Stueckelberg action

In field theory, the Stueckelberg action (named after Ernst Stueckelberg) describes a massive spin-1 field as a R (the real numbers are the Lie algebra of U(1)) Yang-Mills theory coupled to a real scalar field φ which takes on values in a real 1D affine representation of R with" m" as the coupling strength.

:mathcal{L}=-frac{1}{4}(partial^mu A^ u-partial^ u A^mu)(partial_mu A_ u-partial_ u A_mu)+frac{1}{2}(partial^mu phi+m A^mu)(partial_mu phi+m A_mu)

The usual Higgs mechanism of spontaneous symmetry breaking applies here. The only difference being we have an affine representation instead of a linear representation.

By gauge-fixing φ=0, we get the Proca action.

This explains why, unlike the case for non-abelian vector fields, quantum electrodynamics with a massive photon is renormalizable even 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

The Stueckelberg Lagrangian of the StSM (Stueckelberg Extension of the Standard Model) consists of a gauge invariant kinetic 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 Higgs mechanism in the context of abelian gauge 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 :mathcal{L}_{St}=-frac{1}{4}C_{mu u }C^{mu u }+g_XC_{mu }mathcal{J}_X^{mu }-frac{1}{2}left(partial _{mu }sigma +M_1C_{mu}+M_2B_{mu } ight)^2.

The first term above is the Stueckelberg field strength, M_1 and M_2 are topological mass parameters and sigma is the axion.After symmetry breaking in the electroweak sector the photon remains massless. The model predicts a new type of gauge boson dubbed Z'_{St} which inherits a very distinct narrow decay width in this model. The St sector of the StSM decouples from the SM in limit M_2/M_1 o 0.

Stueckelberg type couplings arise quite naturally in theories involving compactifications of higher dimensional string theory, in particular, these couplings appear in the dimensional reduction of the ten dimensional N = 1 supergravity coupled to supersymmetric Yang-Mills gauge fields in the presence of internal gauge fluxes. In the context of intersecting D brane model building, 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-Klein model) and compactify down to a four dimensional theory. The resulting Lagrangian will contain massive vector gauge bosons that acquire masses through the Stueckelberg mechanism.

References

* [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


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Ernst Stueckelberg — This article is about the physicist; for his grandfather, the Swiss artist, see Ernst Alfred Stueckelberg Ernst Carl Gerlach Stueckelberg (February 1, 1905, Basel September 4, 1984, Basel) was a Swiss mathematician and physicist.In 1926… …   Wikipedia

  • Z' boson — In particle physics, a Z ′ boson (or Z prime boson) refers to a hypothetical new neutral gauge boson (named in analogy with the Standard Model Z boson).Infobox Particle bgcolour = name = Z Boson caption = num types = composition = Elementary… …   Wikipedia

  • Covariant formulation of classical electromagnetism — Electromagnetism Electricity · …   Wikipedia

  • Renormalization group — In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the… …   Wikipedia

  • Detailed balance — The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions): At equilibrium, each elementary process should be equilibrated by its reverse… …   Wikipedia

  • Théorie de jauge sur réseau — Traduction à relire Lattice gauge theory → …   Wikipédia en Français

  • Pran Nath — Infobox Scientist image width = 150px name = Pran Nath box width = birth date = 1939 birth place = death date = death place = residence = USA citizenship = nationality = ethnicity = field = Particle physics work institutions = Northeastern… …   Wikipedia

  • Renormalisation — Traduction à relire Renormalization → Reno …   Wikipédia en Français

  • CHAMPS (THÉORIE DES) — La théorie des champs étudie la dynamique des systèmes à un nombre infini de degrés de liberté. Elle trouve son origine dans l’électromagnétisme et s’est développée en intégrant mécanique quantique et relativité. Après en avoir suivi l’évolution …   Encyclopédie Universelle

  • Groupe De Renormalisation — En mécanique statistique, le groupe de renormalisation (qui est plutôt un semi groupe, les transformations n étant pas inversibles) est un ensemble de transformations qui permettent de transformer un hamiltonien en un autre hamiltonien par… …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.