Prompt production of charmonium $\chi_{c0}$, $\chi_{c1}$ and $\chi_{c2}$ mesons is studied using protonproton collisions at the LHC at a centreofmass energy of $\sqrt{s}=7$TeV. The $\chi_{c}$ mesons are identified through their decay to $J/\psi\gamma$, with $J/\psi\to\mu^+\mu^$ using photons that converted in the detector. A data sample, corresponding to an integrated luminosity of $1.0\mathrm{fb}^{1}$ collected by the LHCb detector, is used to measure the relative prompt production rate of $\chi_{c1}$ and $\chi_{c2}$ in the rapidity range $2.0<y<4.5$ as a function of the $J/\psi$ transverse momentum from 3 to 20 GeV$/c$. First evidence for $\chi_{c0}$ meson production at a highenergy hadron collider is also presented.
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} $. 
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(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). 
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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) 45 $ {\mathrm{ Ge V /}c}$ and (b) 1113 $ {\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 dotdashed curve) and the $\chi _{ c 0}$ signal (purple longdashed curve). 
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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 dotdashed curve) and $\chi _{ c 0}$ signal (purple longdashed curve). 
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(left) Ratio of $\chi _{ c 2}$ to $\chi _{ c 1}$ crosssections 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. 
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Comparison of the ratio of $\chi _{ c 2}$ to $\chi _{ c 1}$ crosssections 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. 
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Animated gif made out of all figures. 
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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. 
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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. 
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Measurements of the ratio of $\chi _{ c 2}$ to $\chi _{ c 1}$ production crosssections 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. 
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Created on 20 August 2019.Citation count from INSPIRE on 20 August 2019.