QCD studies with processes involving a $J/\psi$ decaying into muons

This thesis reports on the measurement of the $\Lambda_b$ polarization and the parity-violating asymmetry parameter in the decay channel $\Lambda_b\to J/\psi\Lambda$ from pp collisions at $\sqrt{s}$ = 7 and 8 TeV, and on the exclusive $J/\psi$ photo-production in ultra peripheral proton-lead collisions at $\sqrt{s_{NN}}=$ 8.16 TeV using data collected by the CMS experiment at the LHC. The $\Lambda_b$ polarization is measured to be 0.00 $\pm$ 0.06 (stat) $\pm$ 0.06 (syst) and the parity-violating asymmetry parameter is determined to be 0.14 $\pm$ 0.14 (stat) $\pm$ 0.10 (syst); results are compared to predictions from perturbative QCD. The measured photo-production cross sections $\sigma(\gamma +p \to J/\psi + p)$ in the $J/\psi$ rapidity intervals 2.0 < y < 2.4 and -2.4 < y < -2.0, and Bjorken-x ranges of 2$\times 10^{-2}$ to 2$\times 10^{-5}$, are 62 $\pm$ 5 $\pm$ 2 nb, and 228 $\pm$ 18 $\pm$ 8 nb, respectively, the first uncertainty is statistical and the second due to luminosity determination; results are compared with measurements from ALICE and LHCb.