Pseudo Goldstone BosonEdit
A pseudo Goldstone boson (PGB) is a light scalar particle that arises when a continuous global symmetry is spontaneously broken, but the symmetry is only approximate because it is explicitly broken by small terms in the underlying theory. If the symmetry were exact, the breaking would produce a massless mode; the explicit breaking lifts this degeneracy and endows the would-be Goldstone boson with a small mass. The lightness of these particles is thus tied to the strength of the explicit symmetry breaking and the scale at which the symmetry is broken, commonly denoted by a decay constant f. For a concise account of the origin and properties of these states, see the discussion of Goldstone boson and spontaneous symmetry breaking.
Pseudo-Goldstone bosons are a central organizing idea in both the Standard Model of particle physics and its extensions. The classic example is the set of pions, which appear as pseudo-Goldstone bosons of the approximate chiral symmetry of quantum chromodynamics (QCD). In beyond-Standard-Model theories, the same mechanism is invoked to keep certain scalar masses light without resorting to extreme fine-tuning. Prominent instances include the idea that the Higgs boson could be a PNGB in composite Higgs scenarios, and axions or axion-like particles (ALPs) arising as PNGBs of a Peccei–Quinn-type symmetry. See pion, axion, Higgs boson, and Composite Higgs for context and applications.
Theoretical basis
Emergence from symmetry breaking: A Goldstone boson (or Nambu–Goldstone boson) appears when a global continuous symmetry is spontaneously broken. If the symmetry is exact, the resulting mode is strictly massless; if the symmetry is only approximate, explicit breaking terms give it a small mass, creating a pseudo-Goldstone boson. See Nambu–Goldstone boson and spontaneous symmetry breaking.
Mass and couplings: The mass of a PNGB is tied to the size of the explicit breaking and the symmetry-breaking scale, typically m_PGB^2 ~ epsilon times a function of the decay constant f, where epsilon parametrizes explicit breaking. Their interactions are largely controlled by the symmetry structure and are often suppressed by powers of 1/f. For QCD pions, the explicit breaking comes from quark masses, while for axions the explicit breaking is related to nonperturbative QCD effects; see Gell-Mann–Oakes–Renner relation for the pion case and Peccei–Quinn symmetry for axions.
Soft versus explicit breaking: In many constructions, breaking terms are “soft” or small and preserve the PNGB character to a good approximation. This protection mechanism is what makes PNGBs attractive as natural explanations for light scalar masses without large radiative corrections.
Examples in physics
QCD pions as PNGBs: The light pions (π^+, π^0, π^−) are the canonical PNGBs of the spontaneously broken chiral symmetry in QCD, specifically SU(2)_L × SU(2)_R → SU(2)_V. They acquire a small mass proportional to the light quark masses (u and d) and are described by chiral perturbation theory at low energies. See pion and chiral symmetry.
Kaons and the eta: In the broader SU(3) flavor context, pions, kaons, and the eta meson arise as pseudo-Goldstone bosons with masses reflecting the hierarchy of quark masses. The eta prime, in particular, is heavier due to anomalous breaking of the axial U(1) symmetry. See kaon and eta meson for the broader picture.
Axions and axion-like particles: The axion is a PNGB of a global Peccei–Quinn symmetry introduced to solve the strong CP problem. Its mass is generated by nonperturbative QCD effects and is inversely related to the symmetry-breaking scale. Axions and related axion-like particles (ALPs) are a major focus of experimental searches and cosmological models. See axion and Peccei–Quinn symmetry.
The Higgs as a PNGB in composite Higgs models: In several beyond-Standard-Model frameworks, the Higgs doublet is realized as a PNGB of a spontaneously broken global symmetry at a higher scale f. This can protect the Higgs mass from large quantum corrections and explain why it is lighter than the underlying new physics scale. Realizations include the broader class of Composite Higgs models and, in specific constructions, the Little Higgs mechanism. See Higgs boson and Composite Higgs.
Other PNGBs in cosmology and beyond: PNGBs appear in models of dark energy (quintessence) and in various dark sector constructions where light scalar degrees of freedom are invoked to explain observations without resorting to heavy, strongly interacting states. See quintessence and axion-like particle.
Role in beyond-Standard-Model physics
Naturalness and model-building: Proponents argue that treating certain scalars as PNGBs provides a natural mechanism to keep masses light without severe fine-tuning, aligning with a long-standing preference for symmetry-based explanations in fundamental physics. This has driven the development of composite Higgs theories and related approaches, where the Higgs mass is protected by its PNGB character.
Experimental constraints: The lack of clear signals for new light PNGBs at current colliders constrains naturalness-based scenarios. The Higgs boson couplings measured at the Large Hadron Collider (LHC) are broadly SM-like, limiting deviations that PNGB-based models typically predict. This has sparked debates about the viability of certain naturalness-motivated PNGB frameworks and has sharpened discussions about the role of naturalness as a guide in theory choice. See Higgs boson and Little Higgs.
Axions and cosmology: If axions or ALPs exist, they have distinctive experimental footprints in laboratory searches and astrophysical observations. Projects aiming to detect axions through their coupling to photons or via astrophysical processes illustrate how PNGB ideas translate into testable science. See axion and axion-like particle.
Debates on naturalness and the data: Critics question how much weight to place on naturalness as a predictive principle, noting that the absence of new PNGB-related states at accessible energies challenges the expectation that symmetry-based protections would yield readily observable consequences. Advocates counter that the PNGB framework remains a robust, falsifiable way to organize and test ideas about mass scales, symmetry structure, and new physics.