Study of $b$- and $c$-jets identification for Higgs coupling measurement at the Muon Collider.

The Muon Collider is a possible option for the next generation of high-energy collider machines. It would permit to achieve very high energy in the center of mass using leptons without occurring in significative synchrotron radiation losses as in electrons rings. Due to the muon decay, the detector has to sustain a high level of background: beam decay products and subsequent particles from secondary interactions with the machine elements can reach the interaction point, limiting the physical performance of the detector. Nevertheless, this machine offers the possibility to produce a lot of Higgs bosons events with respect to the corresponding backgrounds, allowing the precise determination of the $b$- and $c$-quark couplings. In this contribution, a study of the identification of $b$- and $c$-jets in the Muon Collider environment will be presented, obtaining an estimation on the statistical precision on the $H\rightarrow b\bar{b}$ cross-section, accounting for the presence of the beam and the physical backgrounds. A preliminary study on the use of machine learning techniques to improve the previous result and to study the $H\rightarrow c\bar{c}$ will also be reported.