Dalitz analysis of $B\to K{\pi }^{+}{\psi }^{\prime }$ decays and the $Z(4430{)}^{+}$

From a Dalitz plot analysis of $B\to K{\pi }^{+}{\psi }^{\prime }$ decays, we find a signal for $Z(4430{)}^{+}\to {\pi }^{+}{\psi }^{\prime }$ with a mass $M=({4443}_{-12-13}^{+15+19})\mathrm{MeV}/c^2$, width $\Gamma =({107}_{-43-56}^{+86+74})\mathrm{MeV}$, product branching fraction $\mathcal{B}({\overline{B}}^0\to K^{-}Z(4430{)}^{+})\times \mathcal{B}(Z(4430{)}^{+}\to {\pi }^{+}{\psi }^{\prime })=({3.2}_{-0.9-1.6}^{+1.8+5.3})\times {10}^{-5}$, and significance of $6.4\sigma$ that agrees with previous Belle measurements based on the same data sample. In addition, we determine the branching fraction $\mathcal{B}(B^0\to K^{*}(892{)}^0{\psi }^{\prime })=({5.52}_{-0.32-0.58}^{+0.35+0.53})\times {10}^{-4}$ and the fraction of $K^{*}(892{)}^0$ mesons that are longitudinally polarized $f_L=({44.8}_{-2.7-5.3}^{+4.0+4.0})\%$. These results are obtained from a $605{\mathrm{fb}}^{-1}$ data sample that contains $657\times {10}^6$ $B\overline{B}$ pairs collected near the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Figure 1

The $B\to K{\pi }^{+}{\psi }^{\prime }$ Dalitz plot for the $\Delta E$ signal region. The solid (dashed) lines delimit the five vertical (three horizontal) slices that are used to present the fit results in subsequent figures. The coordinates of the vertical lines are $M^2(K{\pi }^{+})=(0.796{)}^2{\mathrm{GeV}}^2/c^4$, $(0.996{)}^2{\mathrm{GeV}}^2/c^4$, $(1.332{)}^2{\mathrm{GeV}}^2/c^4$, and $(1.532{)}^2{\mathrm{GeV}}^2/c^4$; the coordinates of the horizontal lines are $M^2({\pi }^{+}{\psi }^{\prime })=19.0{\mathrm{GeV}}^2/c^4$ and $20.5{\mathrm{GeV}}^2/c^4$.

Figure 2

Dalitz plot projections for the slices defined in Fig. 1: (a)–(e) correspond to vertical slices from left to right, (f)–(h) correspond to horizontal slices from bottom to top; in (f)–(h), plots including the full vertical scale are shown inset. The points with error bars represent data, the solid (dotted) histograms are the fit results for the default model that includes all low-lying $K\pi$ resonances and a single (without any) ${\pi }^{+}{\psi }^{\prime }$ state, and the dashed histograms represent the background.

Figure 3

The Dalitz plot projection with the $K^{*}$ veto applied. The points with error bars represent data, the solid (dotted) histogram is the Dalitz plot fit result for the fit model with all $K\pi$ resonances and a single (without any) ${\pi }^{+}{\psi }^{\prime }$ state, and the dashed histogram represents the background.

Figure 4

Dalitz plot projections as described for Fig. 2. The points with error bars represent data, the solid (dotted) histograms are the fit results for the model that includes all low-lying $K\pi$ resonances as well as the $K_3^{*}(1780)$ and a single (without any) ${\pi }^{+}{\psi }^{\prime }$ state, and the dashed histograms represent the background.