gaugesinglet

A gauge singlet is a field that is invariant under the Standard Model gauge group, having no charges under SU(3)c, SU(2)L, or U(1)Y. In the Standard Model context, such a field transforms as (1,1,0) and therefore does not interact with the SM gauge bosons at renormalizable level. Gauge singlets can be scalars, fermions, or vector fields, though scalar and fermionic singlets are the most common in model building.

Scalar gauge singlets are often introduced to extend the Higgs sector. The renormalizable potential typically includes terms like m_S^2 S^2, κ S^2 H†H, and λ_S S^4, possibly with a linear term or a Z2 symmetry to stabilize S. Through the Higgs portal (the S–Higgs interactions), a scalar singlet can mix with the Higgs, modify Higgs phenomenology, enable invisible decays, or serve as a dark-matter candidate when stabilized by symmetry.

Gauge-singlet fermions include right-handed neutrinos N, which couple to SM lepton doublets via Yukawa terms y L H N. After electroweak symmetry breaking, these interactions can generate neutrino masses via a seesaw mechanism and can contribute to leptogenesis. Singlet fermions also provide dark-matter possibilities in models where the lightest singlet is stable.

Beyond the Standard Model, gauge-singlet fields commonly arise in hidden or dark sectors and couple to the SM through portal interactions (scalar, neutrino, or other portals). They are also discussed in cosmology and inflationary contexts, where singlet scalars may influence early-universe dynamics.