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Observation of the resonant character of the $Z(4430)^-$ state

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Abstract

Resonant structures in $B^0\to\psi'\pi^-K^+$ decays are analyzed by performing a four-dimensional fit of the decay amplitude, using $pp$ collision data corresponding to $\rm 3 fb^{-1}$ collected with the LHCb detector. The data cannot be described with $K^+\pi^-$ resonances alone, which is confirmed with a model-independent approach. A highly significant $Z(4430)^-\to\psi'\pi^-$ component is required, thus confirming the existence of this state. The observed evolution of the $Z(4430)^-$ amplitude with the $\psi'\pi^-$ mass establishes the resonant nature of this particle. The mass and width measurements are substantially improved. The spin-parity is determined unambiguously to be $1^+$.

Figures and captions

Background-subtracted and efficiency-corrected $m_{\psi'\pi^-}$ distribution (black data points), superimposed with the reflections of $\cos\theta_{K^*}$ moments up to order four allowing for $J(K^*)\le 2$ (blue line) and their correlated statistical uncertainty (yellow band bounded by blue dashed lines). The distributions have been normalized to unity.

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Distributions of the fit variables (black data points) together with the projections of the 4D fit. The red solid (brown dashed) histogram represents the total amplitude with (without) the $ Z_1^-$ . The other points illustrate various subcomponents of the fit that includes the $ Z_1^-$ : the upper (lower) blue points represent the $ Z_1^-$ component removed (taken alone). The orange, magenta, cyan, yellow, green, and red points represent the $K^*(892)$, total $S$-wave, $K^*(1410)$, $K^*(1680)$, $K^*_2(1430)$ and background terms, respectively.

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Fitted values of the $ Z_1^-$ amplitude in six $m_{\psi'\pi^-}^2$ bins, shown in an Argand diagram (connected points with the error bars, $m_{\psi'\pi^-}^2$ increases counterclockwise). The red curve is the prediction from the Breit-Wigner formula with a resonance mass (width) of 4475 (172) $\mathrm{ Me V}$ and magnitude scaled to intersect the bin with the largest magnitude centered at (4477 MeV)$^2$. Units are arbitrary. The phase convention assumes the helicity-zero $K^*(892)$ amplitude to be real.

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Distribution of $m_{\psi'\pi^-}^2$ in the data (black points) for $1.0<m_{K^+\pi^-}^2<1.8$ GeV$^2$ ($K^*(892)$, $K^*_2(1430)$ veto region) compared with the fit with two, $0^-$ and $1^+$ (solid-line red histogram) and only one $1^+$ (dashed-line green histogram) $Z^-$ resonances. Individual $Z^-$ terms (blue points) are shown for the fit with two $Z^-$ resonances.

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Animated gif made out of all figures.

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplemetary material for the publication LHCb-PAPER-2014-014. The files are: supplementary.pdf : An overview of the extra figures *.pdf : The figures in the PDF format

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Created on 07 August 2020.