Distribution of the mass difference $\Delta M\equiv M(\mu ^+\mu ^- \gamma )-M(\mu ^+\mu ^- )$ for $\chi _{c}$ candidates with $3< p_{\rm T}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } <20 {\mathrm{ Ge V /}c} $.

(a) Efficiency of converted photon reconstruction and selection relative to the calorimetric photon efficiency for data (red circles) and simulated events (blue triangles) as a function of $p_{\rm T}^{\gamma }$ . (b) Ratio of photon efficiencies $\varepsilon^{\gamma }_{\chi _{ c 1} }/\varepsilon^{\gamma }_{\chi _{ c 2} }$ as a function of $p_{\rm T}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ from simulation (blue triangles) and after correcting the simulation for the converted photon efficiency measured in data (red circles) taken from plot (a).

Distribution of $\Delta M=M(\mu ^+\mu ^- \gamma )-M(\mu ^+\mu ^- )$ for $p_{\rm T}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ in the range (a) 4--5 $ {\mathrm{ Ge V /}c}$ and (b) 11--13 $ {\mathrm{ Ge V /}c}$ . The results of the fit are also shown, with the total fitted function (blue solid curve), the $\chi _{ c 1}$ signal (green dashed curve), the $\chi _{ c 2}$ signal (red dot-dashed curve) and the $\chi _{ c 0}$ signal (purple long-dashed curve).

Distribution of $\Delta M=M(\mu ^+\mu ^- \gamma )-M(\mu ^+\mu ^- )$ (blue histogram) for $4< p_{\rm T}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } <20 {\mathrm{ Ge V /}c} $. (a) The background estimated using fake photons (green) is superimposed on the $\Delta M$ distribution, together with the function used to parametrize it (black solid line). (b) The same $\Delta M$ distribution after background subtraction (using the shape shown in (a) and its fitted normalization): total fitted function (blue solid curve), $\chi _{ c 1}$ signal (green dashed curve), $\chi _{ c 2}$ signal (red dot-dashed curve) and $\chi _{ c 0}$ signal (purple long-dashed curve).

(left) Ratio of $\chi _{ c 2}$ to $\chi _{ c 1}$ cross-sections at $\sqrt{s}=7$ $\mathrm{ Te V}$ for $2.0<y<4.5$. The statistical uncertainty is shown with a red error bar and the systematic uncertainty with a hashed rectangle. (right) Comparison of the LHCb results (with total uncertainty) with the NLO NRQCD calculation from Ref. [5] (blue shading) and the LO NRQCD calculation of Ref. [24] (solid green). The LHCb results are obtained assuming the $\chi _{c}$ mesons are produced unpolarized.

Comparison of the ratio of $\chi _{ c 2}$ to $\chi _{ c 1}$ cross-sections obtained by LHCb using calorimetric photons [12] (green open squares), CMS result [11] (blue filled squares), CDF result (purple filled triangles) [10] and the result presented here (red open circles) under the assumption (left) of unpolarized states and (right) under the assumption $(m_{\chi _{ c 1} },m_{\chi _{ c 2} })=(0,0)$ in the helicity frame. The uncertainty due to the limited knowledge of the branching fractions of $\chi _{c} \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \gamma$, which is common to all the measurements, is not included here.

Animated gif made out of all figures.

Systematic uncertainties on the ratio of $\chi _{ c 2}$ and $\chi _{ c 1}$ yields for each $p_{\rm T}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ bin (in percent). The total systematic uncertainty is defined as the quadratic sum of all the systematic uncertainties.

Correction factors to be applied to the final $\sigma(\chi _{ c 2} )/\sigma(\chi _{ c 1} )$ results for each $p_{\rm T}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ bin for different combinations of $\chi _{ c 1}$ and $\chi _{ c 2}$ polarization states $|J,m_{\chi_{cJ}}>$ with $|m_{\chi_{cJ}}|=0,...,J$ ("unpol" means the $\chi _{c}$ is unpolarized). The polarization axis is defined as the direction of the $\chi _{c}$ in the laboratory frame.

Measurements of the ratio of $\chi _{ c 2}$ to $\chi _{ c 1}$ production cross-sections for the given $p_{\rm T}^{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ range assuming unpolarized $\chi _{c}$ production. The first uncertainty is statistical, the second is systematic, the third is from the branching fractions used and the last gives the maximum correction due to the unknown polarization.