Prompt production of charmonium $\chi_{c0}$, $\chi_{c1}$ and $\chi_{c2}$ mesons is studied using proton-proton collisions at the LHC at a centre-of-mass 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
Measurements of the ratio of $\chi_{c2}$ to $\chi_{c1}$ production cross-sections for the given $J/\psi$ $p_T$ 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.
Ratio of $\chi_{c0}$ to $\chi_{c2}$ in the observed $J/\psi$\ $p_T$ range from 4-20 GeV. Also given is the $\chi_{c2}$ to $\chi_{c1}$ ratio in the same PT range for comparison. The first systematic error is dominated by the photon efficiency,the $\chi_{c1}$ tail parameters and background modelling, the third from the choiceof $p_T$ spectrum and the fourth from the branching fraction uncertainty.
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