Prompt charmonia production and polarization at LHC in the NRQCD with $k_T$-factorization. II. ${\chi }_c$ mesons

In the framework of the $k_T$-factorization approach, the production of prompt $\psi (2S)$ mesons in $pp$ collisions at the LHC energies is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses $g^{*}{g}^{*}\to {\chi }_{cJ}$ and nonrelativistic QCD formalism for bound states. The transverse-momentum-dependent (unintegrated) gluon densities in a proton were derived from the Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with the Kimber-Martin-Ryskin prescription. Taking into account both color-singlet and color-octet contributions, we deduce the corresponding nonperturbative long-distance matrix elements from the fits to the latest ATLAS data on ${\chi }_{c1}$ and ${\chi }_{c2}$ transverse-momentum distributions at $\sqrt{s}=7\mathrm{TeV}$. We find that these distributions at small and moderate $p_T$ are formed mainly by the color-singlet components. We successfully described the data on the relative production rates $\sigma ({\chi }_{c2})/\sigma ({\chi }_{c1})$ presented by the ATLAS, CMS, and LHCb Collaborations. We find that the fit points to unequal wave functions of ${\chi }_{c1}$ and ${\chi }_{c2}$ states.

Figure 1

The prompt ${\chi }_c$ production at the LHC calculated as a function of ${\chi }_c$ meson transverse momenta at $\sqrt{s}=7\mathrm{TeV}$. Left panel: The dashed and dotted curves correspond to the color-singlet ${{}^{3}P}_J^{(1)}$ and color-octet ${}^3{S}_1^{(8)}$ contributions, respectively, calculated with the KMR gluon density. The solid curve represent the sum of CS and CO terms. Right panel: The solid, dashed, and dash-dotted curves correspond to the predictions obtained with the A0, JH, and KMR gluon densities, respectively. The experimental data are from ATLAS [39].

Figure 2

The prompt ${\chi }_c$ production at the LHC calculated as a function of decay $J/\psi$ transverse momenta at $\sqrt{s}=7\mathrm{TeV}$. The solid, dashed, and dash-dotted curves correspond to the predictions obtained with the A0, JH, and KMR gluon densities, respectively. The experimental data are from ATLAS [39].

Figure 3

The relative production rate $\sigma ({\chi }_{c2})/\sigma ({\chi }_{c1})$ calculated as a function of $J/\psi$ meson transverse momenta at $\sqrt{s}=7\mathrm{TeV}$. The notation of all curves is the same as in Fig. 2. The experimental data are from ATLAS [39], CMS [40], and LHCb [41].