The clockwork mechanism would be completely spoiled by the presence of a cosmological constant in the bulk of its 5D construction, or by analogous terms in the discrete case. It is believed that supersymmetry is required to forbid the appearance of these fatal terms, thus apparently tying the fate of the clockwork to the presence of supersymmetry. In this letter we argue that a robust clockwork can be obtained also without supersymmetry, by providing a model for the clockwork/linear dilaton EFT where this protection is instead related to diffeomorphism invariance in a higher number of extra dimensions. We show that the clockwork mechanism is a quite general setup that emerges, rather minimally, from pure gravity in the presence of $D-5$ additional flat extra dimensions. The linear dilaton model is obtained asymptotically in the limit of infinitely many extra dimensions. We then study the finite-$D$ theory, which is a deformation of the linear dilaton one, but still a clockwork theory for $D$ large enough.
Implications of supersymmetrizing the clockwork axions are studied. Supersymmetry ensures that the saxions and axinos have the same pattern of the coupling hierarchy as the clockwork axions. If we assume supersymmetry breaking is universal over the clockwork sites, the coupling structure is preserved, while the mass orderings of the saxions and axinos can differ depending on the supersymmetry breaking scale. While the massive saxions and axions quickly decay, the lightest axino can be stable and thus a dark matter candidate. The relic abundance of the axino dark matter from thermal production …
The clockwork mechanism is a means of naturally generating exponential hierarchies in theories without significant hierarchies among fundamental parameters. We emphasize the role of interactions in the clockwork mechanism, demonstrating that clockwork is an intrinsically abelian phenomenon precluded in non-abelian theories such as Yang-Mills, non-linear sigma models, and gravity. We also show that clockwork is not realized in extra-dimensional theories through purely geometric effects, but may be generated by appropriate localization of zero modes.
We consider the higher order clockwork theory of gravitational interactions, whereby a number of gravitons are coupled together with TeV strength, but nevertheless generate a Planck scale coupling to matter without the need for a dilaton. It is shown that the framework naturally lends itself to a five-dimensional geometry, and we find the 5D continuum version of such deconstructed 4D gravitational clockwork models. Moreover, the clockwork picture has matter coupled to particular gravitons, which in the 5D framework looks like a braneworld model, with the Randall-Sundrum model being a special c…
The clockwork mechanism can explain interactions which are dimensionally very weak without the need for very large mass scales. We present a model in which the clockwork mechanism generates the very small Higgs portal coupling and dark matter particle mass necessary to explain cold dark matter via the freeze-in mechanism. We introduce a TeV-scale scalar clockwork sector which couples to the Standard Model via the Higgs portal. The dark matter particle is the lightest scalar of the clockwork sector. We show that the freeze-in mechanism is dominated by decay of the heavy clockwork scalars to lig…
We incorporate clockwork mechanism into the Standard Model flavour sector and show that the observed pattern of fermion masses and mixing can be obtained without any unnaturally small or large parameter in the fundamental theory. By introducing $N_f$ pairs of vectorlike fermions, as clockwork gears, for each generation of the Standard Model fermions and setting up a characteristic clockwork potential, it is shown that the inter-generational mass hierarchies are determined by $N_f$. For a given type of fermions, strong or mild hierarchy in the masses and mixing parameters can be obtained by tak…
We consider various bulk fields with general dilaton couplings in the linear dilaton background in five dimensions as the continuum limit of clockwork models. We show that the localization of the zero modes of bulk fields and the mass gap in the KK spectrum depend not only on the bulk dilaton coupling, but also on the bulk mass parameter in the case of a bulk fermion. The consistency from universality and perturbativity of gauge couplings constrain the dilaton couplings to the brane-localized matter fields as well as the bulk gauge bosons. Constructing the Clockwork Standard Model (SM) in the …
Cosmic inflation driven by the vacuum energy associated with the $D$-term of a supersymmetric abelian gauge group and a possible existence of long-range force mediated by an ultra-light gauge boson $Z^\prime$ are two extreme examples of models based on extra $U(1)$ symmetries. Large vacuum energy sets the scale of inflation while the scales of long-range forces induced by anomaly free extra gauged $U(1)$ symmetries are constrained by neutrino oscillations, binary pulsar timings and invisible neutrino decay. There exists a difference of about 40 orders of magnitude between the scales of these t…
The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. The holomorphy conditions are reminiscent of supersymmetry, even though the SMEFT is not a supersymmetric theory.
We consider heterotic string backgrounds in four-dimensional Minkowski space, where N=1 supersymmetry is spontaneously broken at a low scale m_{3/2} by a stringy Scherk-Schwarz mechanism. We review how the effective gauge couplings at 1-loop may evade the "decompactification problem", namely the proportionality of the gauge threshold corrections, with the large volume of the compact space involved in the supersymmetry breaking.
In models of low-energy gauge mediation, the observed Higgs mass is in tension with the cosmological limit on the gravitino mass $m_{3/2} \lesssim 16$ eV. We present an alternative mediation mechanism of supersymmetry breaking via a $U(1)$ $D$-term with an $E_6$-inspired particle content, which we call "vector mediation". The gravitino mass can be in the eV range. The sfermion masses are at the 10 TeV scale, while gauginos around a TeV. This mechanism also greatly ameliorates the $μ$-problem.
We derive a new class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and anti-holomorphic weights, $(w,\overline w) =(n - h,n+h)$, where $n$ and $h$ are the number …
We construct the first smooth bubbling geometries using the Weyl formalism. The solutions are obtained from Einstein theory coupled to a two-form gauge field in six dimensions with two compact directions. We classify the charged Weyl solutions in this framework. Smooth solutions consist of a chain of Kaluza-Klein bubbles that can be neutral or wrapped by electromagnetic fluxes, and are free of curvature and conical singularities. We discuss how such topological structures are prevented from gravitational collapse without struts. When embedded in type IIB, the class of solutions describes D1-D5…
I consider models in which non-standard supersymmetry breaking terms, including Dirac gaugino masses, arise from F-term breaking mediated by operators with a $1/M^3$ suppression. In these models, the supersoft properties found in the case of D-term breaking are absent in general, but can be obtained as a special case that is a fixed point of the renormalization group equations. The $μ$ term is replaced by three distinct supersymmetry-breaking parameters, decoupling the Higgs scalar potential from the Higgsino masses. Both holomorphic and non-holomorphic scalar cubic interactions with minimal f…
It is a possibility that the superworld (supersymmetric partners of our world) does exist without supersymmetry. The two worlds are being distinguished by an unbroken discrete $Z_2$ symmetry (similar to R-parity in supersymmetry). We lose the solution to the hierarchy problem. However, such a scenario has several motivations. For example, the lightest neutral superworld particle will be a candidate for dark matter. The other being, as in supersymmetry, it is possible to achieve gauge coupling unification. One major difference with the supersymmetric theory is that such a theory is much more ge…
在没有超对称性的情况下，具有5个希格斯双重态的标准模型中的规范耦合统一在10^14 GeV附近。在这种情况下，具有对称性破缺所需的最小希格斯扇区的三化模型SU（3）_C x SU（3）_L x SU（3）_R x Z_3是理想的大统一候选者。小质量的中微子是通过辐射跷跷板机制产生的，不需要中间尺度，额外的希格斯场或高维算子。质子寿命高于实验极限，衰变模式p -> \bar νK^+和p -> mu^+ K^0是可能观测到的。这个模型的分裂超对称性版本，有一个轻的希格斯双重态，同样有吸引力。
A long-lived decaying dark matter as a resolution to Fermi, PAMELA and ATIC anomalies is investigated in the framework of split supersymmetry (SUSY) without R-parity, where the neutralino is regarded as the dark matter and the extreme fine-tuned couplings for the long-lived neutralino are naturally evaded in the usual approach.
