arXiv subjects

Stephen F. King

Publications and source records attributed to Stephen F. King.

At least 127 records · Page 7Linked to original sources

arXiv2017

Spontaneous CP violation in multi-Higgs potentials with triplets of $Δ(3n^2)$ and $Δ(6n^2)$

Motivated by discrete flavour symmetry models, we analyse Spontaneous CP Violation (SCPV) for potentials involving three or six Higgs fields (both electroweak doublets and singlets) which fall into irreducible triplet representations of discrete symmetries belonging to the $Δ(3n^2)$ and $Δ(6n^2)$ series, including $A_4$, $S_4$, $Δ(27)$ and $Δ(54)$. For each case, we give the potential and find various global mimima for different regions of the parameter space of the potential. Using CP-odd basis Invariants that indicate the presence of Spontaneous CP Violation we separate the VEVs into those that do or do not violate CP. In cases where CP is preserved we reveal a CP symmetry of the potential that is preserved by those VEVs, otherwise we display a non-zero CP-odd Invariant. Finally we identify interesting cases where there is Spontaneous Geometrical CP Violation in which the VEVs have calculable phases.

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arXiv2017

Golden Littlest Seesaw

We propose and analyse a new class of Littlest Seesaw models, with two right-handed neutrinos in their diagonal mass basis, based on preserving the first column of the Golden Ratio mixing matrix. We perform an exhaustive analysis of all possible remnant symmetries of the group $A_5$ which can be used to enforce various vacuum alignments for the flavon controlling solar mixing, for two simple cases of the atmospheric flavon vacuum alignment. The solar and atmospheric flavon vacuum alignments are enforced by {\em different} remnant symmetries. We examine the phenomenological viability of each of the possible Littlest Seesaw alignments in $A_5$, which preserve the first column of the Golden ratio mixing matrix, using figures and extensive tables of benchmark points and comparing our predictions to a recent global analysis of neutrino data. We also repeat the analysis for an alternative form of Golden Ratio mixing matrix.

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arXiv2017

Minima of multi-Higgs potentials with triplets of $Δ(3n^2)$ and $Δ(6n^2)$

We analyse the minima of scalar potentials for multi-Higgs models where the scalars are arranged as either one triplet or two triplets of the discrete symmetries $A_4$, $S_4$, $Δ(27)$, $Δ(54)$, as well as $Δ(3n^2)$ and $Δ(6n^2)$ with $n>3$. The results should be useful for both multi-Higgs models involving electroweak doublets and multi-flavon models involving electroweak singlets, where in both cases the fields transform as triplets under some non-Abelian discrete symmetry.

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arXiv2017

Starobinsky-like inflation in no-scale supergravity Wess-Zumino model with Polonyi term

We propose a simple modification of the no-scale supergravity Wess-Zumino model of Starobinsky-like inflation to include a Polonyi term in the superpotential. The purpose of this term is to provide an explicit mechanism for supersymmetry breaking at the end of inflation. We show how successful inflation can be achieved for a gravitino mass satisfying the strict upper bound $m_{3/2}< 10^3$ TeV, with favoured values $m_{3/2}\lesssim\mathcal{O}(1)$ TeV. The model suggests that SUSY may be discovered in collider physics experiments such as the LHC or the FCC.

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arXiv2017

Leptogenesis after Chaotic Sneutrino Inflation and the Supersymmetry Breaking Scale

We discuss resonant leptogenesis arising from the decays of two nearly-degenerate right-handed neutrinos, identified as the inflaton and stabiliser superfields in a model of chaotic sneutrino inflation. We compare an analytical estimate of the baryon asymmetry $ η_B $ in the Boltzmann approximation to a numerical solution of the full density matrix equations, and find that the analytical result fails to capture the correct physics in certain regions of parameter space. The observed baryon asymmetry can be realised for a breaking of the mass degeneracy as small as $ \mathcal{O}(10^{-8}) $. The origin of such a small mass splitting is explained by considering supersymmetry (SUSY) breaking in supergravity, which requires a constant in the superpotential of the order of the gravitino mass $ m_{3/2} $ to cancel the cosmological constant. This yields additional terms in the (s)neutrino mass matrices, lifting the degeneracy and linking $ η_B $ to the SUSY breaking scale. We find that achieving the correct baryon asymmetry requires a gravitino mass $ m_{3/2} \geq \mathcal{O}(100) $ TeV.

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arXiv2017

Supersymmetric Majoron Inflation

We propose supersymmetric Majoron inflation in which the Majoron field $Φ$ responsible for generating right-handed neutrino masses may also be suitable for giving low scale "hilltop" inflation, with a discrete lepton number $Z_N$ spontaneously broken at the end of inflation, while avoiding the domain wall problem. In the framework of non-minimal supergravity, we show that a successful spectral index can result with small running together with small tensor modes. We show that a range of heaviest right-handed neutrino masses can be generated, $m_N\sim 10^1-10^{16}$ GeV, consistent with the constraints from reheating and domain walls.

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arXiv2017

Leptogenesis in a $Δ(27) \times SO(10)$ SUSY GUT

Although $SO(10)$ Supersymmetric (SUSY) Grand Unification Theories (GUTs) are very attractive for neutrino mass and mixing, it is often quite difficult to achieve successful leptogenesis from the lightest right-handed neutrino $N_1$ due to the strong relations between neutrino and up-type quark Yukawa couplings. We show that in a realistic model these constraints are relaxed, making $N_1$ leptogenesis viable. To illustrate this, we calculate the baryon asymmetry of the Universe $ Y_B $ from flavoured $ N_1 $ leptogenesis in a recently proposed $ Δ(27) \times SO(10) $ SUSY GUT. The flavoured Boltzmann equations are solved numerically, and comparison with the observed $ Y_B $ places constraints on the allowed values of right-handed neutrino masses and neutrino Yukawa couplings. The flavoured $SO(10)$ SUSY GUT is not only fairly complete and predictive in the lepton sector, but can also explain the BAU through leptogenesis with natural values in the lepton sector albeit with some tuning in the quark sector.

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arXiv2016

Precision neutrino experiments vs the Littlest Seesaw

We study to what extent upcoming precision neutrino oscillation experiments will be able to exclude one of the most predictive models of neutrino mass and mixing: the Littlest Seesaw. We show that this model provides a good fit to current data, predicting eight observables from two input parameters, and provide new assessments of its predictions and their correlations. We then assess the ability to exclude this model using simulations of upcoming neutrino oscillation experiments including the medium-distance reactor experiments JUNO and RENO-50 and the long-baseline accelerator experiments DUNE and T2HK. We find that an accurate determination of the currently least well measured parameters, namely the atmospheric and solar angles and the CP phase $δ$, provide crucial independent tests of the model. For $θ_{13}$ and the two mass-squared differences, however, the model's exclusion requires a combination of measurements coming from a varied experimental programme. Our results show that the synergy and complementarity of future experiments will play a vital role in efficiently discriminating between predictive models of neutrino flavour, and hence, towards advancing our understanding of neutrino oscillations in the context of the flavour puzzle of the Standard Model.

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arXiv2016

Renormalisation Group Corrections to the Littlest Seesaw Model and Maximal Atmospheric Mixing

The Littlest Seesaw (LS) model involves two right-handed neutrinos and a very constrained Dirac neutrino mass matrix, involving one texture zero and two independent Dirac masses, leading to a highly predictive scheme in which all neutrino masses and the entire PMNS matrix is successfully predicted in terms of just two real parameters. We calculate the renormalisation group (RG) corrections to the LS predictions, with and without supersymmetry, including also the threshold effects induced by the decoupling of heavy Majorana neutrinos both analytically and numerically. We find that the predictions for neutrino mixing angles and mass ratios are rather stable under RG corrections. For example we find that the LS model with RG corrections predicts close to maximal atmospheric mixing, $θ_{23}=45^\circ \pm 1^\circ$, in most considered cases, in tension with the latest NOvA results. The techniques used here apply to other seesaw models with a strong normal mass hierarchy.

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arXiv2016

R-Parity violation in F-Theory

We discuss R-parity violation (RPV) in semi-local and local F-theory constructions. We first present a detailed analysis of all possible combinations of RPV operators arising from semi-local F-theory spectral cover constructions, assuming an $SU(5)$ GUT. We provide a classification of all possible allowed combinations of RPV operators originating from operators of the form $10\cdot \bar 5\cdot \bar 5$, including the effect of $U(1)$ fluxes with global restrictions. We then relax the global constraints and perform explicit computations of the bottom/tau and RPV Yukawa couplings, at an $SO(12)$ local point of enhancement in the presence of general fluxes subject only to local flux restrictions. We compare our results to the experimental limits on each allowed RPV operator, and show that operators such as $LLe^c$, $LQd^c$ and $u^cd^cd^c$ may be present separately within current bounds, possibly on the edge of observability, suggesting lepton number violation or neutron-antineutron oscillations could constrain F-theory models.

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arXiv2016

CP-odd invariants for multi-Higgs models: applications with discrete symmetry

CP-odd invariants provide a basis independent way of studying the CP properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are CP-odd or CP-even, then systematically construct all of the simplest CP-odd invariants up to a given order, finding many new ones. The CP-odd invariants are valid for general potentials when expressed in a standard form. We then apply our results to scalar potentials involving three (or six) Higgs fields which form irreducible triplets under a discrete symmetry, including invariants for both explicit as well as spontaneous CP violation. The considered cases include one triplet of Standard Model (SM) gauge singlet scalars, one triplet of SM Higgs doublets, two triplets of SM singlets, and two triplets of SM Higgs doublets. For each case we study the potential symmetric under one of the simplest discrete symmetries with irreducible triplet representations, namely $A_4$, $S_4$, $Δ(27)$ or $Δ(54)$, as well as the infinite classes of discrete symmetries $Δ(3n^2)$ or $Δ(6n^2)$.

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arXiv2016

Littlest Seesaw model from S4 x U(1)

We show how a minimal (littlest) seesaw model involving two right-handed neutrinos and a very constrained Dirac mass matrix, with one texture zero and two independent Dirac masses, may arise from $S_4\times U(1)$ symmetry in a semi-direct supersymmetric model. The resulting CSD3 form of neutrino mass matrix only depends on two real mass parameters plus one undetermined phase. We show how the phase may be fixed to be one of the cube roots of unity by extending the $S_4\times U(1)$ symmetry to include a product of $Z_3$ factors together with a CP symmetry, which is spontaneously broken leaving a single residual $Z_3$ in the charged lepton sector and a residual $Z_2$ in the neutrino sector, with suppressed higher order corrections. With the phase chosen from the cube roots of unity to be $-2π/3$, the model predicts a normal neutrino mass hierarchy with $m_1=0$, reactor angle $θ_{13}=8.7^\circ$, solar angle $θ_{12}=34^\circ$, atmospheric angle $θ_{23}=44^\circ$, and CP violating oscillation phase $δ_{\rm CP}=-93^\circ$, depending on the fit of the model to the neutrino masses.

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arXiv2016

Neutrino mass from M Theory SO(10)

We study the origin of neutrino mass from $SO(10)$ arising from $M$ Theory compactified on a $G_2$-manifold. This is linked to the problem of the breaking of the extra $U(1)$ gauge group, in the $SU(5)\times U(1)$ subgroup of $SO(10)$, which we show can achieved via a (generalised) Kolda-Martin mechanism. The resulting neutrino masses arise from a combination of the seesaw mechanism and induced R-parity breaking contributions. The rather complicated neutrino mass matrix is analysed for one neutrino family and it is shown how phenomenologically acceptable neutrino masses can emerge.

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arXiv2016

Direct and Semi-Direct Approaches to Lepton Mixing with a Massless Neutrino

We discuss the possibility of enforcing a massless Majorana neutrino in the direct and semi-direct approaches to lepton mixing, in which the PMNS matrix is partly predicted by subgroups of a discrete family symmetry, extending previous group searches up to order 1535. We find a phenomenologically viable scheme for the semi-direct approach based on $Q(648)$ which contains $Δ(27)$ and the quaternion group as subgroups. This leads to novel predictions for the first column of the PMNS matrix corresponding to a normal neutrino mass hierarchy with $m_1=0$, and sum rules for the mixing angles and phase which are characterised by the solar angle being on the low side $θ_{12}\sim 31^{\circ}$ and the Dirac (oscillation) CP phase $δ$ being either about $\pm 45^\circ$ or $\pm π$.

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arXiv2016

Probing the Origin of Neutrino Masses and Mixings via Doubly Charged Scalars: Complementarity of the Intensity and the Energy Frontiers

We discuss how the intensity and the energy frontiers provide complementary constraints within a minimal model of neutrino mass involving just one new field beyond the Standard Model at accessible energy, namely a doubly charged scalar $S^{++}$ and its antiparticle $S^{--}$. In particular we focus on the complementarity between high-energy LHC searches and low-energy probes such as lepton flavor violation. Our setting is a prime example of how high- and low-energy physics can cross-fertilize each other.

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arXiv2016

Phenomenological Implications of an SU(5) x S4 x U(1) SUSY GUT of Flavour

We discuss the characteristic low energy phenomenological implications of an SU(5) Supersymmetric Grand Unified Theory (SUSY GUT) whose flavour structure is controlled by the family symmetry S4 x U(1), which provides a good description of all quark and lepton masses, mixings as well as CP violation. Although the model closely mimics Minimal Flavour Violation (MFV) as shown in arXiv:1511.07886, here we focus on the differences. We first present numerical estimates of the low energy mass insertion parameters, including canonical normalisation and renormalisation group running, for well-defined ranges of SUSY parameters and compare the naive model expectations to the numerical scans and the experimental bounds. Our results are then used to estimate the model-specific predictions for Electric Dipole Moments (EDMs), Lepton Flavour Violation (LFV), B and K meson mixing as well as rare B decays. The largest observable deviations from MFV come from the LFV process mu --> e gamma and the electron EDM.

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arXiv2016

CP Violating Two-Higgs-Doublet Model: Constraints and LHC Predictions

Two-Higgs-Doublet Models (2HDMs) are amongst the simplest extensions of the Standard Model. Such models allow for tree-level CP Violation (CPV) in the Higgs sector. We analyse a class of CPV 2HDM (of Type-I) in which only one of the two Higgs doublets couples to quarks and leptons, avoiding dangerous Flavour Changing Neutral Currents. We provide an up to date and comprehensive analysis of the constraints and Large Hadron Collider (LHC) predictions of such a model. Of immediate interest to the LHC Run 2 is the golden channel where all three neutral Higgs bosons are observed to decay into gauge boson pairs, $WW$ and $ZZ$, providing a smoking gun signature of the CPV 2HDM.

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arXiv2016

Towards a complete $Δ(27) \times SO(10)$ SUSY GUT

We propose a renormalisable model based on $Δ(27)$ family symmetry with an $SO(10)$ grand unified theory (GUT) leading to a novel form of spontaneous geometrical CP violation. The symmetries, including $Δ(27)$ and $\mathbb{Z}_{9} \times \mathbb{Z}_{12} \times \mathbb{Z}_{4}^{R}$, are broken close to the GUT breaking scale to yield the minimal supersymmetric standard model (MSSM) with the standard R-parity. $SO(10)$ is broken via $SU(5)$ with doublet-triplet splitting achieved by a version of the Dimopoulos-Wilczek (missing VEV) mechanism. Low-scale Yukawa structure is dictated by the coupling of matter to $ Δ(27) $ antitriplets $ \barϕ $ whose VEVs are aligned in the CSD3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from a specific implementation of the seesaw mechanism within $SO(10)$. The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass $ m_1 = 0.13 $ meV and the PMNS mixing parameters $θ^l_{13} \approx 8.35^{\circ}$, $θ^l_{12}\approx 34^{\circ}$, $θ^l_{23}\approx 43^{\circ}$ and an oscillation phase $δ^l\approx -90^{\circ}$.

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