An angular analysis of $B^0\to J/\psi K^+\pi^$ decays is performed, using protonproton 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 threedimensional 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 modelindependent 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.
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 dotdashed lines mark the specific region, ${ m( K ^+ \pi ^ ) \in [1085,1445]}$ $\text{\,Me V}$ , employed for determining the significance of exotic contributions. 
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Comparison of $m(J\psi \pi^)$ in the $ m( K ^+ \pi ^ ) \in[1085,1265]$ $\text{\,Me V}$ region between the backgroundsubtracted data and simulated events weighted by moments models with $J^k_{\rm max}=2$ and $J^k_{\rm max}=15$. 
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Likelihoodratio 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). 
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Backgroundsubtracted 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. 
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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 backtoback with a common $\hat{y}$ axis. 
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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. 
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Comparison of $m(J/\psi\pi^)$ in the $m(K^+\pi^)\in[880,910]$ MeV region between the backgroundsubtracted data and simulation data weighted by moments models with $J^k_{\rm max}=2$ and $J^k_{\rm max}=15$. 
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Comparison of $m(J/\psi\pi^)$ in the $m(K^+\pi^)\in[1265,1445]$ MeV region between the backgroundsubtracted data and simulation data weighted by moments models with $J^k_{\rm max}=2$ and $J^k_{\rm max}=15$. 
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Animated gif made out of all figures. 
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The transversitybasis moments of the 28 orthonormal angular functions $f_i(\Omega)$ in Eq. 2 till spin2 in the $ K ^+ \pi ^ $ system. 
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The 12 angular terms for each additional spin$J$ wave in the $ K ^+ \pi ^ $ system, for $J\geq3$. 
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Created on 19 April 2019.Citation count from INSPIRE on 25 April 2019.