Сharmonium production using decays to hadronic final states at LHCb

Non Relativistic QCD (NRQCD) provides so far the most successful framework to describe the production of the $J^{PC}=1^{--}$ quarkonium states. However, a comprehensive description of the production and polarisation of the $J/\psi$ state at Tevatron and LHC in the complete $p_T$ and rapidity range remains a challenge. The heavy quark spin symmetry yields direct links between the long distance matrix elements describing hadroproduction of different charmonium states. The production of linked charmonium states - $\eta_c$ and $J/\psi$, $\eta_c(2S)$ and $\psi(2S)$, and the three $\chi_c$ states - can thus be described simultaneously. Experimentally the production of non-$1^{--}$ charmonium states can be studied by reconstructing their decays to fully hadronic final states. The LHCb measurement of the $\eta_c(1S)$ prompt production and production in inclusive b-hadron decays via the decay $\eta_c(1S)\to p\bar{p}$ is discussed together with its strong impact on NRQCD-based theory models. Recent LHCb measurement of the $\chi_c$ and $\eta_c(2S)$ states production in inclusive b-hadron decays using their decays to $\phi\phi$ is also presented; the discrepancy with existing theoretical prediction is demonstrated. Prospects of measuring prompt $\eta_c(2S)$ production at the LHCb using 2018 data is discussed.