$\chi_{c1}$ and $\chi_{c2}$ polarization as a probe of color octet channel

We analyze joint LHC data on the production of $\chi _{c1}$ and $\chi _{c2}$ mesons together with the polarization data obtained very recently by the CMS Collaboration at $\sqrt{s} = 8$ TeV. Our consideration is based on the $k_T$-factorization approach and nonrelativistic QCD formalism for the formation of bound states. The observed polar anisotropy of $\chi _{c1}$ and $\chi _{c2}$ decays can be described as a combined effect of the color-singlet and color-octet contributions. We extract the corresponding long-distance matrix elements from the fits. Our fits point to unequal color singlet wave functions for $\chi _{c1}$ and $\chi _{c2}$ states.