(a) Invariant mass of the $\mu ^+ \mu ^- $ pair for selected $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ candidates. The solid red curve corresponds to the signal and the background is shown as a dashed purple curve. (b) and (c) show the $\Delta M {=} M\left(\mu ^+ \mu ^- \gamma\right) {-} M\left(\mu ^+ \mu ^- \right)$ distributions of selected $\chi _{c}$ candidates with (b) converted and (c) non-converted photons. The upper solid blue curve corresponds to the overall fit function described in Ref. [3]. The lower solid curves correspond to the fitted $\chi _{ c 0}$ , $\chi _{ c 1}$ and $\chi _{ c 2}$ contributions from left to right, respectively (the $\chi _{ c 0}$ peak is barely visible). The background distribution is shown as a dashed purple curve.

(a) Ratio of the reconstruction and selection efficiency for direct $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ compared to $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ from $\chi _{c}$ decays, $\epsilon^{\mathrm{dir}}_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }/\epsilon^{\chi _{c} }_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ , and (b) the photon reconstruction and selection efficiency multiplied by the $\chi _{c}$ selection efficiency, $\epsilon^{\chi_{cJ}}_{\gamma}\epsilon^{\chi_{cJ}}_{\mathrm{sel}}$ , obtained from simulation. The efficiencies are presented separately for the $\chi _{ c 1}$ (red triangles) and $\chi _{ c 2}$ (inverted blue triangles) states, and as a function of $ p_{\mathrm{T}}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ .

(a) Reconstructed $\Delta M_{B^+}=M(\mu ^+ \mu ^- \gamma K)-M(\mu ^+ \mu ^- \gamma)$ mass distribution for $ B^+\rightarrow \chi _{c} K^+$ candidates and (b) the reconstructed $ B^+$ mass distribution for $ B^+\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+$ candidates. The LHCb data are shown as solid black points, the full fit functions with a solid blue (upper) curve, the contribution from signal candidates with a dashed red (lower curve) and the background with a dashed purple curve.

Ratio $\sigma(\chi _{c} \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \gamma) / \sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$ in bins of $ p_{\mathrm{T}}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ in the range $ 2 {<} p_{\mathrm{T}}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } {<} 15 {\mathrm{ Ge V /}c} $ . The LHCb results, in the rapidity range $ 2.0 {<} y^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } {<} 4.5$ and assuming the production of unpolarised $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\chi _{c}$ mesons, are shown with solid black circles and the internal error bars correspond to the statistical error; the external error bars include the contribution from the systematic uncertainties (apart from the polarisation). The lines surrounding the data points show the maximum effect of the unknown $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\chi _{c}$ polarisations on the result. The upper and lower limits correspond to the spin states as described in the text. The CDF data points, at $\sqrt{s} {=} {1.8}\:{\mathrm{ Te V} }$ in $ p\bar{p}$ collisions and in the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ pseudo-rapidity range $ |\eta^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }|<1.0$ , are shown in (a) with open blue circles [5]. The two hatched bands in (b) correspond to the ChiGen Monte Carlo generator prediction [16] and NLO NRQCD [17].

Animated gif made out of all figures.

Polarisation weights in $ p_{\mathrm{T}}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ bins for different combinations of the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ , $\chi _{ c 1}$ and $\chi _{ c 2}$ polarisations. $\lambda_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ is the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ polarisation parameter; $\lambda_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }=+1, -1, 0$ corresponds to fully transverse, fully longitudinal and no polarisation respectively. $ m_{\chi_{cJ}}$ is the azimuthal angular momentum quantum number corresponding to total angular momentum $J$; Unpol means the $\chi _{c}$ is unpolarised.

Summary of the systematic uncertainties on $\sigma(\chi _{c} \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \gamma) / \sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$ in each $ p_{\mathrm{T}}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ bin.

Ratio $\sigma(\chi _{c} \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \gamma) / \sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$ in bins of $ p_{\mathrm{T}}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ in the range $ 2 {<} p_{\mathrm{T}}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } {<} 15 {\mathrm{ Ge V /}c} $ and in the rapidity range $ 2.0 {<} y^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } {<} 4.5$ . The first error is statistical and the second is systematic (apart from the polarisation). Also given is the maximum effect of the unknown polarisations on the results as described in Sect. 5.