This short chapter touches on the limitations of the SM. The SM does not include gravity, and it does not explain the major components of the mass–energy budget of the universe, dark matter and dark energy, the latter being probably the cosmological constant. CP violation in the quark sector is too small to explain the matter–antimatter asymmetry of the Universe, but, if confirmed, the non-SM CP violation in the neutrino sector might be large enough. The ‘strong CP violation’ problem might be solved with the existence of a very light particle, the axion; experiments are reaching the requested sensitivity. Supersymmetric particles present in some extensions of the SM have been searched for, but not found so far.
The SM contains too many free parameters: the masses of the fermions and of the bosons, and the mixing angles. The masses of the fermions, from neutrinos to the top quark, span 13 orders of magnitude. Why such big difference? Why is mixing small in the quark sector, and large in the neutrino sector? Why do the proton and the electron have exactly equal (and opposite) charges? Why are there just three families? Are there any spatial dimensions beyond the three we know? And so on.