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Publication# Chiral Asymmetry from a 5D Higgs Mechanism

2007

Journal paper

Journal paper

Abstract

An intriguing feature of the Standard Model is that the representations of the unbroken gauge symmetries are vector-like whereas those of the spontaneously broken gauge symmetries are chiral. Here we provide a toy model which shows that a natural explanation of this property could emerge in higher dimensional field theories and discuss the difficulties that arise in the attempt to construct a realistic theory. An interesting aspect of this type of models is that the 4D low energy effective theory is not generically gauge invariant. However, the non-invariant contributions to the observable quantities are very small, of the order of the square of the ratio between the light particle mass scale and the Kaluza-Klein mass scale. Remarkably, when we take the unbroken limit both the chiral asymmetry and the non-invariant terms disappear. © SISSA 2007.

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Symmetries are omnipresent and play a fundamental role in the description of Nature. Thanks to them, we have at our disposal nontrivial selection rules that dictate how a theory should be constructed. This thesis, which is naturally divided into two parts, is devoted to the broad physical implications that spacetime symmetries can have on the systems that posses them. In the first part, we focus on local symmetries. We review in detail the techniques of a self-consistent framework -- the coset construction -- that we employed in order to discuss the dynamics of the theories of interest. The merit of this approach lies in that we can make the (spacetime) symmetry group act internally and thus, be effectively separated from coordinate transformations. We investigate under which conditions it is not needed to introduce extra compensating fields to make relativistic as well as nonrelativistic theories invariant under local spacetime symmetries and more precisely under scale (Weyl) transformations. In addition, we clarify the role that the field strength associated with shifts (torsion) plays in this context. We also highlight the difference between the frequently mixed concepts of Weyl and conformal invariance and we demonstrate that not all conformal theories (in flat or curved spacetime), can be coupled to gravity in a Weyl invariant way. Once this ``minimalistic'' treatment for gauging symmetries is left aside, new possibilities appear. Namely, if we consider the Poincar'e group, the presence of the compensating modes leads to nontrivial particle dynamics. We investigate in detail their behavior and we derive constraints such that the theory is free from pathologies. In the second part of the thesis, we make clear that even when not gauged, the presence of spontaneously broken (global) scale invariance can be quite appealing. First of all, it makes possible for the various dimensionful parameters that appear in a theory to be generated dynamically and be sourced by the vacuum expectation value of the Goldstone boson of the nonlinearly realized symmetry -- the dilaton. If the Standard Model of particle physics is embedded into a scale-invariant framework, a number of interesting implications for cosmology arise. As it turns out, the early inflationary stage of our Universe and its present-day acceleration become linked, a connection that might give us some insight into the dark energy dynamics. Moreover, we show that in the context of gravitational theories which are invariant under restricted coordinate transformations, the dilaton instead of being introduced ad hoc, can emerge from the gravitational part of a theory. Finally, we discuss the consequences of the nontrivial way this field emerges in the action.

We consider a relativistic plasma of fermions coupled to an Abelian gauge field and carrying a chiral charge asymmetry, which might arise in the early Universe through baryogenesis. It is known that on large length scales, lambda greater than or similar to 1/(alpha mu(5)), the chiral anomaly opens an instability toward the erasure of chiral charge and growth of magnetic helicity. Here the chemical potential mu(5) parametrizes the chiral asymmetry and alpha is the fine-structure constant. We study the process of chiral charge erasure through the thermal fluctuations of magnetic helicity and contrast with the well-studied phenomenon of Chern-Simons number diffusion. Through the fluctuation-dissipation theorem we estimate the amplitude and time scale of helicity fluctuations on the length scale lambda, finding delta H similar to lambda T and tau similar to alpha lambda T-3(2) for a relativistic plasma at temperature T. We argue that the presence of a chiral asymmetry allows the helicity to grow diffusively for a time t similar to T-3/(alpha(5)mu(4)(5)) until it reaches an equilibrium value H similar to mu T-5(2)/alpha, and the chiral asymmetry is partially erased. If the chiral asymmetry is small, mu(5) < T/alpha, this avenue for chiral charge erasure is found to be slower than the chiral magnetic effect for which t similar to T/(alpha(3)mu(2)(5)). This mechanism for chiral charge erasure can be important for the hypercharge sector of the Standard Model as well as extensions including U(1) gauge interactions, such as asymmetric dark matter models.

We study higher-dimensional non-supersymmetric orbifold models where the Higgs field is identified with some internal component of a gauge field. We address two important and related issues that constitute severe obstacles towards model building within this type of constructions: the possibilities of achieving satisfactory Yukawa couplings and Higgs potentials. We consider models where matter fermions are localized at the orbifold fixed-points and couple to additional heavy fermions in the bulk. When integrated out, the latter induce tree-level non-local Yukawa interactions and a quantum contribution to the Higgs potential that we explicitly evaluate and analyse. The general features of these highly constrained models are illustrated through a minimal but potentially realistic five-dimensional example. Finally, we discuss possible cures for the persisting difficulties in achieving acceptable top and Higgs masses. In particular, we consider in some detail the effects induced in these models by adding localized kinetic terms for gauge fields. (C) 2003 Elsevier B.V. All rights reserved.

2003