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Register a new userNaturally light scalar particles: a generic and simple mechanism
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The hierarchy problem in the Standard Model is usually understood as both a technical problem of stability of the calculation of the quantum corrections to the masses of the Higgs sector and of the unnatural difference between the Planck and gauge breaking scales. Leaving aside the gauge sector, we implement on a purely scalar model a mechanism for generating naturally light scalar particles where both of these issues are solved. In this model, on top of terms invariant under a continuous symmetry, a highly non-renormalizable term is added to the action that explicitly breaks this symmetry down to a discrete one. In the spontaneously broken phase, the mass of the pseudo-Goldstone is then driven by quantum fluctuations to values that are non-vanishing but that are generically, that is, without fine-tuning, orders of magnitude smaller than the UV scale.
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Nonrelativistic scalar field theories can exhibit a natural cascading hierarchy of scales, protected by a hierarchy of polynomial shift symmetries. Using a simple model, we argue that a high-energy cross-over to such nonrelativistic behavior naturally leads to light scalars, and thus represents a useful ingredient for technically natural resolutions of scalar mass hierarchies, perhaps even the Higgs mass hierarchy puzzle.
We present a 5D axion-neutrino model that explains the Standard Model fermion mass hierarchy and flavor structure, while simultaneously generating a high-quality axion. The axion and right-handed neutrinos transform under a 5D Peccei-Quinn gauge symmetry, and have highly suppressed profiles on the UV brane where the symmetry is explicitly broken. This setup allows neutrinos to be either Dirac, or Majorana with hierarchically small sterile neutrino masses. The axion decay constant originates from the IR scale, which in the holographically dual 4D description corresponds to the confinement scale of some new strong dynamics with a high-quality global Peccei-Quinn symmetry that produces a composite axion and light, composite sterile neutrinos. The sterile neutrinos could be observed in astrophysical or laboratory experiments, and the model predicts specific axion--neutrino couplings.
We show that it is possible to accommodate physical scalar resonances within a minimal nonlinearly realized electroweak theory in a way compatible with a natural Hopf algebra selection criterion (Weak Power Counting) and the relevant functional identities of the model (Local Functional Equation, Slavnov-Taylor identity, ghost equations, b-equations). The Beyond-the-Standard-Model (BSM) sector of the theory is studied by BRST techniques. The presence of a mass generation mechanism `a la Stuckelberg allows for two mass invariants in the gauge boson sector. The corresponding t Hooft gauge-fixing is constructed by respecting all the symmetries of the theory. The model interpolates between the Higgs and a purely Stuckelberg scenario. Despite the presence of physical scalar resonances, we show that tree-level violation of unitarity in the scattering of longitudinally polarized charged gauge bosons occurs at sufficiently high energies, if a fraction of the mass is generated by the Stuckelberg mechanism. The formal properties of the physically favoured limit after LHC7-8 data, where BSM effects are small and custodial symmetry in the gauge boson sector is respected, are studied.
We present a non-supersymmetric theory with a naturally light dilaton. It is based on a 5D holographic description of a conformal theory perturbed by a close-to-marginal operator of dimension 4-epsilon, which develops a condensate. As long as the dimension of the perturbing operator remains very close to marginal (even for large couplings) a stable minimum at hierarchically small scales is achieved, where the dilaton mass squared is suppressed by epsilon. At the same time the cosmological constant in this sector is also suppressed by epsilon, and thus parametrically smaller than in a broken SUSY theory. As a byproduct we also present an exact solution to the scalar-gravity system that can be interpreted as a new holographic realization of spontaneously broken conformal symmetry. Even though this metric deviates substantially from AdS space in the deep IR it still describes a non-linearly realized exactly conformal theory. We also display the effective potential for the dilaton for arbitrary holographic backgrounds.
I give explicit fromulae for full propagators of vector and scalar fields in a generic spin-1 gauge model quantized in an arbitrary linear covariant gauge. The propagators, expressed in terms of all-order one-particle-irreducible correlation functions, have a remarkably simple form because of constraints originating from Slavnov-Taylor identities of Becchi-Rouet-Stora symmetry. I also determine the behavior of the propagators in the neighborhood of the poles, and give a simple prescription for the coefficients that generalize (to the case with an arbitrary vector-scalar mixing) the standard $sqrt{mathcal{Z}}$ factors of Lehmann, Symanzik and Zimmermann. So obtained generalized $sqrt{mathcal{Z}}$ factors, are indispensable to the correct extraction of physical amplitudes from the amputated correlation functions in the presence of mixing. The standard $R_xi$ guauges form a particularly important subclass of gauges considered in this paper. While the tree-level vector-scalar mixing is, by construction, absent in $R_xi$ gauges, it unavoidably reappears at higher orders. Therefore the prescription for the generalized $sqrt{mathcal{Z}}$ factors given in this paper is directly relevant for the extraction of amplitudes in $R_xi$ gauges.
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