# Model-independent observation of exotic contributions to $B^0\to J/\psi K^+\pi^-$ decays

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## Abstract

An angular analysis of $B^0\to J/\psi K^+\pi^-$ decays is performed, using proton-proton collision data corresponding to an integrated luminosity of 3 ${\rm fb}^{-1}$ collected with the LHCb detector. The $m(K^+\pi^-)$ spectrum is divided into fine bins. In each $m(K^+\pi^-)$ bin, the hypothesis that the three-dimensional angular distribution can be described by structures induced only by $K^\ast$ resonances is examined, making minimal assumptions about the $K^+\pi^-$ system. The data reject the $K^\ast$-only hypothesis with a large significance, implying the observation of exotic contributions in a model-independent fashion. Inspection of the $m(J/\psi\pi^-)$ versus $m(K^+\pi^-)$ plane suggests structures near $m(J/\psi\pi^-)=4200$ MeV and 4600 MeV.

## Figures and captions

 Spectrum of $K^\ast_J$ resonances from Ref. [7], with the vertical span of the boxes indicating $\pm\Gamma_0$, where $\Gamma_0$ is the width of each resonance. The horizontal dashed lines mark the $m( K ^+ \pi ^- )$ physical region for ${B^0\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+\pi^-}$ decays, while the dot-dashed lines mark the specific region, ${ m( K ^+ \pi ^- ) \in [1085,1445]}$ $\text{ Me V}$ , employed for determining the significance of exotic contributions. Fig1.pdf [581 KiB] HiDef png [497 KiB] Thumbnail [320 KiB] *.C file Comparison of $m(J\psi \pi^-)$ in the $m( K ^+ \pi ^- ) \in[1085,1265]$ $\text{ Me V}$ region between the background-subtracted data and simulated events weighted by moments models with $J^k_{\rm max}=2$ and $J^k_{\rm max}=15$. Fig2.pdf [505 KiB] HiDef png [348 KiB] Thumbnail [277 KiB] *.C file Likelihood-ratio test for exotic significance. The data shows a $10\sigma$ deviation from the pseudoexperiments generated according to the null hypothesis ($K^\ast_J$-only contributions). Fig3.pdf [538 KiB] HiDef png [393 KiB] Thumbnail [316 KiB] *.C file Background-subtracted 2D distribution of $m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^-)$ versus $m( K ^+ \pi ^- )$ in the region ${ m( K ^+ \pi ^- ) \in[745,1545]}$ $\text{ Me V}$ . The intensity ($z$-axis) scale has been highly truncated to limit the strong $K^\ast(892)^0$ contribution. Fig4.pdf [2 MiB] HiDef png [1 MiB] Thumbnail [702 KiB] *.C file Angle conventions as described in Ref. [18] for (a) $\overline{ B } {}^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow \mu ^- \mu ^+ ) K ^- \pi ^+$ and (b) ${ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow \mu ^+ \mu ^- ) K ^+ \pi ^- }$. The leptonic ($\mu ^+ \mu ^-$) and hadronic ($K^+\pi^-$) frames are back-to-back with a common $\hat{y}$ axis. Fig5a.pdf [14 KiB] HiDef png [280 KiB] Thumbnail [145 KiB] *.C file Fig5b.pdf [14 KiB] HiDef png [280 KiB] Thumbnail [145 KiB] *.C file Fit to the invariant mass $m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+\pi^-)$ in the $m( K ^+ \pi ^- ) \in [1235,1265]$ $\text{ Me V}$ bin. Fig6.pdf [558 KiB] HiDef png [438 KiB] Thumbnail [323 KiB] *.C file Comparison of $m(J/\psi\pi^-)$ in the $m(K^+\pi^-)\in[880,910]$ MeV region between the background-subtracted data and simulation data weighted by moments models with $J^k_{\rm max}=2$ and $J^k_{\rm max}=15$. Fig7.pdf [479 KiB] HiDef png [304 KiB] Thumbnail [245 KiB] *.C file Comparison of $m(J/\psi\pi^-)$ in the $m(K^+\pi^-)\in[1265,1445]$ MeV region between the background-subtracted data and simulation data weighted by moments models with $J^k_{\rm max}=2$ and $J^k_{\rm max}=15$. Fig8.pdf [500 KiB] HiDef png [333 KiB] Thumbnail [271 KiB] *.C file Animated gif made out of all figures. PAPER-2018-043.gif Thumbnail

## Tables and captions

 The transversity-basis moments of the 28 orthonormal angular functions $f_i(\Omega)$ in Eq. 2 till spin-2 in the $K ^+ \pi ^-$ system. Table_1.pdf [66 KiB] HiDef png [260 KiB] Thumbnail [131 KiB] tex code The 12 angular terms for each additional spin-$J$ wave in the $K ^+ \pi ^-$ system, for $J\geq3$. Table_2.pdf [49 KiB] HiDef png [380 KiB] Thumbnail [146 KiB] tex code

Created on 20 August 2019.Citation count from INSPIRE on 23 August 2019.