The prompt production of charmonium $\chi_{c}$ and $J/\psi$ states is studied in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=7$ TeV at the Large Hadron Collider. The $\chi_{c}$ and $J/\psi$ mesons are identified through their decays $\chi_{c}\rightarrow J/\psi \gamma$ and $J/\psi\rightarrow \mu^+\mu^-$ using 36 pb$^{-1}$ of data collected by the LHCb detector in 2010. The ratio of the prompt production cross-sections for $\chi_{c}$ and $J/\psi$, $\sigma (\chi_{c}\rightarrow J/\psi \gamma)/ \sigma (J/\psi)$, is determined as a function of the $J/\psi$ transverse momentum in the range $2 < p_{\mathrm T}^{J/\psi} < 15$ GeV/$c$. The results are in excellent agreement with next-to-leading order non-relativistic expectations and show a significant discrepancy compared with the colour singlet model prediction at leading order, especially in the low $p_{\mathrm T}^{J/\psi}$ region.
Ratio of cross sections for Chi_c to J/psi production in bins of J/psi transverse momentum over the J/psi rapidity range 2.0 to 4.5. The maximum uncertainties from the unknown Chi_c polarizations shown separately.
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