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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.

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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 $J^k_{\rm max}=15$.

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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).

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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.

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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 back-to-back 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 background-subtracted 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 background-subtracted 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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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.

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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 26 April 2024.