Pseudogoldstone

A pseudo-Goldstone boson is a light scalar particle that arises when a global continuous symmetry is spontaneously broken and is also explicitly broken by small symmetry-violating effects. In the exact symmetry limit, spontaneous breaking produces massless Goldstone bosons with derivative interactions. When the symmetry is only approximate, the explicit breaking lifts their mass slightly, producing pseudo-Goldstone bosons with a small but nonzero mass and a potential.

The mass and interactions of a pseudo-Goldstone boson are controlled by the scale of spontaneous breaking f and by the strength of the explicit symmetry-breaking terms. Typically they are lighter than other states in the same theory and interact more weakly than generic scalars, because their couplings are constrained by the approximate symmetry.

Well-known examples include pions in quantum chromodynamics, which are pseudo-Goldstone bosons of the approximate chiral SU(2)_L x SU(2)_R symmetry; their small mass arises from nonzero up and down quark masses, with pion masses around 135–140 MeV. Another prominent example is the axion, a pseudo-Goldstone boson of a spontaneously broken Peccei-Quinn symmetry, whose mass is generated by QCD dynamics, and which features as a possible dark matter candidate. In some beyond-Standard Model theories, the Higgs boson itself is described as a pseudo-Goldstone boson of a larger global symmetry, with explicit breaking from electroweak gauge and Yukawa interactions providing its potential.

Pseudo-Goldstone bosons thus embody how approximate symmetries can yield light, weakly coupled scalars with important roles in particle physics and cosmology.