Measurement of the relative cross-section $\sigma(\chi_{c_2})/\sigma(\chi_{c_1})$ of prompt $\chi_c$ mesons using at LHCb

The production of heavy quarkonia remains a challenging problem for understanding Quantum Chromodynamics (QCD). This note reports on the production cross-section ratio of $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ with the $\chi_c$ state decaying into $\chi_c \rightarrow J/\psi \gamma$. The $J\psi$ is identified via the decay $J/\psi \rightarrow \mu^+ \mu^-$ while the photon is reconstructed from conversions in the detector material. The analysis is based on a data sample of 370 pb$^{-1}$ recorded by the LHCb experiment at the Large Hadron Collider in 2011. The results are compared to a study in which the photons are detected in the LHCb calorimeter using 37 pb$^{-1}$ of data recorded in 2010, as well as theoretical predictions.