Studio della produzione del bosone $Z$ in associazione a jets a LHCb e ad un futuro Muon Collider

The goal of this thesis is to study $Z+$jets events at LHCb, one of the main LHC experiments, and at a proposed future Muon Collider, with collision energy of 3 TeV. At LHCb the measurements of $Z+1$ jet and $Z+2$ jets differential cross sections have been done, using data from Run 2 taken with collision energy of 13 TeV. The integrated cross sections found are: $$\sigma(Z+1\,\textrm{jet}) = 18.96 \pm 0.09 ^{+0.25}_{-0.34} \pm 0.38\ \textrm{pb}$$ $$\sigma(Z+2\,\textrm{jets}) = 1.34 \pm 0.03 \pm 0.15 \pm 0.03\ \textrm{pb}$$ where the first uncertainty is statistical, the second is systematic and the third is due to luminosity determination. At the Muon Collider the expected sensitivity on the Higgs total width $\Gamma_H$ has been evaluated, combining $ZZ$ productions studied in the semi-leptonic channel with $H \to ZZ$. The resolution found is: $$\frac{\Gamma_H}{\Gamma_H^{SM}} = 1^{+71\%}_{-88\%}$$