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With the discovery of a particle that seems rather consistent with the minimal Standard Model Higgs boson, attention turns to questions of naturalness, fine-tuning, and what they imply for physics beyond the Standard Model and its discovery prospects at run II of the LHC. In this article we revisit the issue of naturalness, discussing some implicit assumptions that underly some of the most common statements, which tend to assign physical significance to certain regularization procedures. Vague arguments concerning fine-tuning can lead to conclusions that are too strong and perhaps not as generic as one would hope. Instead, we explore a more pragmatic definition of the hierarchy problem that does not rely on peeking beyond the murky boundaries of quantum field theory: we investigate the fine-tuning of the electroweak scale associated with thresholds from heavy particles, which is both calculable and dependent on the nature of the would-be ultraviolet completion of the Standard Model. We discuss different manifestations of new high-energy scales that are favored by experimental hints for new physics with an eye toward making use of fine-tuning in order to determine natural regions of the new physics parameter spaces.
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Inspired by the localization phenomenon in condensed matter systems, we explore constructions in the theory space of multiple scalar fields, in which exponentially suppressed couplings could originate from random parameters. In particular, we find a new class of non-local theory space models, in which scalar fields at non-adjacent sites interact with each other but with strengths decaying exponentially with the site separation. Such a model could have very different localization properties, compared to the local theory space scenarios with only nearest-site interactions, based on the original Anderson localization model. More specifically, we find that a particular non-local interaction pattern leads to bi-localization of the two lightest eigenstates. Exponential localization (and thus exponentially suppressed couplings) then emerges only and immediately when randomness is introduced, no matter how tiny it is. We discuss variants of the model and possible UV completions as well.
The mass hierarchy among the three generations of quarks and charged leptons is one of the greatest mysteries in particle physics. In various flavor models, the origin of this phenomenon is attributed to a series of hierarchical spontaneous symmetry breakings, most of which are beyond the reach of particle colliders. We point out that the observation of a multi-peaked stochastic gravitational wave signal from a series of cosmological phase transitions could well be a unique probe of the mechanism behind flavor hierarchies. To illustrate this point, we show how near future ground- and space-based gravitational wave observatories could detect up to three peaks in the recently proposed $PS^3$ model.
We obtain a relationship between the hierarchies of mixing angles and of masses pertinent to the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton mixing matrix. Using this relationship, we argue that the more severe hierarchy of the charge-$frac{2}{3}$ quark masses requires that the CKM matrix be close to a unit matrix whereas the milder hierarchy of the neutrino masses allows the PMNS matrix to depart markedly from the CKM matrix and contain large mixing angles of the type that are observed.
We give a general analysis of neutrino mixing in the seesaw mechanism with three flavors. Assuming that the Dirac and u-quark mass matrices are similar, we establish simple relations between the neutrino parameters and individual Majorana masses. They are shown to depend rather strongly on the physical neutrino mixing angles. We calculate explicitly the implied Majorana mass hierarchies for parameter sets corresponding to different solutions to the solar neutrino problem.
The clockwork mechanism, which can naturally explain the origin of small numbers, is implemented in $SO(10)$ grand unified theories to address the origin of hierarchies in fermion masses and mixings. We show that a minimal Yukawa sector involving a $10_H$ and $overline{126}_H$ of Higgs bosons, extended with two clockwork chains consisting of $16+overline{16}$ vector-like fermions, can explain the hierarchical patterns with all the Yukawa couplings being of order one. Emergence of a realistic mass spectrum does not require any symmetry that distinguishes the three generations. We develop clockwork-extended $SO(10)$ GUTs both in the context of SUSY and non-SUSY frameworks. Implementation of the mechanism in non-SUSY scenario assumes a Peccei-Quinn symmetry realized at an intermediate scale, with the clockwork sector carrying non-trivial charges, which solves the strong CP problem and provides axion as a dark matter candidate.
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