# Quantum numbers of the $X(3872)$ state and orbital angular momentum in its $\rho^0 J/\psi$ decays

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## Abstract

Angular correlations in $B^+\to X(3872) K^+$ decays, with $X(3872)\to \rho^0 J/\psi$, $\rho^0\to\pi^+\pi^-$ and $J/\psi \to\mu^+\mu^-$, are used to measure orbital angular momentum contributions and to determine the $J^{PC}$ value of the $X(3872)$ meson. The data correspond to an integrated luminosity of 3.0 fb$^{-1}$ of proton-proton collisions collected with the LHCb detector. This determination, for the first time performed without assuming a value for the orbital angular momentum, confirms the quantum numbers to be $J^{PC}=1^{++}$. The $X(3872)$ is found to decay predominantly through S wave and an upper limit of $4\%$ at $95\%$ C.L. is set on the fraction of D wave.

## Figures and captions

 Distribution of $\Delta M$ for $B^+\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+\pi^+\pi^-$ candidates. The fit of the $X(3872)$ signal is displayed. The solid (blue), dashed (red), and dotted (green) lines represent the total fit, signal component, and background component, respectively. jppj_f[..].pdf [26 KiB] HiDef png [210 KiB] Thumbnail [70 KiB] *.C file Likelihood-weighted distribution of the D--wave fraction. The distribution is normalized to unity. dfracL.pdf [17 KiB] HiDef png [136 KiB] Thumbnail [47 KiB] *.C file Distributions of the test statistic $t \equiv -2\ln[{\cal L}(J_X^{\rm alt}))/{\cal L}(1^{++})]$, for the simulated experiments under the $J^{PC}=J_X^{\rm alt}$ hypothesis (blue solid histograms) and under the $J^{PC}=1^{++}$ hypothesis (red dashed histograms). The values of the test statistics for the data, $t_{\rm data}$, are shown by the solid vertical lines. spinana.pdf [27 KiB] HiDef png [362 KiB] Thumbnail [123 KiB] *.C file Background-subtracted distributions of all angles for the data (points with error bars) and for the $1^{++}$ fit projections (solid histograms). angles1P.pdf [20 KiB] HiDef png [227 KiB] Thumbnail [116 KiB] *.C file Background-subtracted distribution of $\cos\theta_X$ for candidates with $|\cos\theta_{\rho}|>0.6$ for the data (points with error bars) compared to the expected distributions for various $X(3872)$ $J^{PC}$ assignments (solid histograms) with the $B_{LS}$ amplitudes obtained by the fit to the data in the five-dimensional angular space. The fit displays are normalized to the observed number of the signal events in the full angular phase space. histos[..].pdf [24 KiB] HiDef png [324 KiB] Thumbnail [162 KiB] *.C file Animated gif made out of all figures. PAPER-2015-015.gif Thumbnail

## Tables and captions

 Parity-allowed $LS$ couplings in the $X(3872)\rightarrow \rho^0 { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ decay. For comparison, we also list a subset of these couplings corresponding to the lowest $L$, used in the previous determinations [14,16,17] of the $X(3872)$ quantum numbers. Table_1.pdf [44 KiB] HiDef png [109 KiB] Thumbnail [17 KiB] tex code

## Supplementary Material [file]

 FigS1.pdf [18 KiB] HiDef png [150 KiB] Thumbnail [58 KiB] *C file FigS2.pdf [15 KiB] HiDef png [104 KiB] Thumbnail [48 KiB] *C file FigS3.pdf [20 KiB] HiDef png [225 KiB] Thumbnail [115 KiB] *C file FigS4.pdf [24 KiB] HiDef png [292 KiB] Thumbnail [138 KiB] *C file LHCb-P[..].pdf [172 KiB] HiDef png [167 KiB] Thumbnail [29 KiB] *C file

Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.