On the first-principles determination of the Standard Model fundamental parameters in the quark sector

The 2-years old observation at LHC of a new boson, with a mass of 126 GeV, is a great achievement. Its interpretation as a Brout-Englert-Higgs boson is very plausible and appealing to complete the zoology of fundamental particles in the Standard Model. The interplay between theorists and experimentalists that we have witnessed has come with a huge work to determine with enough precision the parameters of the Standard Model: couplings, masses, mixing angles. Among the various tools developed by physicists, lattice QCD is particularly suitable to know those parameters in the quark sector. In this report I discuss the lattice measurement of Standard Model fundamental parameters that are closely related to Higgs boson: its main production mode is the gluon-gluon fusion, whose the magnitude is governed by the strong coupling constant, while its most favored decay channel, $H \to b \bar{b}$, has a coupling proportional to the $b$ quark mass. I outline the improvements brought by the lattice community: simulations with $N_f=2+1+1$ dynamical quarks are crucial to study how much the charm quark impacts the strong coupling constant calculation. A non perturbative matching between Heavy Quark Effective Theory and QCD is welcome to handle in an appropriate way the $b$ quark physics. An extensive methodological exploration is necessary to get rid of contribution from excited states in correlation functions computed to extract hadron masses and decay constants. The effort to measure the $u/d$, $s$ and $c$ quark masses is also discussed, illustrating the benefit of using an automatic $O(a)$ improved lattice regularization.