field theory, the Stueckelberg action (named after Ernst Stueckelberg) describes a massive spin-1 field as a R (the real numbers are the Lie algebraof U(1)) Yang-Mills theorycoupled to a real scalar fieldφ which takes on values in a real 1D affine representationof R with" m" as the coupling strength.
Higgs mechanismof spontaneous symmetry breakingapplies here. The only difference being we have an affine representation instead of a linear representation.
By gauge-fixing φ=0, we get the
This explains why, unlike the case for non-abelian vector fields,
quantum electrodynamicswith a massive photon is renormalizableeven though it's not manifestly gauge invariant(after the Stückelberg scalar has been eliminated in the Proca action).
The Stueckelberg Extension of the Standard Model
Stueckelberg Lagrangianof the StSM ( Stueckelberg Extensionof the Standard Model) consists of a gauge invariantkinetic term for a massive U(1)gauge field. Such a term can be implemented into the Lagrangian of the Standard Modelwithout destroying the renormalizability of the theory and further provides a mechanism formass generation that is distinct from the Higgsmechanism in the context of abeliangauge theories.
The model involves a non-trivialmixing of the Stueckelberg and the Standard Model sectors by including an additional term in the effective Lagrangian of the Standard Model given by :
The first term above is the Stueckelberg field strength, and are topological mass parameters and is the axion.After symmetry breaking in the electroweak sector the photon remains massless. The model predicts a new type of gauge boson dubbed which inherits a very distinct narrow decay width in this model. The St sector of the StSM decouples from the SM in limit .
Stueckelberg type couplings arise quite naturally in theories involving
compactificationsof higher dimensional string theory, in particular, these couplings appear in the dimensional reduction of the ten dimensional N = 1 supergravitycoupled to supersymmetricYang-Mills gauge fields in the presence of internal gauge fluxes. In the context of intersecting D brane modelbuilding, products of abelian gauge groups are broken to their SU(N)subgroups via the Stueckelberg couplings and thus the abelian gauge fields become massive. Further, in a much simpler fashion one may consider a model with only one extra dimension (a type of Kaluza-Kleinmodel) and compactify down to a four dimensional theory. The resulting Lagrangian will contain massive vector gauge bosons that acquire masses through the Stueckelberg mechanism.
* [http://arxiv.org/abs/hep-th/0304245 Review:Stueckelberg Extension of the Standard Model and the MSSM]
* Boris Kors, Pran Nath
http://arxiv.org/abs/hep-ph/0402047 http://arxiv.org/abs/hep-ph/0406167 http://arxiv.org/abs/hep-ph/0503208
Searching for Stueckelberg
* Daniel Feldman, Zuowei Liu, Pran Nathhttp://arxiv.org/abs/hep-ph/0603039http://arxiv.org/abs/hep-ph/0606294
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