The points show the data after efficiency correction and $\Delta E$ sideband subtraction. The dashed curves show the $K{\pi }^{-}$ reflection for a flat $\cos {\theta }_K$ distribution, while the solid curves show the result of $\cos {\theta }_K$ weighting. The shaded bands represent the effect of statistical uncertainty on the normalized moments. In (b), the dot-dashed curve indicates the effect of weighting with the normalized $J/\psi {\pi }^{-}K$ moments. The dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$. In (c) and (d), we show the residuals (data—solid curve) for (a) and (b), respectively.

Figure 22

The $\cos {\theta }_{\psi }$ versus $m_{\psi {\pi }^{-}}$ rectangular Dalitz plots for (a) $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$, and (b) $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$; (c) and (d), the corresponding plots indicating the loci of the $K^{*}(892)$ and $K_2^{*}(1430)$ resonance bands defined in the text; regions A–E, defined by Eqs. (36, 37, 38, 39, 40), are indicated. The dashed vertical lines show the mass range $4.400<m_{\psi {\pi }^{-}}<4.460\mathrm{GeV}/c^2$.

Figure 23

(a) The curve of Fig. 21, and (b) that of Fig. 21, obtained by $\cos {\theta }_K$ weighting; the shaded regions near threshold correspond to $P({\pi }^{-})<0.1\mathrm{GeV}/c$ in the laboratory frame, while the crosshatched regions near maximum $\psi {\pi }^{-}$ mass represent $P(K)<0.25\mathrm{GeV}/c$ in the laboratory frame; the dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 24

The cumulative $\psi {\pi }^{-}$ mass distributions for the $K_S^0$ and $K^{+}$ decay modes (a) and (d) before, and (b) and (e) after, efficiency correction. The ratio of uncorrected to corrected data is shown in (c) and (f). The fitted line in (f) is described in the text.

Figure 25

The $\psi {\pi }^{-}$ mass distributions in regions A–E of $K{\pi }^{-}$ mass for the combined decay modes [(a)–(e)] $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$, and [(f)–(j)] $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$; the open dots represent the data, and the solid curves and shaded bands are as in Fig. 21, but calculated for the relevant $K{\pi }^{-}$ mass region using the same overall normalization constant as for Fig. 17. In (f)–(j), the dot-dashed curves are obtained using $K{\pi }^{-}$ normalized moments for $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$ in Eq. (35), instead of those from $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$; the dot-dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 26

The residuals (data—solid curve) corresponding to Fig. 25; the dot-dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 27

The $\psi {\pi }^{-}$ mass distributions for (a) $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$, and (b) $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$, for $m_{K{\pi }^{-}}$ regions B and D combined; the open dots represent the data, the solid, dashed, and dot-dashed curves, and the shaded bands, correspond to those of Figs. 21 and 21; (c) and (d) are the corresponding residual distributions. The dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 28

The $\psi {\pi }^{-}$ mass distributions for (a) $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$, and (b) $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$, for $m_{K{\pi }^{-}}$ regions A, C, and E, combined; the open dots represent the data, the solid, dashed, and dot-dashed curves, and the shaded bands, correspond to those of Figs. 21 and 21; (c) and (d) are the corresponding residual distributions. The dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 29

(a) The $\psi (2S){\pi }^{-}$ mass distribution after $K^{*}$ veto from Ref. [12]; the data points represent the signal region (we have assigned $\sqrt{N}$ errors at present), and the shaded histogram represents the background contribution estimated from the $\Delta E$ sideband regions; (b) shows the corresponding distribution from the BABAR analysis. The dashed vertical line indicates $m_{\psi (2S){\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 30

(a) The distribution of Fig. 29 after combining mass intervals for $m_{\psi (2S){\pi }^{-}}<4.18\mathrm{GeV}/c^2$ and $m_{\psi (2S){\pi }^{-}}>4.55\mathrm{GeV}/c^2$, and carrying out sideband subtraction. (b) The distribution of Fig. 29 after following the same procedure, and in addition scaling by 1.18, as described in the text. (c) The difference, (a)–(b), where the errors have been combined in quadrature; ${\chi }^2/\mathrm{NDF}=54.7/58$ ($\mathrm{\text{Probability}}=59.9\%$) excluding the low-efficiency regions (crosshatched).

Figure 31

The $\cos {\theta }_{\pi }$ distributions for the combined $K{\pi }^{-}$ mass regions A, C, and E, (a), (b) for the decay modes $B^{-,0}\to J/\psi {\pi }^{-}{K}^{0,+}$, and (c), (d) for $B^{-,0}\to \psi (2S){\pi }^{-}{K}^{0,+}$. In (a) and (c), the points represent the data in the signal region, and the shaded histograms show the $\Delta E$ sideband events. In (b) and (d), the signal region distributions are shown after sideband subtraction. No efficiency correction is applied to the data.

Figure 32

The results of the fits to the corrected mass distributions, (a)–(c) for $J/\psi {\pi }^{-}$, and (d)–(f) for $\psi (2S){\pi }^{-}$. In each figure, the open dots represent the data, and the solid curve represents the fit function, which consists of the $K{\pi }^{-}$ background distribution with normalization free, and a relativistic $S$-wave BW line shape, with mass, width, and normalization free; the dotted curves indicate the $K{\pi }^{-}$ background functions; the dashed vertical lines indicate $m_{\psi {\pi }^{-}}=4.433\mathrm{GeV}/c^2$.

Figure 33

The $\cos {\theta }_K$ versus $m_{K{\pi }^{-}}$ rectangular Dalitz plot for the $B^{-,0}\to Z(4430{)}^{-}{K}^{0,+}$, $Z(4430{)}^{-}\to \psi (2S){\pi }^{-}$ MC events generated using $m_Z=4.433\mathrm{GeV}/c^2$, ${\Gamma }_Z=0.045\mathrm{GeV}$, and with isotropic $Z(4430{)}^{-}$ decay.

Figure 34

(a) The combined $m_{\psi (2S){\pi }^{-}}$ mass distribution for the data of Fig. 21 and the MC $Z(4430{)}^{-}$ sample generated as described in the text; the shaded histogram represents the MC sample. (b) The $K{\pi }^{-}$ mass distribution corresponding to Fig. 34; the shaded histogram represents the reflection of the MC $Z(4430{)}^{-}$ events, and the curve shows the result of the fit.

Figure 35

The $m_{\psi (2S){\pi }^{-}}$ distribution of Fig. 34 for the data and MC samples combined as described in the text. The dashed curve represents the $K{\pi }^{-}$ background distribution, obtained as described in the text, and the shaded histogram represents the difference between this dashed curve and the solid curve of Fig. 21, i.e. it represents the impact of the MC $Z(4430{)}^{-}$ signal. The solid curve is the result of a fit using the $K{\pi }^{-}$ background function and a relativistic $S$-wave BW, and the dotted curve shows the resulting renormalized dashed curve.

Figure 36

The $\cos {\theta }_K$ distributions in $50\mathrm{MeV}/c^2$ $K{\pi }^{-}$ mass intervals for the decay mode $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The points represent the data, and the curves show the functions calculated from the moments.

Figure 37

The $K{\pi }^{-}$ mass dependence of the coefficients $E_1$ through $E_{12}$ for the decay mode $B^0\to \psi (2S){\pi }^{-}{K}^{+}$. The points show the calculated values, and the curves result from fits to the data using a fifth-order polynomial.