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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]
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jppj_fit_x3872.pdf

Likelihood-weighted distribution of the D--wave fraction. The distribution is normalized to unity.

dfracL.pdf [17 KiB]
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dfracL.pdf

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]
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spinana.pdf

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]
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angles1P.pdf

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]
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histos_cosX_cosrho.pdf

Animated gif made out of all figures.

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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]
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tex code
Table_1.pdf

Supplementary Material [file]

FigS1.pdf [18 KiB]
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FigS4.pdf
LHCb-P[..].pdf [172 KiB]
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LHCb-PAPER-2015-015-supplemental.pdf

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