Boson half-integer spin particles cannot be bosons and integer spin particles cannot be fermions. In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities — when their wave functions overlap. At low densities, both types of statistics are well approximated by Maxwell–Boltzmann statistics, which is described by classical mechanics. All observed elementary particles are either fermions or bosons. The observed elementary bosons are all gauge bosons: photons, W and Z bosons, gluons, except the Higgs boson which is a scalar boson. Finally, many approaches to quantum gravity postulate a force carrier for gravity, the graviton,
W and Z bosons the pillars of the Standard Model of particle physics, particularly given the 2012 discovery of the Higgs boson by the CMS and ATLAS experiments. The model predicts that W and Z bosons have the following masses: where g is the SU(2) gauge coupling, g' is U(1) gauge coupling, and v is the Higgs vacuum expectation value. Unlike beta decay, the observation of neutral current interactions that involve particles requires huge investments in particle accelerators and detectors, such as are available in only a few high-energy physics laboratories in the world (and then only after 1983). This is because Z-bosons behave