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Register a new userAsymptotically Free Non-Abelian Gauge Theories With Fermions and Scalars As Alternatives to QCD
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In this paper we construct non-Abelian gauge theories with fermions and scalars that nevertheless possess asymptotic freedom.The scalars are taken to be in a chiral multiplet transforming as $(2,2)$ under $SU(2)_Lotimes SU(2)_R$ and transforming as singlets under the colour SU(3) group. We consider two distinct scenarios, one in which the additional scalars are light and another in which they are heavier than half the Z-boson mass. It is shown that asymptotic freedom is obtained without requiring that all additional couplings keep fixed ratios with each other. It is also shown that both scenarios can not be ruled out by what are considered standard tests of QCD like R- parameter, g-2 for muons or deep inelastic phenomena. The light mass scenario is however ruled out by high precision Z-width data (and only by that one data).The heavy mass scenario is still viable and is shown to naturally pass the test of flavour changing neutral currents. It also is not ruled out by precision electroweak oblique parameters. Many distinctive experimental signatures of these models are also discussed.
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We construct chiral theories with the smallest number $n_chi$ of Weyl fermions that form an anomaly-free set under various Abelian gauge groups. For the $U(1)$ group, where $n_chi = 5$, we show that the general solution to the anomaly equations is a set of charges given by cubic polynomials in three integer parameters. For the $U(1) times U(1)$ gauge group we find $n_chi = 6$, and derive the general solution to the anomaly equations, in terms of 6 parameters. For $U(1) times U(1) times U(1)$ we show that $n_chi = 8$, and present some families of solutions. These chiral gauge theories have potential applications to dark matter models, right-handed neutrino interactions, and other extensions of the Standard Model. As an example, we present a simple dark sector with a natural mass hierarchy between three dark matter components.
We study the relationship between three non-Abelian topologically massive gauge theories, viz. the naive non-Abelian generalization of the Abelian model, Freedman-Townsend model and the dynamical 2-form theory, in the canonical framework. Hamiltonian formulation of the naive non-Abelian theory is presented first. The other two non-Abelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2-form theory in the canonical framework and show that the dynamical 2-form theory cannot be considered as the embedded version of naive non-Abelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.
Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Greens functions for a Yang--Mills theory with composite and background fields are introduced, including the generating functional of vertex Greens functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and utilized on a systematic basis. On the one hand, this involves the consideration of (modified) Ward identities with a field-dependent anticommuting parameter, also depending on a non-trivial background. On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov--Zwanziger theory and by the Volovich--Katanaev model of two-dimensional gravity with dynamical torsion.
We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.
We study the solution to the Slavnov-Taylor (ST) identities in spontaneously broken effective gauge theories for a non-Abelian gauge group. The procedure to extract the $beta$-functions of the theory in the presence of (generalized) non-polynomial field redefinitions is elucidated.
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